Matriz Inversa en Visual Basic 6
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The University of Tennessee Modified by Nilson
MATRIZ INVERSA EN VISUAL BASIC 6.0
He visto que muchas personas que programan con Visual Basic preguntan sobre la matriz inversa, me doy cuenta que es un poco difícil encontrarla en Internet. En este documento me gustaría colocar como se hace. 1) Inicia VB6.0 en un proyecto estándar en blanco (figura 1):
Figura 1 2) Coloca un botón de comando en el formulario, que sea de tamaño relativamente pequeño (figura 2) y coloque la propiedad AUTOREDRAW = True del Form1. Botón Command1
AutoRedraw = True
Figura 2
The University of Tennessee Modified by Nilson
3) Agregar un Modulo. (Figura 3) *Click en el menú Proyecto *Clic en Agregar Modulo
Figura 3 *Si esta ventana aparece, pulsar abrir
Figura 4
The University of Tennessee Modified by Nilson
4) Introducir código de la matriz inversa en el Module 1. En la ventana proyecto, haga doble clic en el Module 1 para ingresar a la ventana código de este modulo.
Doble click
Figura 5. Aparecerá la ventana código (figura 6)
Figura 6 Copie el siguiente código y péguelo dentro de esta ventana (el tamaño de la letra fue reducido para ahorrar espacio en este documento, NO NECESITA LEERLO):
The University of Tennessee Modified by Nilson
Private Const LUNB As Long = 8# Public Type Complex X As Double Y As Double End Type Public Const MachineEpsilon = 5E-16 Public Const MaxRealNumber = 1E+300 Public Const MinRealNumber = 1E-300 Private Const BigNumber As Double = 1E+70 Private Const SmallNumber As Double = 1E-70 Private Const PiNumber As Double = 3.14159265358979 Public Function MaxReal(ByVal M1 As Double, ByVal M2 As Double) As Double If M1 > M2 Then MaxReal = M1 Else MaxReal = M2 End If End Function Public Function MinReal(ByVal M1 As Double, ByVal M2 As Double) As Double If M1 < M2 Then MinReal = M1 Else MinReal = M2 End If End Function Public Function MaxInt(ByVal M1 As Long, ByVal M2 As Long) As Long If M1 > M2 Then MaxInt = M1 Else MaxInt = M2 End If End Function Public Function MinInt(ByVal M1 As Long, ByVal M2 As Long) As Long If M1 < M2 Then MinInt = M1 Else MinInt = M2 End If End Function Public Function ArcSin(ByVal X As Double) As Double Dim T As Double T = Sqr(1 - X * X) If T < SmallNumber Then ArcSin = Atn(BigNumber * Sgn(X)) Else ArcSin = Atn(X / T) End If End Function Public Function ArcCos(ByVal X As Double) As Double Dim T As Double T = Sqr(1 - X * X) If T < SmallNumber Then ArcCos = Atn(BigNumber * Sgn(-X)) + 2 * Atn(1) Else ArcCos = Atn(-X / T) + 2 * Atn(1) End If End Function Public Function SinH(ByVal X As Double) As Double SinH = (Exp(X) - Exp(-X)) / 2 End Function Public Function CosH(ByVal X As Double) As Double CosH = (Exp(X) + Exp(-X)) / 2 End Function Public Function TanH(ByVal X As Double) As Double TanH = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X)) End Function Public Function Pi() As Double Pi = PiNumber End Function Public Function Power(ByVal Base As Double, ByVal Exponent As Double) As Double Power = Base ^ Exponent End Function Public Function Square(ByVal X As Double) As Double Square = X * X End Function Public Function Log10(ByVal X As Double) As Double Log10 = Log(X) / Log(10) End Function Public Function Ceil(ByVal X As Double) As Double Ceil = -Int(-X) End Function Public Function RandomInteger(ByVal X As Long) As Long RandomInteger = Int(Rnd() * X) End Function Public Function Atn2(ByVal Y As Double, ByVal X As Double) As Double If SmallNumber * Abs(Y) < Abs(X) Then If X < 0 Then If Y = 0 Then Atn2 = Pi() Else Atn2 = Atn(Y / X) + Pi() * Sgn(Y) End If Else Atn2 = Atn(Y / X) End If Else Atn2 = Sgn(Y) * Pi() / 2 End If End Function Public Function C_Complex(ByVal X As Double) As Complex Dim Result As Complex Result.X = X Result.Y = 0 C_Complex = Result End Function Public Function AbsComplex(ByRef Z As Complex) As Double Dim Result As Double Dim W As Double Dim XABS As Double Dim YABS As Double Dim V As Double XABS = Abs(Z.X) YABS = Abs(Z.Y) W = MaxReal(XABS, YABS) V = MinReal(XABS, YABS) If V = 0 Then Result = W Else Result = W * Sqr(1 + Square(V / W)) End If AbsComplex = Result End Function
