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  • 12/20/2021
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ZHESV 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. * ============================================================================= * * ZHESV Example. * ============== * * The program computes the solution to the system of linear equations * with a Hermitian matrix A and multiple right-hand sides B, * where A is the coefficient matrix: * * ( -2.90, 0.00) ( 0.31, 4.46) ( 9.66, -5.66) ( -2.28, 2.14) * ( 0.31, -4.46) ( -7.93, 0.00) ( 9.55, -4.62) ( -3.51, 3.11) * ( 9.66, 5.66) ( 9.55, 4.62) ( 0.30, 0.00) ( 9.33, -9.66) * ( -2.28, -2.14) ( -3.51, -3.11) ( 9.33, 9.66) ( 2.40, 0.00) * * and B is the right-hand side matrix: * * ( -5.69, -8.21) ( -2.83, 6.46) * ( -3.57, 1.99) ( -7.64, 1.10) * ( 8.42, -9.83) ( -2.33, -4.23) * ( -5.00, 3.85) ( 6.48, -3.81) * * Description. * ============ * * The routine solves for X the complex system of linear equations A*X = B, * where A is an n-by-n Hermitian 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*UH or * A = L*D*LH, where U (or L) is a product of permutation and unit upper * (lower) triangular matrices, and D is Hermitian 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. * ======================== * * ZHESV Example Program Results * * Solution * ( 0.22, -0.95) ( -1.13, 0.18) * ( -1.42, -1.30) ( 0.70, 1.13) * ( -0.65, -0.40) ( 0.04, 0.07) * ( -0.48, 1.35) ( 1.15, -0.27) * * Details of factorization * ( 3.17, 0.00) ( 7.32, 3.28) ( -0.36, 0.06) ( 0.20, -0.82) * ( 0.00, 0.00) ( 0.03, 0.00) ( -0.48, 0.03) ( 0.25, -0.76) * ( 0.00, 0.00) ( 0.00, 0.00) ( 0.30, 0.00) ( 9.33, -9.66) * ( 0.00, 0.00) ( 0.00, 0.00) ( 0.00, 0.00) ( 2.40, 0.00) * * Pivot indices * -1 -1 -3 -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*16 A( LDA, N ), B( LDB, NRHS ), WORK( LWMAX ) DATA A/ $ (-2.90, 0.00),( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00), $ ( 0.31, 4.46),(-7.93, 0.00),( 0.00, 0.00),( 0.00, 0.00), $ ( 9.66,-5.66),( 9.55,-4.62),( 0.30, 0.00),( 0.00, 0.00), $ (-2.28, 2.14),(-3.51, 3.11),( 9.33,-9.66),( 2.40, 0.00) $ / DATA B/ $ (-5.69,-8.21),(-3.57, 1.99),( 8.42,-9.83),(-5.00, 3.85), $ (-2.83, 6.46),(-7.64, 1.10),(-2.33,-4.23),( 6.48,-3.81) $ / * * .. External Subroutines .. EXTERNAL ZHESV EXTERNAL PRINT_MATRIX, PRINT_INT_VECTOR * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'ZHESV Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL ZHESV( 'Upper', N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, $ INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve the equations A*X = B. * CALL ZHESV( '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 ZHESV Example. * * ============================================================================= * * Auxiliary routine: printing a matrix. * SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA ) CHARACTER*(*) DESC INTEGER M, N, LDA COMPLEX*16 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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