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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.     det2x2
  15.         value: (partialDerivative value: func1 value: x value: y value: h value: 'x')
  16.         value: (partialDerivative value: func1 value: x value: y value: h value: 'y')
  17.         value: (partialDerivative value: func2 value: x value: y value: h value: 'x')
  18.         value: (partialDerivative value: func2 value: x value: y value: h value: 'y')].
  19. aN := [:func1 :func2 :x :y :h |
  20.     det2x2
  21.         value: (func1 value: x value: y)
  22.         value: (partialDerivative value: func1 value: x value: y value: h value: 'y')
  23.         value: (func2 value: x value: y)
  24.         value: (partialDerivative value: func2 value: x value: y value: h value: 'y')].
  25. bN := [:func1 :func2 :x :y :h |
  26.     det2x2
  27.         value: (partialDerivative value: func1 value: x value: y value: h value: 'x')
  28.         value: (func1 value: x value: y)
  29.         value: (partialDerivative value: func2 value: x value: y value: h value: 'x')
  30.         value: (func2 value: x value: y)].
  31.  
  32. " Функция для вычисления метода Ньютона "
  33. newtonMethod := [:func1 :func2 :x0 :y0 :h :epsilon |
  34.     | x y continueIteration |
  35.     x := x0.
  36.     y := y0.
  37.     continueIteration := true.
  38.     [continueIteration] whileTrue: [
  39.         | jacobianValue aNValue bNValue newX newY |
  40.         jacobianValue := jacobian value: func1 value: func2 value: x value: y value: h.
  41.         aNValue := aN value: func1 value: func2 value: x value: y value: h.
  42.         bNValue := bN value: func1 value: func2 value: x value: y value: h.
  43.         newX := x - aNValue / jacobianValue.
  44.         newY := y - bNValue / jacobianValue.
  45.         (newX - x) abs <= epsilon and: [(newY - y) abs <= epsilon] ifTrue: [continueIteration := false] ifFalse: [x := newX. y := newY].
  46.     ].
  47.     ^ Array with: x with: y].
  48.  
  49. " Начальные значения и параметры "
  50. x0 := 1.0.
  51. y0 := 1.0.
  52. h := 1e-6.
  53. epsilon := 1e-10.
  54.  
  55. " Вычисление метода Ньютона "
  56. | result |
  57. result := newtonMethod value: f value: g value: x0 value: y0 value: h value: epsilon.
  58. Transcript show: 'x = ', result first printString, ', y = ', result second printString.
Success #stdin #stdout 0.01s 10520KB
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Standard input is empty
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Object: BlockClosure new "<0x7f4a7d8a3e70>" error: did not understand #value:value:value:value:value:value:
MessageNotUnderstood(Exception)>>signal (ExcHandling.st:254)
BlockClosure(Object)>>doesNotUnderstand: #value:value:value:value:value:value: (SysExcept.st:1448)
UndefinedObject>>executeStatements (prog:56)
Object: nil error: did not understand #first
MessageNotUnderstood(Exception)>>signal (ExcHandling.st:254)
UndefinedObject(Object)>>doesNotUnderstand: #first (SysExcept.st:1448)
UndefinedObject>>executeStatements (prog:58)
https://ideone.com/bVGd5V
language:
Smalltalk (gst 3.2.5)
created:
4 days ago
visibility:
public

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