The University of Tennessee Modified by Nilson
Public Function C_Opposite(ByRef Z As Complex) As Complex Dim Result As Complex Result.X = -Z.X Result.Y = -Z.Y C_Opposite = Result End Function Public Function Conj(ByRef Z As Complex) As Complex Dim Result As Complex Result.X = Z.X Result.Y = -Z.Y Conj = Result End Function Public Function CSqr(ByRef Z As Complex) As Complex Dim Result As Complex Result.X = Square(Z.X) - Square(Z.Y) Result.Y = 2 * Z.X * Z.Y CSqr = Result End Function Public Function C_Add(ByRef Z1 As Complex, ByRef Z2 As Complex) As Complex Dim Result As Complex Result.X = Z1.X + Z2.X Result.Y = Z1.Y + Z2.Y C_Add = Result End Function Public Function C_Mul(ByRef Z1 As Complex, ByRef Z2 As Complex) As Complex Dim Result As Complex Result.X = Z1.X * Z2.X - Z1.Y * Z2.Y Result.Y = Z1.X * Z2.Y + Z1.Y * Z2.X C_Mul = Result End Function Public Function C_AddR(ByRef Z1 As Complex, ByVal R As Double) As Complex Dim Result As Complex Result.X = Z1.X + R Result.Y = Z1.Y C_AddR = Result End Function Public Function C_MulR(ByRef Z1 As Complex, ByVal R As Double) As Complex Dim Result As Complex Result.X = Z1.X * R Result.Y = Z1.Y * R C_MulR = Result End Function Public Function C_Sub(ByRef Z1 As Complex, ByRef Z2 As Complex) As Complex Dim Result As Complex Result.X = Z1.X - Z2.X Result.Y = Z1.Y - Z2.Y C_Sub = Result End Function Public Function C_SubR(ByRef Z1 As Complex, ByVal R As Double) As Complex Dim Result As Complex Result.X = Z1.X - R Result.Y = Z1.Y C_SubR = Result End Function Public Function C_RSub(ByVal R As Double, ByRef Z1 As Complex) As Complex Dim Result As Complex Result.X = R - Z1.X Result.Y = -Z1.Y C_RSub = Result End Function Public Function C_Div(ByRef Z1 As Complex, ByRef Z2 As Complex) As Complex Dim Result As Complex Dim A As Double Dim B As Double Dim C As Double Dim D As Double Dim E As Double Dim F As Double A = Z1.X B = Z1.Y C = Z2.X D = Z2.Y If Abs(D) < Abs(C) Then E=D/C F=C+D*E Result.X = (A + B * E) / F Result.Y = (B - A * E) / F Else E=C/D F=D+C*E Result.X = (B + A * E) / F Result.Y = (-A + B * E) / F End If C_Div = Result End Function Public Function C_DivR(ByRef Z1 As Complex, ByVal R As Double) As Complex Dim Result As Complex Result.X = Z1.X / R Result.Y = Z1.Y / R C_DivR = Result End Function Public Function C_RDiv(ByVal R As Double, ByRef Z2 As Complex) As Complex Dim Result As Complex Dim A As Double Dim C As Double Dim D As Double Dim E As Double Dim F As Double A=R C = Z2.X D = Z2.Y
The University of Tennessee Modified by Nilson
If Abs(D) < Abs(C) Then E=D/C F=C+D*E Result.X = A / F Result.Y = -(A * E / F) Else E=C/D F=D+C*E Result.X = A * E / F Result.Y = -(A / F) End If C_RDiv = Result End Function Public Function C_Equal(ByRef Z1 As Complex, ByRef Z2 As Complex) As Boolean Dim Result As Boolean Result = Z1.X = Z2.X And Z1.Y = Z2.Y C_Equal = Result End Function Public Function C_NotEqual(ByRef Z1 As Complex, _ ByRef Z2 As Complex) As Boolean Dim Result As Boolean Result = Z1.X Z2.X Or Z1.Y Z2.Y C_NotEqual = Result End Function Public Function C_EqualR(ByRef Z1 As Complex, ByVal R As Double) As Boolean Dim Result As Boolean Result = Z1.X = R And Z1.Y = 0 C_EqualR = Result End