Instruction stringlengths 45 106 | input_code stringlengths 1 13.7k | output_code stringlengths 1 13.7k |
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Port the provided Mathematica code into C while preserving the original functionality. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Change the following Mathematica code into C# without altering its purpose. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Generate an equivalent C++ version of this Mathematica code. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Transform the following Mathematica implementation into Java, maintaining the same output and logic. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Write the same code in Python as shown below in Mathematica. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Can you help me rewrite this code in VB instead of Mathematica, keeping it the same logically? | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Rewrite the snippet below in Go so it works the same as the original Mathematica code. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Write a version of this MATLAB function in C with identical behavior. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Write the same algorithm in C# as shown in this MATLAB implementation. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Maintain the same structure and functionality when rewriting this code in C++. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Convert the following code from MATLAB to Java, ensuring the logic remains intact. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Translate this program into Python but keep the logic exactly as in MATLAB. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Change the following MATLAB code into VB without altering its purpose. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Generate a Go translation of this MATLAB snippet without changing its computational steps. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Transform the following Nim implementation into C, maintaining the same output and logic. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Write a version of this Nim function in C# with identical behavior. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Preserve the algorithm and functionality while converting the code from Nim to C++. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Can you help me rewrite this code in Java instead of Nim, keeping it the same logically? | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Produce a language-to-language conversion: from Nim to Python, same semantics. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Produce a language-to-language conversion: from Nim to VB, same semantics. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Port the following code from Nim to Go with equivalent syntax and logic. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Change the programming language of this snippet from OCaml to C without modifying what it does. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Transform the following OCaml implementation into C#, maintaining the same output and logic. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Generate a C++ translation of this OCaml snippet without changing its computational steps. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Port the provided OCaml code into Java while preserving the original functionality. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Write a version of this OCaml function in Python with identical behavior. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Please provide an equivalent version of this OCaml code in VB. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Write a version of this OCaml function in Go with identical behavior. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Convert this Perl block to C, preserving its control flow and logic. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Keep all operations the same but rewrite the snippet in C#. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Generate a C++ translation of this Perl snippet without changing its computational steps. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Convert this Perl block to Java, preserving its control flow and logic. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Port the following code from Perl to Python with equivalent syntax and logic. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Write the same code in VB as shown below in Perl. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Translate this program into Go but keep the logic exactly as in Perl. