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  • 12/20/2021
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CGESV Example Program in Fortran

* Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ============================================================================= * * CGESV Example. * ============== * * The program computes the solution to the system of linear * equations with a square matrix A and multiple * right-hand sides B, where A is the coefficient matrix: * * ( 1.23, -5.50) ( 7.91, -5.38) ( -9.80, -4.86) ( -7.32, 7.57) * ( -2.14, -1.12) ( -9.92, -0.79) ( -9.18, -1.12) ( 1.37, 0.43) * ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) * ( 1.27, 7.29) ( 8.90, 6.92) ( -8.82, 1.25) ( 5.41, 5.37) * * and B is the right-hand side matrix: * * ( 8.33, -7.32) ( -6.11, -3.81) * ( -6.18, -4.80) ( 0.14, -7.71) * ( -5.71, -2.80) ( 1.41, 3.40) * ( -1.60, 3.08) ( 8.54, -4.05) * * Description. * ============ * * The routine solves for X the system of linear equations A*X = B, * where A is an n-by-n matrix, the columns of matrix B are individual * right-hand sides, and the columns of X are the corresponding * solutions. * * The LU decomposition with partial pivoting and row interchanges is * used to factor A as A = P*L*U, where P is a permutation matrix, L * is unit lower triangular, and U is upper triangular. The factored * form of A is then used to solve the system of equations A*X = B. * * Example Program Results. * ======================== * * CGESV Example Program Results * * Solution * ( -1.09, -0.18) ( 1.28, 1.21) * ( 0.97, 0.52) ( -0.22, -0.97) * ( -0.20, 0.19) ( 0.53, 1.36) * ( -0.59, 0.92) ( 2.22, -1.00) * * Details of LU factorization * ( -4.30, -7.10) ( -6.47, 2.52) ( -6.51, -2.67) ( -5.86, 7.38) * ( 0.49, 0.47) ( 12.26, -3.57) ( -7.87, -0.49) ( -0.98, 6.71) * ( 0.25, -0.15) ( -0.60, -0.37) (-11.70, -4.64) ( -1.35, 1.38) * ( -0.83, -0.32) ( 0.05, 0.58) ( 0.93, -0.50) ( 2.66, 7.86) * * Pivot indices * 3 3 3 4 * ============================================================================= * * .. Parameters .. INTEGER N, NRHS PARAMETER ( N = 4, NRHS = 2 ) INTEGER LDA, LDB PARAMETER ( LDA = N, LDB = N ) * * .. Local Scalars .. INTEGER INFO * * .. Local Arrays .. INTEGER IPIV( N ) COMPLEX A( LDA, N ), B( LDB, NRHS ) DATA A/ $ ( 1.23,-5.50),(-2.14,-1.12),(-4.30,-7.10),( 1.27, 7.29), $ ( 7.91,-5.38),(-9.92,-0.79),(-6.47, 2.52),( 8.90, 6.92), $ (-9.80,-4.86),(-9.18,-1.12),(-6.51,-2.67),(-8.82, 1.25), $ (-7.32, 7.57),( 1.37, 0.43),(-5.86, 7.38),( 5.41, 5.37) $ / DATA B/ $ ( 8.33,-7.32),(-6.18,-4.80),(-5.71,-2.80),(-1.60, 3.08), $ (-6.11,-3.81),( 0.14,-7.71),( 1.41, 3.40),( 8.54,-4.05) $ / * * .. External Subroutines .. EXTERNAL CGESV EXTERNAL PRINT_MATRIX, PRINT_INT_VECTOR * * .. Executable Statements .. WRITE(*,*)'CGESV Example Program Results' * * Solve the equations A*X = B. * CALL CGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * Check for the exact singularity. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The diagonal element of the triangular factor of A,' WRITE(*,*)'U(',INFO,',',INFO,') is zero, so that' WRITE(*,*)'A is singular; the solution could not be computed.' STOP END IF * * Print solution. * CALL PRINT_MATRIX( 'Solution', N, NRHS, B, LDB ) * * Print details of LU factorization. * CALL PRINT_MATRIX( 'Details of LU factorization', N, N, A, LDA ) * * Print pivot indices. * CALL PRINT_INT_VECTOR( 'Pivot indices', N, IPIV ) STOP END * * End of CGESV Example. * * ============================================================================= * * Auxiliary routine: printing a matrix. * SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA ) CHARACTER*(*) DESC INTEGER M, N, LDA COMPLEX A( LDA, * ) * INTEGER I, J * WRITE(*,*) WRITE(*,*) DESC DO I = 1, M WRITE(*,9998) ( A( I, J ), J = 1, N ) END DO * 9998 FORMAT( 11(:,1X,'(',F6.2,',',F6.2,')') ) RETURN END * * Auxiliary routine: printing a vector of integers. * SUBROUTINE PRINT_INT_VECTOR( DESC, N, A ) CHARACTER*(*) DESC INTEGER N INTEGER A( N ) * INTEGER I * WRITE(*,*) WRITE(*,*) DESC WRITE(*,9999) ( A( I ), I = 1, N ) * 9999 FORMAT( 11(:,1X,I6) ) RETURN END

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