File size: 18,293 Bytes
b1b3bae |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 |
' Copyright 2020 Daniel Wagner O. de Medeiros
'
' This file is part of DWSIM.
'
' DWSIM is free software: you can redistribute it and/or modify
' it under the terms of the GNU General Public License as published by
' the Free Software Foundation, either version 3 of the License, or
' (at your option) any later version.
'
' DWSIM is distributed in the hope that it will be useful,
' but WITHOUT ANY WARRANTY; without even the implied warranty of
' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
' GNU General Public License for more details.
'
' You should have received a copy of the GNU General Public License
' along with DWSIM. If not, see <http://www.gnu.org/licenses/>.
Namespace MathEx.Optimization
Public Class NewtonSolver
Public Property Tolerance As Double = 0.0001
Public Property MaxIterations As Integer = 100
Public Property EnableDamping As Boolean = True
Public Property UseBroydenApproximation As Boolean = False
Public Property ExpandFactor As Double = 1.5
Public Property MaximumDelta As Double = 0.5
Public Property Epsilon As Double = Double.NaN
Private _Iterations As Integer = 0
Private fxb As Func(Of Double(), Double())
Private broydengrad As Double(,)
Private brentsolver As New BrentOpt.BrentMinimize
Private tmpx As Double(), tmpdx As Double()
Private _jacobian As Boolean
Private dfdx As Func(Of Double(), Double(,))
Private _error As Double
Private _jac As Double(,)
Public ReadOnly Property Jacobian As Double(,)
Get
Return _jac
End Get
End Property
Public ReadOnly Property BuildingJacobian As Boolean
Get
Return _jacobian
End Get
End Property
Public ReadOnly Property Iterations As Integer
Get
Return _Iterations
End Get
End Property
Sub New()
brentsolver.DefineFuncDelegate(AddressOf minimizeerror)
End Sub
Public Sub Reset()
_Iterations = 0
_error = 0.0
End Sub
Public Shared Function FindRoots(functionbody As Func(Of Double(), Double()), vars As Double(),
maxits As Integer, tol As Double) As Double()
Dim newton As New NewtonSolver
newton.Tolerance = tol
newton.MaxIterations = maxits
Return newton.Solve(functionbody, vars)
End Function
''' <summary>
''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
''' </summary>
''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
''' <param name="vars">initial values for x</param>
''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()
Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}
Dim leave As Boolean = False
Dim finalx As Double() = vars
dfdx = Nothing
If Not Double.IsNaN(Epsilon) Then epsilons = New Double() {Epsilon}
If EnableDamping Then
For Each d In dfacs
If leave Then Exit For
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(d, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
Next
Else
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(1.0, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
End If
If Not leave Then Throw New Exception("Newton Convergence Error")
Return finalx
End Function
''' <summary>
''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
''' </summary>
''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
''' <param name="vars">initial values for x</param>
''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
Function Solve(functionbody As Func(Of Double(), Double()), functiongradient As Func(Of Double(), Double(,)), vars As Double()) As Double()
Dim dfacs As Double() = New Double() {0.1, 0.2, 0.4, 0.6, 0.8, 1.0}
Dim epsilons As Double() = New Double() {0.000000000001, 0.00000001, 0.0001, 0.001, 0.01, 0.1}
Dim leave As Boolean = False
Dim finalx As Double() = vars
dfdx = functiongradient
If EnableDamping Then
For Each d In dfacs
If leave Then Exit For
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(d, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
Next
Else