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Write the same algorithm in C as shown in this Racket implementation. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Keep all operations the same but rewrite the snippet in C#. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Change the programming language of this snippet from Racket to C++ without modifying what it does. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Convert the following code from Racket to Java, ensuring the logic remains intact. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Produce a functionally identical Python code for the snippet given in Racket. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Maintain the same structure and functionality when rewriting this code in VB. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Rewrite this program in Go while keeping its functionality equivalent to the Racket version. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Ensure the translated C code behaves exactly like the original REXX snippet. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Generate a C# translation of this REXX snippet without changing its computational steps. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Transform the following REXX implementation into C++, maintaining the same output and logic. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Write the same code in Java as shown below in REXX. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Rewrite this program in Python while keeping its functionality equivalent to the REXX version. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Port the provided REXX code into VB while preserving the original functionality. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Produce a functionally identical Go code for the snippet given in REXX. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Change the following Ruby code into C without altering its purpose. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Generate an equivalent C# version of this Ruby code. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Write a version of this Ruby function in C++ with identical behavior. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Convert this Ruby snippet to Java and keep its semantics consistent. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Rewrite this program in Python while keeping its functionality equivalent to the Ruby version. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Change the following Ruby code into VB without altering its purpose. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Preserve the algorithm and functionality while converting the code from Ruby to Go. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Maintain the same structure and functionality when rewriting this code in C. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Convert this Scala snippet to C# and keep its semantics consistent. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Write the same algorithm in C++ as shown in this Scala implementation. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Convert this Scala snippet to Java and keep its semantics consistent. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Maintain the same structure and functionality when rewriting this code in Python. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Transform the following Scala implementation into VB, maintaining the same output and logic. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Convert this Scala snippet to Go and keep its semantics consistent. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Can you help me rewrite this code in C instead of Swift, keeping it the same logically? | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Generate a C# translation of this Swift snippet without changing its computational steps. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Convert this Swift block to C++, preserving its control flow and logic. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Please provide an equivalent version of this Swift code in Java. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Produce a functionally identical Python code for the snippet given in Swift. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Rewrite the snippet below in VB so it works the same as the original Swift code. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Write the same algorithm in Go as shown in this Swift implementation. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Preserve the algorithm and functionality while converting the code from Tcl to C. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| #include <stdio.h>