Function Public Function C_NotEqualR(ByRef Z1 As Complex, _ ByVal R As Double) As Boolean Dim Result As Boolean Result = Z1.X R Or Z1.Y 0 C_NotEqualR = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Copyright (c) 1992-2007 The University of Tennessee. All rights reserved. ' 'Contributors: ' * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to ' pseudocode. ' 'See subroutines comments for additional copyrights. ' 'Redistribution and use in source and binary forms, with or without 'modification, are permitted provided that the following conditions are 'met: ' '- Redistributions of source code must retain the above copyright ' notice, this list of condition s and the following disclaimer. ' '- Redistributions in binary form must reproduce the above copyright ' notice, this list of conditions and the following disclaimer listed ' in this license in the documentation and/or other materials ' provided with the distribution. ' '- Neither the name of the copyright holders nor the names of its ' contributors may be used to endorse or promote products derived from ' this software without specific prior written permission. ' 'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS '"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 'LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 'A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 'OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 'SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 'LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 'DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 'THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT '(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 'OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Routines '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Inversion of a matrix given by its LU decomposition. ' 'Input parameters: ' A - LU decomposition of the matrix (output of RMatrixLU subroutine). ' Pivots - table of permutations which were made during the LU decomposition ' (the output of RMatrixLU subroutine). ' N - size of matrix A. ' 'Output parameters: ' A - inverse of matrix A. ' Array whose indexes range within [0..N-1, 0..N-1]. ' 'Result: ' True, if the matrix is not singular. ' False, if the matrix is singular. ' ' -- LAPACK routine (versio n 3.0) -' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., ' Courant Institute, Argonne National Lab, and Rice University ' February 29, 1992 ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Function RMatrixLUInverse(ByRef A() As Double, _ ByRef Pivots() As Long, _ ByVal N As Long) As Boolean Dim Result As Boolean Dim WORK() As Double Dim I As Long Dim IWS As Long Dim J As Long Dim JB As Long Dim JJ As Long Dim JP As Long Dim V As Double Dim i_ As Long Result = True ' ' Quick return if possible ' If N = 0# Then RMatrixLUInverse = Result Exit Function End If ReDim WORK(0# To N - 1#) ' ' Form inv(U) ' If Not RMatrixTRInverse(A, N, True, False) Then Result = False RMatrixLUInverse = Result Exit Function End If ' ' Solve the equation inv(A)*L = inv(U) for inv(A). '
The University of Tennessee Modified by Nilson
