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  • 2022.1
  • 12/20/2021
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DGESV 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. * ============================================================================= * * DGESV 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: * * 6.80 -6.05 -0.45 8.32 -9.67 * -2.11 -3.30 2.58 2.71 -5.14 * 5.66 5.36 -2.70 4.35 -7.26 * 5.97 -4.44 0.27 -7.17 6.08 * 8.23 1.08 9.04 2.14 -6.87 * * and B is the right-hand side matrix: * * 4.02 -1.56 9.81 * 6.19 4.00 -4.09 * -8.22 -8.67 -4.57 * -7.57 1.75 -8.61 * -3.03 2.86 8.99 * * 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. * ======================== * * DGESV Example Program Results * * Solution * -0.80 -0.39 0.96 * -0.70 -0.55 0.22 * 0.59 0.84 1.90 * 1.32 -0.10 5.36 * 0.57 0.11 4.04 * * Details of LU factorization * 8.23 1.08 9.04 2.14 -6.87 * 0.83 -6.94 -7.92 6.55 -3.99 * 0.69 -0.67 -14.18 7.24 -5.19 * 0.73 0.75 0.02 -13.82 14.19 * -0.26 0.44 -0.59 -0.34 -3.43 * * Pivot indices * 5 5 3 4 5 * ============================================================================= * * .. Parameters .. INTEGER N, NRHS PARAMETER ( N = 5, NRHS = 3 ) INTEGER LDA, LDB PARAMETER ( LDA = N, LDB = N ) * * .. Local Scalars .. INTEGER INFO * * .. Local Arrays .. INTEGER IPIV( N ) DOUBLE PRECISION A( LDA, N ), B( LDB, NRHS ) DATA A/ $ 6.80,-2.11, 5.66, 5.97, 8.23, $ -6.05,-3.30, 5.36,-4.44, 1.08, $ -0.45, 2.58,-2.70, 0.27, 9.04, $ 8.32, 2.71, 4.35,-7.17, 2.14, $ -9.67,-5.14,-7.26, 6.08,-6.87 $ / DATA B/ $ 4.02, 6.19,-8.22,-7.57,-3.03, $ -1.56, 4.00,-8.67, 1.75, 2.86, $ 9.81,-4.09,-4.57,-8.61, 8.99 $ / * * .. External Subroutines .. EXTERNAL DGESV EXTERNAL PRINT_MATRIX, PRINT_INT_VECTOR * * .. Executable Statements .. WRITE(*,*)'DGESV Example Program Results' * * Solve the equations A*X = B. * CALL DGESV( 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 DGESV Example. * * ============================================================================= * * Auxiliary routine: printing a matrix. * SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA ) CHARACTER*(*) DESC INTEGER M, N, LDA DOUBLE PRECISION 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) ) 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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