#define TALLOC(n,typ) malloc(n*sizeof(typ))
#define EL_Type int
typedef struct sMtx {
int dim_x, dim_y;
EL_Type *m_stor;
EL_Type **mtx;
} *Matrix, sMatrix;
typedef struct sRvec {
int dim_x;
EL_Type *m_stor;
} *RowVec, sRowVec;
Matrix NewMatrix( int x_dim, int y_dim )
{
int n;
Matrix m;
m = TALLOC( 1, sMatrix);
n = x_dim * y_dim;
m->dim_x = x_dim;
m->dim_y = y_dim;
m->m_stor = TALLOC(n, EL_Type);
m->mtx = TALLOC(m->dim_y, EL_Type *);
for(n=0; n<y_dim; n++) {
m->mtx[n] = m->m_stor+n*x_dim;
}
return m;
}
void MtxSetRow(Matrix m, int irow, EL_Type *v)
{
int ix;
EL_Type *mr;
mr = m->mtx[irow];
for(ix=0; ix<m->dim_x; ix++)
mr[ix] = v[ix];
}
Matrix InitMatrix( int x_dim, int y_dim, EL_Type **v)
{
Matrix m;
int iy;
m = NewMatrix(x_dim, y_dim);
for (iy=0; iy<y_dim; iy++)
MtxSetRow(m, iy, v[iy]);
return m;
}
void MtxDisplay( Matrix m )
{
int iy, ix;
const char *sc;
for (iy=0; iy<m->dim_y; iy++) {
printf(" ");
sc = " ";
for (ix=0; ix<m->dim_x; ix++) {
printf("%s %3d", sc, m->mtx[iy][ix]);
sc = ",";
}
printf("\n");
}
printf("\n");
}
void MtxMulAndAddRows(Matrix m, int ixrdest, int ixrsrc, EL_Type mplr)
{
int ix;
EL_Type *drow, *srow;
drow = m->mtx[ixrdest];
srow = m->mtx[ixrsrc];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] += mplr * srow[ix];
}
void MtxSwapRows( Matrix m, int rix1, int rix2)
{
EL_Type *r1, *r2, temp;
int ix;
if (rix1 == rix2) return;
r1 = m->mtx[rix1];
r2 = m->mtx[rix2];
for (ix=0; ix<m->dim_x; ix++)
temp = r1[ix]; r1[ix]=r2[ix]; r2[ix]=temp;
}
void MtxNormalizeRow( Matrix m, int rix, int lead)
{
int ix;
EL_Type *drow;
EL_Type lv;
drow = m->mtx[rix];
lv = drow[lead];
for (ix=0; ix<m->dim_x; ix++)
drow[ix] /= lv;
}
#define MtxGet( m, rix, cix ) m->mtx[rix][cix]
void MtxToReducedREForm(Matrix m)
{
int lead;
int rix, iix;
EL_Type lv;
int rowCount = m->dim_y;
lead = 0;
for (rix=0; rix<rowCount; rix++) {
if (lead >= m->dim_x)
return;
iix = rix;
while (0 == MtxGet(m, iix,lead)) {
iix++;
if (iix == rowCount) {
iix = rix;
lead++;
if (lead == m->dim_x)
return;
}
}
MtxSwapRows(m, iix, rix );
MtxNormalizeRow(m, rix, lead );
for (iix=0; iix<rowCount; iix++) {
if ( iix != rix ) {
lv = MtxGet(m, iix, lead );
MtxMulAndAddRows(m,iix, rix, -lv) ;
}
}
lead++;
}
}
int main()
{
Matrix m1;
static EL_Type r1[] = {1,2,-1,-4};
static EL_Type r2[] = {2,3,-1,-11};
static EL_Type r3[] = {-2,0,-3,22};
static EL_Type *im[] = { r1, r2, r3 };
m1 = InitMatrix( 4,3, im );
printf("Initial\n");
MtxDisplay(m1);
MtxToReducedREForm(m1);
printf("Reduced R-E form\n");
MtxDisplay(m1);
return 0;
}
|
Keep all operations the same but rewrite the snippet in C#. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| using System;
namespace rref
{
class Program
{
static void Main(string[] args)
{
int[,] matrix = new int[3, 4]{
{ 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 }
};
matrix = rref(matrix);
}
private static int[,] rref(int[,] matrix)
{
int lead = 0, rowCount = matrix.GetLength(0), columnCount = matrix.GetLength(1);
for (int r = 0; r < rowCount; r++)
{
if (columnCount <= lead) break;
int i = r;
while (matrix[i, lead] == 0)
{
i++;
if (i == rowCount)
{
i = r;
lead++;
if (columnCount == lead)
{
lead--;
break;
}
}
}
for (int j = 0; j < columnCount; j++)
{
int temp = matrix[r, j];
matrix[r, j] = matrix[i, j];
matrix[i, j] = temp;
}
int div = matrix[r, lead];
if(div != 0)
for (int j = 0; j < columnCount; j++) matrix[r, j] /= div;
for (int j = 0; j < rowCount; j++)
{
if (j != r)
{
int sub = matrix[j, lead];
for (int k = 0; k < columnCount; k++) matrix[j, k] -= (sub * matrix[r, k]);
}
}
lead++;
}
return matrix;
}
}
}
|
Maintain the same structure and functionality when rewriting this code in C++. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| #include <algorithm>
#include <cstddef>
#include <cassert>
template<typename MatrixType> struct matrix_traits
{
typedef typename MatrixType::index_type index_type;
typedef typename MatrixType::value_type value_type;
static index_type min_row(MatrixType const& A)
{ return A.min_row(); }
static index_type max_row(MatrixType const& A)
{ return A.max_row(); }
static index_type min_column(MatrixType const& A)
{ return A.min_column(); }
static index_type max_column(MatrixType const& A)
{ return A.max_column(); }
static value_type& element(MatrixType& A, index_type i, index_type k)
{ return A(i,k); }
static value_type element(MatrixType const& A, index_type i, index_type k)
{ return A(i,k); }
};
template<typename T, std::size_t rows, std::size_t columns>
struct matrix_traits<T[rows][columns]>
{
typedef std::size_t index_type;
typedef T value_type;
static index_type min_row(T const (&)[rows][columns])
{ return 0; }
static index_type max_row(T const (&)[rows][columns])
{ return rows-1; }