For J = N - 1# To 0# Step -1 ' ' Copy current column of L to WORK and replace with zeros. ' For I = J + 1# To N - 1# Step 1 WORK(I) = A(I, J) A(I, J) = 0# Next I ' ' Compute current column of inv(A). ' If J < N - 1# Then For I = 0# To N - 1# Step 1 V = 0# For i_ = J + 1# To N - 1# Step 1 V = V + A(I, i_) * WORK(i_) Next i_ A(I, J) = A(I, J) - V Next I End If Next J ' ' Apply column interchanges. ' For J = N - 2# To 0# Step -1 JP = Pivots(J) If JP J Then For i_ = 0# To N - 1# Step 1 WORK(i_) = A(i_, J) Next i_ For i_ = 0# To N - 1# Step 1 A(i_, J) = A(i_, JP) Next i_ For i_ = 0# To N - 1# Step 1 A(i_, JP) = WORK(i_) Next i_ End If Next J RMatrixLUInverse = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Inversion of a general matrix. ' 'Input parameters: ' A - matrix. Array whose indexes range within [0..N-1, 0..N-1]. ' N - size of matrix A. ' 'Output parameters: ' A - inverse of matrix A. ' Array whose indexes range within [0..N-1, 0..N-1]. ' 'Result: ' True, if the matrix is not singular. ' False, if the matrix is singular. ' ' -- ALGLIB -' Copyright 2005 by Bochkanov Sergey ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Function RMatrixInverse(ByRef A() As Double, ByVal N As Long) As Boolean Dim Result As Boolean Dim Pivots() As Long Call RMatrixLU(A, N, N, Pivots) Result = RMatrixLUInverse(A, Pivots, N) RMatrixInverse = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Obsolete 1-based subroutine. ' 'See RMatrixLUInverse for 0-based replacement. ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Function InverseLU(ByRef A() As Double, _ ByRef Pivots() As Long, _ ByVal N As Long) As Boolean Dim Result As Boolean Dim WORK() As Double Dim I As Long Dim IWS As Long Dim J As Long Dim JB As Long Dim JJ As Long Dim JP As Long Dim JP1 As Long Dim V As Double Dim i_ As Long Result = True ' ' Quick return if possible ' If N = 0# Then InverseLU = Result Exit Function End If ReDim WORK(1# To N) ' ' Form inv(U) ' If Not InvTriangular(A, N, True, False) Then Result = False InverseLU = Result Exit Function End If ' ' Solve the equation inv(A)*L = inv(U) for inv(A). ' For J = N To 1# Step -1 ' ' Copy current column of L to WORK and replace with zeros. ' For I = J + 1# To N Step 1 WORK(I) = A(I, J) A(I, J) = 0# Next I ' ' Compute current column of inv(A). ' If J < N Then JP1 = J + 1# For I = 1# To N Step 1 V = 0# For i_ = JP1 To N Step 1 V = V + A(I, i_) * WORK(i_) Next i_ A(I, J) = A(I, J) - V Next I End If Next J ' ' Apply column interchanges. ' For J = N - 1# To 1# Step -1 JP = Pivots(J)
The University of Tennessee Modified by Nilson
If JP J Then For i_ = 1# To N Step 1 WORK(i_) = A(i_, J) Next i_ For i_ = 1# To N Step 1 A(i_, J) = A(i_, JP) Next i_ For i_ = 1# To N Step 1 A(i_, JP) = WORK(i_) Next i_ End If Next J InverseLU = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Obsolete 1-based subroutine. ' 'See RMatrixInverse for 0-based replacement. ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Function Inverse(ByRef A() As Double, ByVal N As Long) As Boolean Dim Result As Boolean Dim Pivots() As Long Call LUDecomposition(A, N, N, Pivots) Result = InverseLU(A, Pivots, N) Inverse = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Copyright (c) 1992-2007 The University of Tennessee. All rights reserved. ' 'Contributors: ' * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to ' pseudocode. ' 'See subroutines comments for additional copyrights. ' 'Redistribution and use in source and binary forms, with or without 'modification, are permitted provided that the following conditions are 'met: ' '- Redistributions of source code must retain the above copyright ' notice, this list of condition s and the following disclaimer. ' '- Redistributions in binary form must reproduce the above copyright ' notice, this list of conditions and the following disclaimer listed ' in this license in the documentation and/or other materials ' provided with the distribution. ' '- Neither the name of the copyright holders nor the names of its ' contributors may be used to endorse or promote products derived from ' this software without specific prior written permission. ' 'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS '"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 'LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 'A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 'OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 'SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 'LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 'DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 'THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT '(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 'OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Global constants
'Routines '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'LU decomposition of a general matrix of size MxN ' 'The subroutine calculates the LU decomposition of a rectangular general 'matrix with partial pivoting (with row permutations). ' 'Input parameters: ' A - matrix A whose indexes range within [0..M-1, 0..N-1]. ' M - number of rows in matrix A. ' N - number of columns in matrix A. ' 'Output parameters: ' A - matrices L and U in compact form (see below). ' Array whose indexes range within [0..M-1, 0..N-1]. ' Pivots - permutation matrix in compact form (see below). ' Array whose index ranges within [0..Min(M-1,N-1)]. ' 'Matrix A is represented as A = P * L * U, where P is a permutation matrix, 'matrix L - lower triangular (or lower trapezoid, if M>N) matrix, 'U - upper triangular (or upper trapezoid, if M Abs(A(JP, J)) Then JP = I End If Next I Pivots(J) = JP If A(JP, J) 0# Then ' 'Apply the interchange to rows ' If JP J Then For i_ = 1# To N Step 1 T1(i_) = A(J, i_) Next i_ For i_ = 1# To N Step 1 A(J, i_) = A(JP, i_) Next i_ For i_ = 1# To N Step 1 A(JP, i_) = T1(i_) Next i_ End If ' 'Compute elements J+1:M of J-th column. ' If J < M Then ' ' CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) ' JP = J + 1# s = 1# / A(J, J) For i_ = JP To M Step 1 A(i_, J) = s * A(i_, J) Next i_ End If End If If J < MinInt(M, N) Then ' 'Update trailing submatrix. 'CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,A( J+1, J+1 ), LDA ) ' JP = J + 1# For I = J + 1# To M Step 1 s = A(I, J) For i_ = JP To N Step 1 A(I, i_) = A(I, i_) - s * A(J, i_) Next i_ Next I End If Next J End Sub '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Obsolete 1-based subroutine. Left for backward compatibility. ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Sub LUDecompositionUnpacked(ByRef A_() As Double, _ ByVal M As Long, _ ByVal N As Long, _ ByRef L() As Double, _ ByRef U() As Double, _ ByRef Pivots() As Long) Dim A() As Double Dim I As Long Dim J As Long Dim MinMN As Long A = A_ If M = 0# Or N = 0# Then Exit Sub End If MinMN = MinInt(M, N) ReDim L(1# To M, 1# To MinMN) ReDim U(1# To MinMN, 1# To N) Call LUDecomposition(A, M, N, Pivots) For I = 1# To M Step 1 For J = 1# To MinMN Step 1 If J > I Then L(I, J) = 0# End If If J = I Then L(I, J) = 1# End If If J < I Then L(I, J) = A(I, J) End If Next J Next I For I = 1# To MinMN Step 1 For J = 1# To N Step 1 If J < I Then U(I, J) = 0# End If If J >= I Then U(I, J) = A(I, J) End If Next J Next I End Sub '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Level 2 BLAS version of RMatrixLU ' ' -- LAPACK routine (versio n 3.0) -' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., ' Courant Institute, Argonne National Lab, and Rice University ' June 30, 1992 ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Private Sub RMatrixLU2(ByRef A() As Double, _ ByVal M As Long, _ ByVal N As Long, _ ByRef Pivots() As Long) Dim I As Long Dim J As Long Dim JP As Long Dim T1() As Double Dim s As Double Dim i_ As Long ReDim Pivots(0# To MinInt(M - 1#, N - 1#)) ReDim T1(0# To MaxInt(M - 1#, N - 1#)) ' ' Quick return if possible ' If M = 0# Or N = 0# Then Exit Sub End If For J = 0# To MinInt(M - 1#, N - 1#) Step 1 ' ' Find pivot and test for singularity. ' JP = J For I = J + 1# To M - 1# Step 1 If Abs(A(I, J)) > Abs(A(JP, J)) Then JP = I End If Next I Pivots(J) = JP If A(JP, J) 0# Then ' 'Apply the interchange to rows '