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(1.0, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
End If
If Not leave Then Throw New Exception("Newton Convergence Error")
Return finalx
End Function
Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()
fxb = functionbody
Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
Dim success As Boolean = False
x = vars.Clone
dx = x.Clone
_Iterations = 0
Do
If _Iterations = 0 Then
fxsum0 = 1.0E+20
Else
fxsum0 = MathEx.Common.SumSqr(fx)
End If
_jacobian = False
fx = fxb.Invoke(x)
_error = MathEx.Common.SumSqr(fx)
fxsum = _error
If fxsum < Tolerance Then
Exit Do
End If
_jacobian = True
dfdx = gradient(epsilon, x, fx)
Dim A = MathNet.Numerics.LinearAlgebra.Matrix(Of Double).Build.DenseOfArray(dfdx)
Dim B = MathNet.Numerics.LinearAlgebra.Vector(Of Double).Build.DenseOfArray(fx)
dx = A.Solve(B).ToArray()
'SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)
'If success Then
If Common.SumSqr(dx) < Tolerance And _Iterations > MaxIterations / 2 Then
Exit Do
End If
If EnableDamping Then
If _Iterations > 5 Then
df = df * ExpandFactor
If df > 1.0 Then df = 1.0
Else
df = mindamp
End If
Else
df = 1.0#
End If
For i = 0 To x.Length - 1
If Math.Abs(x(i)) < 1.0E-20 Then
x(i) -= dx(i) * df
Else
If Math.Abs(dx(i) / x(i)) > MaximumDelta Then
dx(i) = Math.Sign(dx(i)) * Math.Abs(x(i)) * MaximumDelta
End If
x(i) -= dx(i) * df
End If
Next
'Else
' For i = 0 To x.Length - 1
' x(i) *= 0.999
' Next
'End If
_Iterations += 1
If _Iterations > 50 And fxsum > fxsum0 Then
Throw New ArgumentException("not converging")
End If
If Double.IsNaN(fxsum) Then
Throw New ArgumentException("not converging")
End If
Loop Until _Iterations > MaxIterations
If _Iterations > MaxIterations Then
Throw New ArgumentException("not converged")
End If
If dfdx Is Nothing Then dfdx = gradient(epsilon, x, fx)
_jac = dfdx
Return x
End Function
Private Function gradient(epsilon As Double, ByVal x() As Double, fx() As Double) As Double(,)
Dim f1(), f2() As Double
Dim g(x.Length - 1, x.Length - 1), x1(x.Length - 1), x2(x.Length - 1), dx(x.Length - 1), xbr(x.Length - 1), fbr(x.Length - 1) As Double
Dim i, j, k, n As Integer
n = x.Length - 1
If UseBroydenApproximation Then
If broydengrad Is Nothing Then broydengrad = g.Clone()
If _Iterations = 0 Then
For i = 0 To n
For j = 0 To n
If i = j Then broydengrad(i, j) = 1.0 Else broydengrad(i, j) = 0.0
Next
Next
Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 0)
Else
Broyden.broydn(n, x, fx, dx, xbr, fbr, broydengrad, 1)
End If
Return broydengrad
Else
If dfdx IsNot Nothing Then
g = dfdx.Invoke(x)
Else
For i = 0 To x.Length - 1
For j = 0 To x.Length - 1
If i <> j Then
x1(j) = x(j)
x2(j) = x(j)
Else
If x(j) = 0.0# Then
x1(j) = epsilon
x2(j) = 2 * epsilon
Else
x1(j) = x(j) * (1 - epsilon)
x2(j) = x(j) * (1 + epsilon)
End If
End If
Next
f1 = fxb.Invoke(x1)
f2 = fxb.Invoke(x2)
For k = 0 To x.Length - 1
g(k, i) = (f2(k) - f1(k)) / (x2(i) - x1(i))
Next
Next
End If
End If
Return g
End Function
Public Function minimizeerror(ByVal t As Double) As Double
Dim tmpx0 As Double() = tmpx.Clone
For i = 0 To tmpx.Length - 1
tmpx0(i) -= tmpdx(i) * t
Next
Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
Return abssum0
End Function
End Class
Public Class NewtonSolver_Old
Public Property Tolerance As Double = 0.0001
Public Property MaxIterations As Integer = 1000
Public Property EnableDamping As Boolean = True
Private _Iterations As Integer = 0
Private fxb As Func(Of Double(), Double())
Private brentsolver As New BrentOpt.BrentMinimize
Private tmpx As Double(), tmpdx As Double()
Private _error As Double
Public ReadOnly Property Iterations
Get
Return _Iterations
End Get
End Property
Sub New()
brentsolver.DefineFuncDelegate(AddressOf minimizeerror)
End Sub
''' <summary>
''' Solves a system of non-linear equations [f(x) = 0] using newton's method.