static index_type min_column(T const (&)[rows][columns])
{ return 0; }
static index_type max_column(T const (&)[rows][columns])
{ return columns-1; }
static value_type& element(T (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
static value_type element(T const (&A)[rows][columns],
index_type i, index_type k)
{ return A[i][k]; }
};
template<typename MatrixType>
void swap_rows(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
std::swap(mt.element(A, i, col), mt.element(A, k, col));
}
template<typename MatrixType>
void divide_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(v != 0);
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) /= v;
}
template<typename MatrixType>
void add_multiple_row(MatrixType& A,
typename matrix_traits<MatrixType>::index_type i,
typename matrix_traits<MatrixType>::index_type k,
typename matrix_traits<MatrixType>::value_type v)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
assert(mt.min_row(A) <= i);
assert(i <= mt.max_row(A));
assert(mt.min_row(A) <= k);
assert(k <= mt.max_row(A));
for (index_type col = mt.min_column(A); col <= mt.max_column(A); ++col)
mt.element(A, i, col) += v * mt.element(A, k, col);
}
template<typename MatrixType>
void to_reduced_row_echelon_form(MatrixType& A)
{
matrix_traits<MatrixType> mt;
typedef typename matrix_traits<MatrixType>::index_type index_type;
index_type lead = mt.min_row(A);
for (index_type row = mt.min_row(A); row <= mt.max_row(A); ++row)
{
if (lead > mt.max_column(A))
return;
index_type i = row;
while (mt.element(A, i, lead) == 0)
{
++i;
if (i > mt.max_row(A))
{
i = row;
++lead;
if (lead > mt.max_column(A))
return;
}
}
swap_rows(A, i, row);
divide_row(A, row, mt.element(A, row, lead));
for (i = mt.min_row(A); i <= mt.max_row(A); ++i)
{
if (i != row)
add_multiple_row(A, i, row, -mt.element(A, i, lead));
}
}
}
#include <iostream>
int main()
{
double M[3][4] = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } };
to_reduced_row_echelon_form(M);
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
std::cout << M[i][j] << '\t';
std::cout << "\n";
}
return EXIT_SUCCESS;
}
|
Ensure the translated Java code behaves exactly like the original Tcl snippet. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| import java.util.*;
import java.lang.Math;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
if (getCoordinate(pivot).doubleValue() != 1) {
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}
|
Translate this program into Python but keep the logic exactly as in Tcl. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| def ToReducedRowEchelonForm( M):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / float(lv) for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22],]
ToReducedRowEchelonForm( mtx )
for rw in mtx:
print ', '.join( (str(rv) for rv in rw) )
|
Convert the following code from Tcl to VB, ensuring the logic remains intact. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| Private Function ToReducedRowEchelonForm(M As Variant) As Variant
Dim lead As Integer: lead = 0
Dim rowCount As Integer: rowCount = UBound(M)
Dim columnCount As Integer: columnCount = UBound(M(0))
Dim i As Integer
For r = 0 To rowCount
If lead >= columnCount Then
Exit For
End If
i = r
Do While M(i)(lead) = 0
i = i + 1
If i = rowCount Then
i = r
lead = lead + 1
If lead = columnCount Then
Exit For
End If
End If
Loop
Dim tmp As Variant
tmp = M(r)
M(r) = M(i)
M(i) = tmp
If M(r)(lead) <> 0 Then
div = M(r)(lead)
For t = LBound(M(r)) To UBound(M(r))
M(r)(t) = M(r)(t) / div
Next t
End If
For j = 0 To rowCount
If j <> r Then
subt = M(j)(lead)
For t = LBound(M(j)) To UBound(M(j))
M(j)(t) = M(j)(t) - subt * M(r)(t)
Next t
End If
Next j
lead = lead + 1
Next r
ToReducedRowEchelonForm = M
End Function
Public Sub main()
r = ToReducedRowEchelonForm(Array( _
Array(1, 2, -1, -4), _
Array(2, 3, -1, -11), _
Array(-2, 0, -3, 22)))
For i = LBound(r) To UBound(r)
Debug.Print Join(r(i), vbTab)
Next i
End Sub
|
Change the programming language of this snippet from Tcl to Go without modifying what it does. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| package main
import "fmt"
type matrix [][]float64
func (m matrix) print() {
for _, r := range m {
fmt.Println(r)
}
fmt.Println("")
}
func main() {
m := matrix{
{ 1, 2, -1, -4},
{ 2, 3, -1, -11},
{-2, 0, -3, 22},
}
m.print()
rref(m)
m.print()
}
func rref(m matrix) {
lead := 0
rowCount := len(m)
columnCount := len(m[0])
for r := 0; r < rowCount; r++ {
if lead >= columnCount {
return
}
i := r
for m[i][lead] == 0 {
i++
if rowCount == i {
i = r
lead++
if columnCount == lead {
return
}
}
}
m[i], m[r] = m[r], m[i]
f := 1 / m[r][lead]
for j, _ := range m[r] {
m[r][j] *= f
}
for i = 0; i < rowCount; i++ {
if i != r {
f = m[i][lead]