The University of Tennessee Modified by Nilson
If JP J Then For i_ = 0# To N - 1# Step 1 T1(i_) = A(J, i_) Next i_ For i_ = 0# To N - 1# Step 1 A(J, i_) = A(JP, i_) Next i_ For i_ = 0# To N - 1# Step 1 A(JP, i_) = T1(i_) Next i_ End If ' 'Compute elements J+1:M of J-th column. ' If J < M Then JP = J + 1# s = 1# / A(J, J) For i_ = JP To M - 1# Step 1 A(i_, J) = s * A(i_, J) Next i_ End If End If If J < MinInt(M, N) - 1# Then ' 'Update trailing submatrix. ' JP = J + 1# For I = J + 1# To M - 1# Step 1 s = A(I, J) For i_ = JP To N - 1# Step 1 A(I, i_) = A(I, i_) - s * A(J, i_) Next i_ Next I End If Next J End Sub '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Copyrigh t (c) 1992-2007 The University of Tennessee. All rights reserved. ' 'Contributors: ' * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to ' pseudocode. ' 'See subroutines comments for additional copyrights. ' 'Redistribution and use in source and binary forms, with or without 'modification, are permitted provided that the following conditions are 'met: ' '- Redistributions of source code must retain the above copyright ' notice, this list of condition s and the following disclaimer. ' '- Redistributions in binary form must reproduce the above copyright ' notice, this list of conditions and the following disclaimer listed ' in this license in the documentation and/or other materials ' provided with the distribution. ' '- Neither the name of the copyright holders nor the names of its ' contributors may be used to endorse or promote products derived from ' this software without specific prior written permission. ' 'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS '"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 'LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 'A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 'OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 'SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 'LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 'DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 'THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT '(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 'OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Routines '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Triangular matrix inversion ' 'The subroutine inverts the following types of matrices: ' * upper triangular ' * upper triangular with unit diagonal ' * lower triangular ' * lower triangular with unit diagonal ' 'In case of an upper (lower) triangular matrix, the inverse matrix will 'also be upper (lower) triangular, and after the end of the algorithm, the 'inverse matrix replaces the source matrix. The elements below (above) the 'main diagonal are not changed by the algorithm. ' 'If the matrix has a unit diagonal, the inverse matrix also has a unit 'diagonal, and the diagonal elements are not passed to the algorithm. ' 'Input parameters: ' A - matrix. ' Array whose indexes range within [0..N-1, 0..N-1]. ' N - size of matrix A. ' IsUpper - True, if the matrix is upper triangular. ' IsUnitTriangular ' - True, if the matrix has a unit diagonal. ' 'Output parameters: ' A - inverse matrix (if the problem is not degenerate). ' 'Result: ' True, if the matrix is not singular. ' False, if the matrix is singular. ' ' -- LAPACK routine (versio n 