Developer Reference

  • 2022.1
  • 12/20/2021
  • Public Content
Contents

CSYSV 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. * ============================================================================= * * CSYSV Example. * ============== * * The program computes the solution to the system of linear equations * with a complex symmetric matrix A and multiple right-hand sides B, * where A is the coefficient matrix: * * ( 9.99, -4.73) ( -5.68, -0.80) ( -8.94, 1.32) ( -9.42, 2.05) * ( -5.68, -0.80) ( -8.01, 4.61) ( 1.64, -6.29) ( 6.79, -2.17) * ( -8.94, 1.32) ( 1.64, -6.29) ( 9.04, 3.96) ( -4.51, -7.54) * ( -9.42, 2.05) ( 6.79, -2.17) ( -4.51, -7.54) ( 0.40, 4.06) * * and B is the right-hand side matrix: * * ( 5.71, -1.20) ( 2.84, -0.18) * ( -7.70, 6.47) ( -8.29, -1.72) * ( 3.77, -7.40) ( -4.28, -8.25) * ( -3.78, 0.33) ( -2.70, -0.39) * * Description. * ============ * * The routine solves for X the complex system of linear equations A*X = B, * where A is an n-by-n symmetric matrix, the columns of matrix B are * individual right-hand sides, and the columns of X are the corresponding * solutions. * * The diagonal pivoting method is used to factor A as A = U*D*UT or * A = L*D*LT , where U (or L) is a product of permutation and unit upper * (lower) triangular matrices, and D is symmetric and block diagonal with * 1-by-1 and 2-by-2 diagonal blocks. * * The factored form of A is then used to solve the system of equations A*X = B. * * Example Program Results. * ======================== * * CSYSV Example Program Results * * Solution * ( 0.13, 0.13) ( 0.63, 0.34) * ( 0.32, -0.07) ( 0.61, 0.21) * ( -0.26, -0.44) ( -0.01, -0.10) * ( -0.40, 0.51) ( 0.21, 0.02) * * Details of factorization * (-16.42, 1.69) ( -0.53, 0.35) ( 0.36, 0.41) ( -0.78, 0.49) * ( 0.00, 0.00) ( 3.69, 0.64) (-16.58, -1.61) ( -0.10, -0.65) * ( 0.00, 0.00) ( 0.00, 0.00) ( 1.02, -3.74) ( -0.73, -0.52) * ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 9.04, 3.96) * * Pivot indices * 1 -1 -1 3 * ============================================================================= * * .. Parameters .. INTEGER N, NRHS PARAMETER ( N = 4, NRHS = 2 ) INTEGER LDA, LDB PARAMETER ( LDA = N, LDB = N ) INTEGER LWMAX PARAMETER ( LWMAX = 100 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. INTEGER IPIV( N ) COMPLEX A( LDA, N ), B( LDB, NRHS ), WORK( LWMAX ) DATA A/ $ ( 9.99,-4.73),( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00), $ (-5.68,-0.80),(-8.01, 4.61),( 0.00, 0.00),( 0.00, 0.00), $ (-8.94, 1.32),( 1.64,-6.29),( 9.04, 3.96),( 0.00, 0.00), $ (-9.42, 2.05),( 6.79,-2.17),(-4.51,-7.54),( 0.40, 4.06) $ / DATA B/ $ ( 5.71,-1.20),(-7.70, 6.47),( 3.77,-7.40),(-3.78, 0.33), $ ( 2.84,-0.18),(-8.29,-1.72),(-4.28,-8.25),(-2.70,-0.39) $ / * * .. External Subroutines .. EXTERNAL CSYSV EXTERNAL PRINT_MATRIX, PRINT_INT_VECTOR * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CSYSV Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL CSYSV( 'Upper', N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, $ INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve the equations A*X = B. * CALL CSYSV( 'Upper', N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, $ INFO ) * * Check for the exact singularity. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The element of the diagonal factor ' WRITE(*,*)'D(',INFO,',',INFO,') is zero, so that' WRITE(*,*)'D is singular; the solution could not be computed.' STOP END IF * * Print solution. * CALL PRINT_MATRIX( 'Solution', N, NRHS, B, LDB ) * * Print details of factorization. * CALL PRINT_MATRIX( 'Details of factorization', N, N, A, LDA ) * * Print pivot indices. * CALL PRINT_INT_VECTOR( 'Pivot indices', N, IPIV ) STOP END * * End of CSYSV 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

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.