for j, e := range m[r] {
m[i][j] -= e * f
}
}
}
lead++
}
}
|
Ensure the translated PHP code behaves exactly like the original Rust snippet. | fn main() {
let mut matrix_to_reduce: Vec<Vec<f64>> = vec![vec![1.0, 2.0 , -1.0, -4.0],
vec![2.0, 3.0, -1.0, -11.0],
vec![-2.0, 0.0, -3.0, 22.0]];
let mut r_mat_to_red = &mut matrix_to_reduce;
let rr_mat_to_red = &mut r_mat_to_red;
println!("Matrix to reduce:\n{:?}", rr_mat_to_red);
let reduced_matrix = reduced_row_echelon_form(rr_mat_to_red);
println!("Reduced matrix:\n{:?}", reduced_matrix);
}
fn reduced_row_echelon_form(matrix: &mut Vec<Vec<f64>>) -> Vec<Vec<f64>> {
let mut matrix_out: Vec<Vec<f64>> = matrix.to_vec();
let mut pivot = 0;
let row_count = matrix_out.len();
let column_count = matrix_out[0].len();
'outer: for r in 0..row_count {
if column_count <= pivot {
break;
}
let mut i = r;
while matrix_out[i][pivot] == 0.0 {
i = i+1;
if i == row_count {
i = r;
pivot = pivot + 1;
if column_count == pivot {
pivot = pivot - 1;
break 'outer;
}
}
}
for j in 0..row_count {
let temp = matrix_out[r][j];
matrix_out[r][j] = matrix_out[i][j];
matrix_out[i][j] = temp;
}
let divisor = matrix_out[r][pivot];
if divisor != 0.0 {
for j in 0..column_count {
matrix_out[r][j] = matrix_out[r][j] / divisor;
}
}
for j in 0..row_count {
if j != r {
let hold = matrix_out[j][pivot];
for k in 0..column_count {
matrix_out[j][k] = matrix_out[j][k] - ( hold * matrix_out[r][k]);
}
}
}
pivot = pivot + 1;
}
matrix_out
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Transform the following Ada implementation into PHP, maintaining the same output and logic. | generic
type Element_Type is private;
Zero : Element_Type;
with function "-" (Left, Right : in Element_Type) return Element_Type is <>;
with function "*" (Left, Right : in Element_Type) return Element_Type is <>;
with function "/" (Left, Right : in Element_Type) return Element_Type is <>;
package Matrices is
type Matrix is
array (Positive range <>, Positive range <>) of Element_Type;
function Reduced_Row_Echelon_form (Source : Matrix) return Matrix;
end Matrices;
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Generate an equivalent PHP version of this AutoHotKey code. | ToReducedRowEchelonForm(M){
rowCount := M.Count()
columnCount := M.1.Count()
r := lead := 1
while (r <= rowCount) {
if (columnCount < lead)
return M
i := r
while (M[i, lead] = 0) {
i++
if (rowCount+1 = i) {
i := r, lead++
if (columnCount+1 = lead)
return M
}
}
if (i<>r)
for col, v in M[i]
tempVal := M[i, col], M[i, col] := M[r, col], M[r, col] := tempVal
num := M[r, lead]
if (M[r, lead] <> 0)
for col, val in M[r]
M[r, col] /= num
i := 2
while (i <= rowCount) {
num := M[i, lead]
if (i <> r)
for col, val in M[i]
M[i, col] -= num * M[r, col]
i++
}
lead++, r++
}
return M
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Change the following BBC_Basic code into PHP without altering its purpose. | DIM matrix(2,3)
matrix() = 1, 2, -1, -4, \
\ 2, 3, -1, -11, \
\ -2, 0, -3, 22
PROCrref(matrix())
FOR row% = 0 TO 2
FOR col% = 0 TO 3
PRINT matrix(row%,col%);
NEXT
PRINT
NEXT row%
END
DEF PROCrref(m())
LOCAL lead%, nrows%, ncols%, i%, j%, r%, n
nrows% = DIM(m(),1)+1
ncols% = DIM(m(),2)+1
FOR r% = 0 TO nrows%-1
IF lead% >= ncols% EXIT FOR
i% = r%
WHILE m(i%,lead%) = 0
i% += 1
IF i% = nrows% THEN
i% = r%
lead% += 1
IF lead% = ncols% EXIT FOR
ENDIF
ENDWHILE
FOR j% = 0 TO ncols%-1 : SWAP m(i%,j%),m(r%,j%) : NEXT
n = m(r%,lead%)
IF n <> 0 FOR j% = 0 TO ncols%-1 : m(r%,j%) /= n : NEXT
FOR i% = 0 TO nrows%-1
IF i% <> r% THEN
n = m(i%,lead%)
FOR j% = 0 TO ncols%-1
m(i%,j%) -= m(r%,j%) * n
NEXT
ENDIF
NEXT
lead% += 1
NEXT r%
ENDPROC
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Change the programming language of this snippet from Common_Lisp to PHP without modifying what it does. | (defun convert-to-row-echelon-form (matrix)
(let* ((dimensions (array-dimensions matrix))
(row-count (first dimensions))
(column-count (second dimensions))
(lead 0))
(labels ((find-pivot (start lead)
(let ((i start))
(loop
:while (zerop (aref matrix i lead))
:do (progn
(incf i)
(when (= i row-count)
(setf i start)
(incf lead)
(when (= lead column-count)
(return-from convert-to-row-echelon-form matrix))))
:finally (return (values i lead)))))
(swap-rows (r1 r2)
(loop
:for c :upfrom 0 :below column-count
:do (rotatef (aref matrix r1 c) (aref matrix r2 c))))
(divide-row (r value)
(loop
:for c :upfrom 0 :below column-count
:do (setf (aref matrix r c)
(/ (aref matrix r c) value)))))
(loop
:for r :upfrom 0 :below row-count
:when (<= column-count lead)
:do (return matrix)
:do (multiple-value-bind (i nlead) (find-pivot r lead)
(setf lead nlead)
(swap-rows i r)
(divide-row r (aref matrix r lead))
(loop