3.0) -' Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., ' Courant Institute, Argonne National Lab, and Rice University ' February 29, 1992 ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Invierte una matriz como esta: '2 0 0 '1 3 0 '3 1 4 'Para invertir una matriz triang. Superior 'InvTriangular(Matr(), nn, False, False) 'Una matriz triangular superior (y tambien triangular inferior) 'Para invertir una matriz triang. Inferior: 'InvTriangular(Matr(), nn, True, False) Public Function RMatrixTRInverse(ByRef A() As Double, _ ByVal N As Long, _ ByVal IsUpper As Boolean, _ ByVal IsUnitTriangular As Boolean) As Boolean Dim Result As Boolean Dim NOUNIT As Boolean Dim I As Long Dim J As Long Dim V As Double Dim AJJ As Double Dim T() As Double Dim i_ As Long Result = True ReDim T(0# To N - 1#) ' ' Test the input parameters. ' NOUNIT = Not IsUnitTriangular If IsUpper Then
The University of Tennessee Modified by Nilson
' ' Compute inverse of upper triangular matrix. ' For J = 0# To N - 1# Step 1 If NOUNIT Then If A(J, J) = 0# Then Result = False RMatrixTRInverse = Result Exit Function End If A(J, J) = 1# / A(J, J) AJJ = -A(J, J) Else AJJ = -1# End If ' ' Compute elements 1:j-1 of j-th column. ' If J > 0# Then For i_ = 0# To J - 1# Step 1 T(i_) = A(i_, J) Next i_ For I = 0# To J - 1# Step 1 If I < J - 1# Then V = 0# For i_ = I + 1# To J - 1# Step 1 V = V + A(I, i_) * T(i_) Next i_ Else V = 0# End If If NOUNIT Then A(I, J) = V + A(I, I) * T(I) Else A(I, J) = V + T(I) End If Next I For i_ = 0# To J - 1# Step 1 A(i_, J) = AJJ * A(i_, J) Next i_ End If Next J Else ' ' Compute inverse of lower triangular matrix. ' For J = N - 1# To 0# Step -1 If NOUNIT Then If A(J, J) = 0# Then Result = False RMatrixTRInverse = Result Exit Function End If A(J, J) = 1# / A(J, J) AJJ = -A(J, J) Else AJJ = -1# End If If J < N - 1# Then ' ' Compute elements j+1:n of j-th column. ' For i_ = J + 1# To N - 1# Step 1 T(i_) = A(i_, J) Next i_ For I = J + 1# To N - 1# Step 1 If I > J + 1# Then V = 0# For i_ = J + 1# To I - 1# Step 1 V = V + A(I, i_) * T(i_) Next i_ Else V = 0# End If If NOUNIT Then A(I, J) = V + A(I, I) * T(I) Else A(I, J) = V + T(I) End If Next I For i_ = J + 1# To N - 1# Step 1 A(i_, J) = AJJ * A(i_, J) Next i_ End If Next J End If RMatrixTRInverse = Result End Function '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' 'Obsolete 1-based subroutine. 'See RMatrixTRInverse for 0-based replacement. ' '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' Public Function InvTriangular(ByRef A() As Double, _ ByVal N As Long, _ ByVal IsUpper As Boolean, _ ByVal IsUnitTriangular As Boolean) As Boolean Dim Result As Boolean Dim NOUNIT As Boolean Dim I As Long Dim J As Long Dim NMJ As Long Dim JM1 As Long Dim JP1 As Long Dim V As Double Dim AJJ As Double Dim T() As Double Dim i_ As Long Result = True ReDim T(1# To N) ' ' Test the input parameters. ' NOUNIT = Not IsUnitTriangular If IsUpper Then ' ' Compute inverse of upper triangular matrix. ' For J = 1# To N Step 1 If NOUNIT Then If A(J, J) = 0# Then Result = False InvTriangular = Result Exit Function End If A(J, J) = 1# / A(J, J) AJJ = -A(J, J) Else AJJ = -1# End If ' ' Compute elements 1:j-1 of j-th column. ' If J > 1# Then JM1 = J - 1# For i_ = 1# To JM1 Step 1 T(i_) = A(i_, J) Next i_ For I = 1# To J - 1# Step 1 If I < J - 1# Then
The University of Tennessee Modified by Nilson