''' </summary>
''' <param name="functionbody">f(x) where x is a vector of double, returns the error values for each x</param>
''' <param name="vars">initial values for x</param>
''' <returns>vector of variables which solve the equations according to the minimum allowable error value (tolerance).</returns>
Function Solve(functionbody As Func(Of Double(), Double()), vars As Double()) As Double()
Dim minimaldampings As Double() = New Double() {1.0E-20, 0.000000000000001, 0.0000000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}
Dim epsilons As Double() = New Double() {0.0000000001, 0.000000001, 0.00000001, 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1}
Dim leave As Boolean = False
Dim finalx As Double() = vars
If EnableDamping Then
For Each mindamp In minimaldampings
If leave Then Exit For
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(mindamp, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
Next
Else
For Each eps In epsilons
If leave Then Exit For
Try
finalx = solve_internal(1.0, eps, functionbody, vars)
leave = True
Catch ex As ArgumentException
'try next parameters
End Try
Next
End If
If Not leave Then Throw New Exception("newton convergence error")
Return finalx
End Function
Private Function solve_internal(mindamp As Double, epsilon As Double, functionbody As Func(Of Double(), Double()), vars As Double()) As Double()
fxb = functionbody
Dim fx(), x(), dx(), dfdx(,), df, fxsum, fxsum0 As Double
Dim success As Boolean = False
x = vars.Clone
dx = x.Clone
_Iterations = 0
Do
If _Iterations = 0 Then
fxsum0 = 1.0E+20
Else
fxsum0 = MathEx.Common.SumSqr(fx)
End If
fx = fxb.Invoke(x)
_error = MathEx.Common.SumSqr(fx)
fxsum = _error
If Common.SumSqr(fx) < Tolerance Then Exit Do
dfdx = gradient(epsilon, x)
success = SysLin.rsolve.rmatrixsolve(dfdx, fx, x.Length, dx)
If success Then
'this call to the brent solver calculates the damping factor which minimizes the error (fval).
If EnableDamping Then
tmpx = x.Clone
tmpdx = dx.Clone
brentsolver.brentoptimize(mindamp, 1.0, mindamp / 10.0#, df)
Else
df = 1.0#
End If
For i = 0 To x.Length - 1
x(i) -= dx(i) * df
Next
Else
For i = 0 To x.Length - 1
x(i) *= 0.999
Next
End If
_Iterations += 1
If _Iterations > 50 And fxsum > fxsum0 Then
Throw New ArgumentException("not converging")
End If
If Double.IsNaN(fxsum) Then
Throw New ArgumentException("not converging")
End If
Loop Until _Iterations > MaxIterations
If _Iterations > MaxIterations Then
Throw New ArgumentException("not converged")
End If
Return x
End Function
Private Function gradient(epsilon As Double, ByVal x() As Double) As Double(,)
Dim f1(), f2() As Double
Dim g(x.Length - 1, x.Length - 1), x2(x.Length - 1) As Double
Dim i, j, k As Integer
f1 = fxb.Invoke(x)
For i = 0 To x.Length - 1
For j = 0 To x.Length - 1
If i <> j Then
x2(j) = x(j)
Else
If x(j) = 0.0# Then
x2(j) = epsilon
Else
x2(j) = x(j) * (1 + epsilon)
End If
End If
Next
f2 = fxb.Invoke(x2)
For k = 0 To x.Length - 1
g(k, i) = (f2(k) - f1(k)) / (x2(i) - x(i))
Next
Next
Return g
End Function
Public Function minimizeerror(ByVal t As Double) As Double
Dim tmpx0 As Double() = tmpx.Clone
For i = 0 To tmpx.Length - 1
tmpx0(i) -= tmpdx(i) * t
Next
Dim abssum0 = MathEx.Common.SumSqr(fxb.Invoke(tmpx0))
If Double.IsNaN(abssum0) Then abssum0 = 1.0E+20
Return abssum0
End Function
End Class
End Namespace |