:for i :upfrom 0 :below row-count
:when (/= i r)
:do (let ((scale (aref matrix i lead)))
(loop
:for c :upfrom 0 :below column-count
:do (decf (aref matrix i c)
(* scale (aref matrix r c))))))
(incf lead))
:finally (return matrix)))))
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Write the same algorithm in PHP as shown in this D implementation. | import std.stdio, std.algorithm, std.array, std.conv;
void toReducedRowEchelonForm(T)(T[][] M) pure nothrow @nogc {
if (M.empty)
return;
immutable nrows = M.length;
immutable ncols = M[0].length;
size_t lead;
foreach (immutable r; 0 .. nrows) {
if (ncols <= lead)
return;
{
size_t i = r;
while (M[i][lead] == 0) {
i++;
if (nrows == i) {
i = r;
lead++;
if (ncols == lead)
return;
}
}
swap(M[i], M[r]);
}
M[r][] /= M[r][lead];
foreach (j, ref mj; M)
if (j != r)
mj[] -= M[r][] * mj[lead];
lead++;
}
}
void main() {
auto A = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]];
A.toReducedRowEchelonForm;
writefln("%(%(%2d %)\n%)", A);
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Port the provided Factor code into PHP while preserving the original functionality. | USE: math.matrices.elimination
{ { 1 2 -1 -4 } { 2 3 -1 -11 } { -2 0 -3 22 } } solution .
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Keep all operations the same but rewrite the snippet in PHP. | module Rref
implicit none
contains
subroutine to_rref(matrix)
real, dimension(:,:), intent(inout) :: matrix
integer :: pivot, norow, nocolumn
integer :: r, i
real, dimension(:), allocatable :: trow
pivot = 1
norow = size(matrix, 1)
nocolumn = size(matrix, 2)
allocate(trow(nocolumn))
do r = 1, norow
if ( nocolumn <= pivot ) exit
i = r
do while ( matrix(i, pivot) == 0 )
i = i + 1
if ( norow == i ) then
i = r
pivot = pivot + 1
if ( nocolumn == pivot ) return
end if
end do
trow = matrix(i, :)
matrix(i, :) = matrix(r, :)
matrix(r, :) = trow
matrix(r, :) = matrix(r, :) / matrix(r, pivot)
do i = 1, norow
if ( i /= r ) matrix(i, :) = matrix(i, :) - matrix(r, :) * matrix(i, pivot)
end do
pivot = pivot + 1
end do
deallocate(trow)
end subroutine to_rref
end module Rref
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Please provide an equivalent version of this Groovy code in PHP. | enum Pivoting {
NONE({ i, it -> 1 }),
PARTIAL({ i, it -> - (it[i].abs()) }),
SCALED({ i, it -> - it[i].abs()/(it.inject(0) { sum, elt -> sum + elt.abs() } ) });
public final Closure comparer
private Pivoting(Closure c) {
comparer = c
}
}
def isReducibleMatrix = { matrix ->
def m = matrix.size()
m > 1 && matrix[0].size() > m && matrix[1..<m].every { row -> row.size() == matrix[0].size() }
}
def reducedRowEchelonForm = { matrix, Pivoting pivoting = Pivoting.NONE ->
assert isReducibleMatrix(matrix)
def m = matrix.size()
def n = matrix[0].size()
(0..<m).each { i ->
matrix[i..<m].sort(pivoting.comparer.curry(i))
matrix[i][i..<n] = matrix[i][i..<n].collect { it/matrix[i][i] }
((0..<i) + ((i+1)..<m)).each { k ->
(i..<n).reverse().each { j ->
matrix[k][j] -= matrix[i][j]*matrix[k][i]
}
}
}
matrix
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Write the same code in PHP as shown below in Haskell. | import Data.List (find)
rref :: Fractional a => [[a]] -> [[a]]
rref m = f m 0 [0 .. rows - 1]
where rows = length m
cols = length $ head m
f m _ [] = m
f m lead (r : rs)
| indices == Nothing = m
| otherwise = f m' (lead' + 1) rs
where indices = find p l
p (col, row) = m !! row !! col /= 0
l = [(col, row) |
col <- [lead .. cols - 1],
row <- [r .. rows - 1]]
Just (lead', i) = indices
newRow = map (/ m !! i !! lead') $ m !! i
m' = zipWith g [0..] $
replace r newRow $
replace i (m !! r) m
g n row
| n == r = row
| otherwise = zipWith h newRow row
where h = subtract . (* row !! lead')
replace :: Int -> a -> [a] -> [a]
replace n e l = a ++ e : b
where (a, _ : b) = splitAt n l
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Rewrite the snippet below in PHP so it works the same as the original J code. | require 'math/misc/linear'
]A=: 1 2 _1 _4 , 2 3 _1 _11 ,: _2 0 _3 22
1 2 _1 _4
2 3 _1 _11
_2 0 _3 22
gauss_jordan A
1 0 0 _8
0 1 0 1
0 0 1 _2
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Please provide an equivalent version of this Lua code in PHP. | function ToReducedRowEchelonForm ( M )
local lead = 1
local n_rows, n_cols = #M, #M[1]
for r = 1, n_rows do
if n_cols <= lead then break end
local i = r
while M[i][lead] == 0 do
i = i + 1
if n_rows == i then
i = r
lead = lead + 1
if n_cols == lead then break end
end
end
M[i], M[r] = M[r], M[i]
local m = M[r][lead]
for k = 1, n_cols do
M[r][k] = M[r][k] / m
end
for i = 1, n_rows do
if i ~= r then
local m = M[i][lead]
for k = 1, n_cols do
M[i][k] = M[i][k] - m * M[r][k]
end
end
end
lead = lead + 1
end
end