V = 0# For i_ = I + 1# To JM1 Step 1 V = V + A(I, i_) * T(i_) Next i_ Else V = 0# End If If NOUNIT Then A(I, J) = V + A(I, I) * T(I) Else A(I, J) = V + T(I) End If Next I For i_ = 1# To JM1 Step 1 A(i_, J) = AJJ * A(i_, J) Next i_ End If Next J Else ' ' Compute inverse of lower triangular matrix. ' For J = N To 1# Step -1 If NOUNIT Then If A(J, J) = 0# Then Result = False InvTriangular = Result Exit Function End If A(J, J) = 1# / A(J, J) AJJ = -A(J, J) Else AJJ = -1# End If If J < N Then ' ' Compute elements j+1:n of j-th column. ' NMJ = N - J JP1 = J + 1# For i_ = JP1 To N Step 1 T(i_) = A(i_, J) Next i_ For I = J + 1# To N Step 1 If I > J + 1# Then V = 0# For i_ = JP1 To I - 1# Step 1 V = V + A(I, i_) * T(i_) Next i_ Else V = 0# End If If NOUNIT Then A(I, J) = V + A(I, I) * T(I) Else A(I, J) = V + T(I) End If Next I For i_ = JP1 To N Step 1 A(i_, J) = AJJ * A(i_, J) Next i_ End If Next J End If InvTriangular = Result End Function
6) Introducir código dentro del Formulario Form1 *Cierre la ventana código del Module 1. *Haga doble Clic en el Form 1 para ingresar a la ventana código del Form1 Aparecerá la siguiente ventana (figura 7):
Figura 7 *Borre las líneas de código mostradas dentro de esta venta, es decir, Private Sub Form_Load() End Sub
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La ventana código del Form 1 quedará en blanco, como en la siguiente figura:
Figura 8 *Ahora Copie el siguiente código y péguelo dentro de esta ventana (NO NECESITA LEERLO): Private Function Let27(Palabra As String) 'Funcion que da una extensidad 'de 27 caracteres a una palabra Dim NumeroEsp As Integer: NumeroEsp = 27 - Len(Palabra) If NumeroEsp < 0 Then Let27 = Left(Palabra, 27) Exit Function End If Let27 = Palabra & String(NumeroEsp, Chr(32)) End Function Private Sub MostrarMatriz(Matriz() As Double, SCI As Boolean) Dim II As Integer Dim JJ As Integer Dim EscribirMat As String For II = 1 To UBound(Matriz()) For JJ = 1 To UBound(Matriz()) If SCI = True Then EscribirMat = EscribirMat & Let27(Str(Format(Matriz(II, JJ), "0.0000000"))) & vbTab ElseIf SCI = False Then EscribirMat = EscribirMat & Let27(Str(Matriz(II, JJ))) & vbTab End If Next JJ EscribirMat = EscribirMat & vbCrLf Next II Print EscribirMat End Sub
Private Sub Command1_Click() Dim II As Integer Dim JJ As Integer Dim Matr() As Double Dim InvNatr() As Double Dim nn As Integer Dim EscribirMat As String nn = Val(InputBox("Tamaño de matriz")) If nn = 0 Then Exit Sub ReDim Matr(nn, nn) As Double For II = 1 To nn For JJ = 1 To nn Matr(II, JJ) = InputBox("Elemento ( " & II & " , " & JJ & " ) = ") Next JJ Next II Me.Cls Print "Matriz a invertir" Call MostrarMatriz(Matr(), False) Print vbCrLf If Inverse(Matr(), nn) Then Print "Tiene Inversa" Else Print "No tiene inversa" Exit Sub End If Call MostrarMatriz(Matr(), True)
End Sub Private Sub Form_Load() End Sub
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7) Ejecución de la aplicación Matriz Inversa en Visual Basic.
Pulse este botón para ejecutar la aplicación
Figura 9. * Ahora puede ejecutar la aplicación. Pulse el botón Iniciar (figura 9). * Pulse el Botón Command1, aparecerá un cuadro InputBox solicitando el tamaño de la matriz cuadrada (Para invertir una matriz, esta debe ser CUADRADA, es decir, de tamaño n x n, NO SE PUEDE SACAR MATRIZ INVERSA A MATRICES QUE NO SEAN CUADRADAS)
Figura 10. * De nuevo aparecerá un cuadro de texto por cada elemento de la matriz, esto es para introducir cada elemento de la matriz cuadrada. * Una vez introducidos todos los elementos de la matriz, el resultado se imprimirá en el formulario.
Figura 11. Y LISTO, YA TIENES LA MATRIZ INVERSA EN VB6.0. Puedes modificar el código para mostrar en mejor forma los resultados de la matriz inversa. * La Matriz Inversa es utilizada para resoluciones de ecuaciones lineales, para el cálculo de estructuras en Ingeniería Civil (Análisis Matricial), y en matemáticas en general. ESPERO QUE LES SIRVA ESTE CÓDIGO.
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