University:
Kentucky State University
Course:
COS 232| Programming I
Academic year:

2024
Views:

498

Pages:

6
Author:

hekeldigzjbz

CHAPTER 14 14.8 Errata: p. 357; The initial value of the variable maxf must be set to some ridiculously small value before the iterations are begun. Add the following line to the beginning of the VBA code: maxf = -999E9 The following code implements the random search algorithm in VBA: Option Explicit Sub RandSearch() Dim n As Long Dim xmin As Single, xmax As Single, ymin As Single, ymax As Single Dim maxf As Single, maxx As Single, maxy As Single xmin xmax ymin ymax = = = = -2 2 -2 2 n = InputBox("n=") Call RndSrch(n, xmin, xmax, ymin, ymax, maxy, maxx, maxf) MsgBox maxf MsgBox maxx MsgBox maxy End Sub Sub RndSrch(n, xmin, xmax, ymin, ymax, maxy, maxx, maxf) Dim j As Long Dim x As Single, y As Single, fn As Single maxf = -999E9 For j = 1 To n x = xmin + (xmax - xmin) * Rnd y = ymin + (ymax - ymin) * Rnd fn = f(x, y) If fn > maxf Then maxf = fn maxx = x maxy = y End If Next j End Sub Function f(x, y) f = 3.5 * x + 2 * y + x ^ 2 - x ^ 4 - 2 * x * y - y ^ 2 End Function 14.9 The following code implements the grid search algorithm in VBA: Option Explicit Sub GridSearch() Dim nx As Long, ny As Long Dim xmin As Single, xmax As Single, ymin As Single, ymax As Single Dim maxf As Single, maxx As Single, maxy As Single xmin xmax ymin ymax nx = ny = = -2 = 2 = -2 = 2 1000 1000 Call GridSrch(nx, ny, xmin, xmax, ymin, ymax, maxy, maxx, maxf) MsgBox maxf MsgBox maxx MsgBox maxy End Sub Sub GridSrch(nx, ny, xmin, xmax, ymin, ymax, maxy, maxx, maxf) Dim i As Long, j As Long Dim x As Single, y As Single, fn As Single Dim xinc As Single, yinc As Single xinc = (xmax - xmin) / nx yinc = (ymax - ymin) / ny maxf = -999000000000# x = xmin For i = 0 To nx y = ymin For j = 0 To ny fn = f(x, y) If fn > maxf Then maxf = fn maxx = x maxy = y End If y = y + yinc Next j x = x + xinc Next i End Sub Function f(x, y) f = y - x - 2 * x ^ 2 - 2 * x * y - y ^ 2 End Function 14.10 f ( x, y ) = 5 x 2 y − 8 y 2 − 7 x 2 ∂f = 10 xy − 14 x ⇒ 10 (2 )(4) − 14( 4) = 24 ∂x ∂f = 5 x 2 − 16 y ⇒ 5( 4) 2 − 16( 2) = 48 ∂y ∇f = 24iˆ + 48 ˆj  ∂f ∂f  f  xo + h , yo + h  = f (4 + 24 h,2 + 48h ) ∂x ∂y   = 5(4 + 24h) 2 (2 + 48h) − 8(2 + 48h) 2 − 7(4 + 24h) 2 g ( x) = 138240h3 + 29376h 2 + 2880h + 16 14.11 f ( x, y ) = 2 x3 y 2 − 6 yx + x 2 + 4 y ∂f = 6 x 2 y 2 − 6 y + 2 x ⇒ 6 (1)(1) − 6(1) + 2(1) = 2 ∂x ∂f = 4 x 3 y − 6 y + 4 ⇒ 4(1)(1) − 6 (1) + 4 = 2 ∂x ∇f = 2iˆ + 2 ˆj f ( xo + 2f 2f h , yo + h ) = f (1 + 2h , 1 + 2h ) 2x 2y = 2(1 + 2h)3 (1 + 2h) 2 − 6(1 + 2h)(1 + 2h) + (1 + 2h) 2 + 4(1 + 2h) g ( x ) = 64h5 + 160h 4 + 160h3 + 60h 2 + 8h + 1