M = { { 1, 2, -1, -4 },
{ 2, 3, -1, -11 },
{ -2, 0, -3, 22 } }
res = ToReducedRowEchelonForm( M )
for i = 1, #M do
for j = 1, #M[1] do
io.write( M[i][j], " " )
end
io.write( "\n" )
end
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Port the following code from Mathematica to PHP with equivalent syntax and logic. | RowReduce[{{1, 2, -1, -4}, {2, 3, -1, -11}, {-2, 0, -3, 22}}]
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Change the following MATLAB code into PHP without altering its purpose. | rref([1, 2, -1, -4; 2, 3, -1, -11; -2, 0, -3, 22])
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Write the same code in PHP as shown below in Nim. | import rationals, strutils
type Fraction = Rational[int]
const Zero: Fraction = 0 // 1
type Matrix[M, N: static Positive] = array[M, array[N, Fraction]]
func toMatrix[M, N: static Positive](a: array[M, array[N, int]]): Matrix[M, N] =
for i in 0..<M:
for j in 0..<N:
result[i][j] = a[i][j] // 1
func transformToRref(mat: var Matrix) =
var lead = 0
for r in 0..<mat.M:
if lead >= mat.N: return
var i = r
while mat[i][lead] == Zero:
inc i
if i == mat.M:
i = r
inc lead
if lead == mat.N: return
swap mat[i], mat[r]
if (let d = mat[r][lead]; d) != Zero:
for item in mat[r].mitems:
item /= d
for i in 0..<mat.M:
if i != r:
let m = mat[i][lead]
for c in 0..<mat.N:
mat[i][c] -= mat[r][c] * m
inc lead
proc `$`(mat: Matrix): string =
for row in mat:
var line = ""
for val in row:
line.addSep(" ", 0)
line.add val.toFloat.formatFloat(ffDecimal, 2).align(7)
echo line
template runTest(mat: Matrix) =
echo "Original matrix:"
echo mat
echo "Reduced row echelon form:"
mat.transformToRref()
echo mat
echo ""
var m1 = [[ 1, 2, -1, -4],
[ 2, 3, -1, -11],
[-2, 0, -3, 22]].toMatrix()
var m2 = [[2, 0, -1, 0, 0],
[1, 0, 0, -1, 0],
[3, 0, 0, -2, -1],
[0, 1, 0, 0, -2],
[0, 1, -1, 0, 0]].toMatrix()
var m3 = [[1, 2, 3, 4, 3, 1],
[2, 4, 6, 2, 6, 2],
[3, 6, 18, 9, 9, -6],
[4, 8, 12, 10, 12, 4],
[5, 10, 24, 11, 15, -4]].toMatrix()
var m4 = [[0, 1],
[1, 2],
[0, 5]].toMatrix()
runTest(m1)
runTest(m2)
runTest(m3)
runTest(m4)
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Rewrite this program in PHP while keeping its functionality equivalent to the OCaml version. | let swap_rows m i j =
let tmp = m.(i) in
m.(i) <- m.(j);
m.(j) <- tmp;
;;
let rref m =
try
let lead = ref 0
and rows = Array.length m
and cols = Array.length m.(0) in
for r = 0 to pred rows do
if cols <= !lead then
raise Exit;
let i = ref r in
while m.(!i).(!lead) = 0 do
incr i;
if rows = !i then begin
i := r;
incr lead;
if cols = !lead then
raise Exit;
end
done;
swap_rows m !i r;
let lv = m.(r).(!lead) in
m.(r) <- Array.map (fun v -> v / lv) m.(r);
for i = 0 to pred rows do
if i <> r then
let lv = m.(i).(!lead) in
m.(i) <- Array.mapi (fun i iv -> iv - lv * m.(r).(i)) m.(i);
done;
incr lead;
done
with Exit -> ()
;;
let () =
let m =
[| [| 1; 2; -1; -4 |];
[| 2; 3; -1; -11 |];
[| -2; 0; -3; 22 |]; |]
in
rref m;
Array.iter (fun row ->
Array.iter (fun v ->
Printf.printf " %d" v
) row;
print_newline()
) m
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Generate a PHP translation of this Perl snippet without changing its computational steps. | sub rref
{our @m; local *m = shift;
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
foreach my $r (0 .. $rows - 1)
{$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead])
{++$i == $rows or next;
$i = $r;
++$lead == $cols and return;}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
foreach my $i (0 .. $rows - 1)
{$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };}
++$lead;}}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@m =
(
[ 1, 2, -1, -4 ],
[ 2, 3, -1, -11 ],
[ -2, 0, -3, 22 ]
);
rref(\@m);
print display(\@m);
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Transform the following Racket implementation into PHP, maintaining the same output and logic. | #lang racket
(require math)
(define (reduced-echelon M)
(matrix-row-echelon M #t #t))
(reduced-echelon
(matrix [[1 2 -1 -4]
[2 3 -1 -11]
[-2 0 -3 22]]))
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Keep all operations the same but rewrite the snippet in PHP. |
cols= 0; w= 0; @. =0
mat.=; mat.1= ' 1 2 -1 -4 '
mat.2= ' 2 3 -1 -11 '
mat.3= ' -2 0 -3 22 '
do r=1 until mat.r==''; _=mat.r
do c=1 until _=''; parse var _ @.r.c _
w= max(w, length(@.r.c) + 1)
end
cols= max(cols, c)
end
rows= r-1
call showMat 'original matrix'
!= 1
do r=1 for rows while cols>!
j= r
do while @.j.!==0; j= j + 1
if j==rows then do; j= r; != ! + 1; if cols==! then leave r; end
end
do _=1 for cols while j\==r; parse value @.r._ @.j._ with @.j._ @._._
end
?= @.r.!
do d=1 for cols while ?\=1; @.r.d= @.r.d / ?
end
do k=1 for rows; ?= @.k.!
