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  1. | f g det2x2 partialDerivative jacobian aN bN newtonMethod x0 y0 h epsilon |
  2.  
  3. " Функции для вычисления определителя матрицы 2х2 и частной производной "
  4. f := [:x :y | x * x + y * y - 4].
  5. g := [:x :y | x - y].
  6. det2x2 := [:a :b :c :d | a * d - b * c].
  7. partialDerivative := [:func :x :y :h :derivativeType |
  8.     derivativeType = 'x'
  9.         ifTrue: [(func value: x + h value: y) - (func value: x value: y) / h]
  10.         ifFalse: [derivativeType = 'y'
  11.             ifTrue: [(func value: x value: y + h) - (func value: x value: y) / h]
  12.             ifFalse: [Error signal: 'Invalid derivative type']]].
  13. jacobian := [:func1 :func2 :x :y :h |
  14.     | dx1 dy1 dx2 dy2 |
  15.     dx1 := partialDerivative valueWithArguments: {func1. x. y. h. 'x'}.
  16.     dy1 := partialDerivative valueWithArguments: {func1. x. y. h. 'y'}.
  17.     dx2 := partialDerivative valueWithArguments: {func2. x. y. h. 'x'}.
  18.     dy2 := partialDerivative valueWithArguments: {func2. x. y. h. 'y'}.
  19.     ^ det2x2 value: dx1 value: dy1 value: dx2 value: dy2.
  20. ].
  21. aN := [:func1 :func2 :x :y :h |
  22.     | fx fy dfy1 dfy2 |
  23.     fx := func1 value: x value: y.
  24.     fy := func2 value: x value: y.
  25.     dfy1 := partialDerivative valueWithArguments: {func1. x. y. h. 'y'}.
  26.     dfy2 := partialDerivative valueWithArguments: {func2. x. y. h. 'y'}.
  27.     ^ det2x2 value: fx value: dfy1 value: fy value: dfy2.
  28. ].
  29. bN := [:func1 :func2 :x :y :h |
  30.     | dfx1 fx dfx2 fy |
  31.     dfx1 := partialDerivative valueWithArguments: {func1. x. y. h. 'x'}.
  32.     fx := func1 value: x value: y.
  33.     dfx2 := partialDerivative valueWithArguments: {func2. x. y. h. 'x'}.
  34.     fy := func2 value: x value: y.
  35.     ^ det2x2 value: dfx1 value: fx value: dfx2 value: fy.
  36. ].
  37.  
  38. " Функция для вычисления метода Ньютона "
  39. newtonMethod := [:func1 :func2 :x0 :y0 :h :epsilon |
  40.     | x y continueIteration |
  41.     x := x0.
  42.     y := y0.
  43.     continueIteration := true.
  44.     [continueIteration] whileTrue: [
  45.         | jacobianValue aNValue bNValue newX newY |
  46.         jacobianValue := jacobian valueWithArguments: {func1. func2. x. y. h}.
  47.         aNValue := aN valueWithArguments: {func1. func2. x. y. h}.
  48.         bNValue := bN valueWithArguments: {func1. func2. x. y. h}.
  49.         newX := x - (aNValue / jacobianValue).
  50.         newY := y - (bNValue / jacobianValue).
  51.         ((newX - x) abs <= epsilon and: [(newY - y) abs <= epsilon])
  52.             ifTrue: [continueIteration := false]
  53.             ifFalse: [x := newX. y := newY].
  54.     ].
  55.     ^ Array with: x with: y.
  56. ].
  57.  
  58. " Начальные значения и параметры "
  59. x0 := 1.0.
  60. y0 := 1.0.
  61. h := 1e-6.
  62. epsilon := 1e-10.
  63.  
  64. " Вычисление метода Ньютона "
  65. | result |
  66. result := newtonMethod valueWithArguments: {f. g. x0. y0. h. epsilon}.
  67. result ifNotNil: [
  68.     Transcript show: 'x = ', result first printString, ', y = ', result second printString; cr.
  69. ] ifNil: [
  70.     Transcript show: 'Метод Ньютона не сошелся'; cr.
  71. ].
  72.  
Success #stdin #stdout 0.01s 10528KB
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Standard input is empty
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Object: BlockClosure new "<0x7f4a7d8924e0>" error: did not understand #value:value:value:value:
MessageNotUnderstood(Exception)>>signal (ExcHandling.st:254)
BlockClosure(Object)>>doesNotUnderstand: #value:value:value:value: (SysExcept.st:1448)
[] in UndefinedObject>>executeStatements (prog:19)
[] in UndefinedObject>>executeStatements (prog:46)
BlockClosure>>whileTrue: (BlkClosure.st:328)
[] in UndefinedObject>>executeStatements (prog:43)
UndefinedObject>>executeStatements (prog:66)
Метод Ньютона не сошелся
https://ideone.com/xOFprf
language:
Smalltalk (gst 3.2.5)
created:
4 days ago
visibility:
public

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