if k==r | ?=0 then iterate
do s=1 for cols; @.k.s= @.k.s - ? * @.r.s
end
end
!= !+1
end
call showMat 'matrix RREF'
exit
showMat: parse arg title; say; say center(title, 3 + (cols+1) * w, '─'); say
do r=1 for rows; _=
do c=1 for cols
if @.r.c=='' then do; say "***error*** matrix element isn't defined:"
say 'row' r", column" c'.'; exit 13
end
_= _ right(@.r.c, w)
end
say _
end
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Preserve the algorithm and functionality while converting the code from Ruby to PHP. |
def reduced_row_echelon_form(ary)
lead = 0
rows = ary.size
cols = ary[0].size
rary = convert_to(ary, :to_r)
catch :done do
rows.times do |r|
throw :done if cols <= lead
i = r
while rary[i][lead] == 0
i += 1
if rows == i
i = r
lead += 1
throw :done if cols == lead
end
end
rary[i], rary[r] = rary[r], rary[i]
v = rary[r][lead]
rary[r].collect! {|x| x / v}
rows.times do |i|
next if i == r
v = rary[i][lead]
rary[i].each_index {|j| rary[i][j] -= v * rary[r][j]}
end
lead += 1
end
end
rary
end
def convert_to(ary, type)
ary.each_with_object([]) do |row, new|
new << row.collect {|elem| elem.send(type)}
end
end
class Rational
alias _to_s to_s
def to_s
denominator==1 ? numerator.to_s : _to_s
end
end
def print_matrix(m)
max = m[0].collect {-1}
m.each {|row| row.each_index {|i| max[i] = [max[i], row[i].to_s.length].max}}
m.each {|row| row.each_index {|i| print "%
end
mtx = [
[ 1, 2, -1, -4],
[ 2, 3, -1,-11],
[-2, 0, -3, 22]
]
print_matrix reduced_row_echelon_form(mtx)
puts
mtx = [
[ 1, 2, 3, 7],
[-4, 7,-2, 7],
[ 3, 3, 0, 7]
]
reduced = reduced_row_echelon_form(mtx)
print_matrix reduced
print_matrix convert_to(reduced, :to_f)
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Convert the following code from Scala to PHP, ensuring the logic remains intact. |
typealias Matrix = Array<DoubleArray>
fun Matrix.toReducedRowEchelonForm() {
var lead = 0
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
if (colCount <= lead) return
var i = r
while (this[i][lead] == 0.0) {
i++
if (rowCount == i) {
i = r
lead++
if (colCount == lead) return
}
}
val temp = this[i]
this[i] = this[r]
this[r] = temp
if (this[r][lead] != 0.0) {
val div = this[r][lead]
for (j in 0 until colCount) this[r][j] /= div
}
for (k in 0 until rowCount) {
if (k != r) {
val mult = this[k][lead]
for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
}
}
lead++
}
}
fun Matrix.printf(title: String) {
println(title)
val rowCount = this.size
val colCount = this[0].size
for (r in 0 until rowCount) {
for (c in 0 until colCount) {
if (this[r][c] == -0.0) this[r][c] = 0.0
print("${"% 6.2f".format(this[r][c])} ")
}
println()
}
println()
}
fun main(args: Array<String>) {
val matrices = listOf(
arrayOf(
doubleArrayOf( 1.0, 2.0, -1.0, -4.0),
doubleArrayOf( 2.0, 3.0, -1.0, -11.0),
doubleArrayOf(-2.0, 0.0, -3.0, 22.0)
),
arrayOf(
doubleArrayOf(1.0, 2.0, 3.0, 4.0, 3.0, 1.0),
doubleArrayOf(2.0, 4.0, 6.0, 2.0, 6.0, 2.0),
doubleArrayOf(3.0, 6.0, 18.0, 9.0, 9.0, -6.0),
doubleArrayOf(4.0, 8.0, 12.0, 10.0, 12.0, 4.0),
doubleArrayOf(5.0, 10.0, 24.0, 11.0, 15.0, -4.0)
)
)
for (m in matrices) {
m.printf("Original matrix:")
m.toReducedRowEchelonForm()
m.printf("Reduced row echelon form:")
}
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Change the programming language of this snippet from Swift to PHP without modifying what it does. | var lead = 0
for r in 0..<rows {
if (cols <= lead) { break }
var i = r
while (m[i][lead] == 0) {
i += 1
if (i == rows) {
i = r
lead += 1
if (cols == lead) {
lead -= 1
break
}
}
}
for j in 0..<cols {
let temp = m[r][j]
m[r][j] = m[i][j]
m[i][j] = temp
}
let div = m[r][lead]
if (div != 0) {
for j in 0..<cols {
m[r][j] /= div
}
}
for j in 0..<rows {
if (j != r) {
let sub = m[j][lead]
for k in 0..<cols {
m[j][k] -= (sub * m[r][k])
}
}
}
lead += 1
}
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
Write a version of this Tcl function in PHP with identical behavior. | package require Tcl 8.5
namespace path {::tcl::mathop ::tcl::mathfunc}
proc toRREF {m} {
set lead 0
lassign [size $m] rows cols
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
return $m
}
}
}
foreach idx [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $idx $row
}
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j [- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
set m {{1 2 -1 -4} {2 3 -1 -11} {-2 0 -3 22}}
print_matrix $m
print_matrix [toRREF $m]
| <?php
function rref($matrix)
{
$lead = 0;
$rowCount = count($matrix);
if ($rowCount == 0)
return $matrix;
$columnCount = 0;
if (isset($matrix[0])) {
$columnCount = count($matrix[0]);
}
for ($r = 0; $r < $rowCount; $r++) {
if ($lead >= $columnCount)
break; {
$i = $r;
while ($matrix[$i][$lead] == 0) {
$i++;
if ($i == $rowCount) {
$i = $r;
$lead++;
if ($lead == $columnCount)
return $matrix;
}
}
$temp = $matrix[$r];
$matrix[$r] = $matrix[$i];
$matrix[$i] = $temp;
} {
$lv = $matrix[$r][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$r][$j] = $matrix[$r][$j] / $lv;
}
}
for ($i = 0; $i < $rowCount; $i++) {
if ($i != $r) {
$lv = $matrix[$i][$lead];
for ($j = 0; $j < $columnCount; $j++) {
$matrix[$i][$j] -= $lv * $matrix[$r][$j];
}
}
}
$lead++;
}
return $matrix;
}
?>
|
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