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  • 12/20/2021
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ZGESVD 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. * ============================================================================= * * ZGESVD Example. * ============== * * Program computes the singular value decomposition of a general * rectangular complex matrix A: * * ( 5.91, -5.69) ( 7.09, 2.72) ( 7.78, -4.06) ( -0.79, -7.21) * ( -3.15, -4.08) ( -1.89, 3.27) ( 4.57, -2.07) ( -3.88, -3.30) * ( -4.89, 4.20) ( 4.10, -6.70) ( 3.28, -3.84) ( 3.84, 1.19) * * Description. * ============ * * The routine computes the singular value decomposition (SVD) of a complex * m-by-n matrix A, optionally computing the left and/or right singular * vectors. The SVD is written as * * A = U*SIGMA*VH * * where SIGMA is an m-by-n matrix which is zero except for its min(m,n) * diagonal elements, U is an m-by-m unitary matrix and VH (V conjugate * transposed) is an n-by-n unitary matrix. The diagonal elements of SIGMA * are the singular values of A; they are real and non-negative, and are * returned in descending order. The first min(m, n) columns of U and V are * the left and right singular vectors of A. * * Note that the routine returns VH, not V. * * Example Program Results. * ======================== * * ZGESVD Example Program Results * * Singular values * 17.63 11.61 6.78 * * Left singular vectors (stored columnwise) * ( -0.86, 0.00) ( 0.40, 0.00) ( 0.32, 0.00) * ( -0.35, 0.13) ( -0.24, -0.21) ( -0.63, 0.60) * ( 0.15, 0.32) ( 0.61, 0.61) ( -0.36, 0.10) * * Right singular vectors (stored rowwise) * ( -0.22, 0.51) ( -0.37, -0.32) ( -0.53, 0.11) ( 0.15, 0.38) * ( 0.31, 0.31) ( 0.09, -0.57) ( 0.18, -0.39) ( 0.38, -0.39) * ( 0.53, 0.24) ( 0.49, 0.28) ( -0.47, -0.25) ( -0.15, 0.19) * ============================================================================= * * .. Parameters .. INTEGER M, N PARAMETER ( M = 3, N = 4 ) INTEGER LDA, LDU, LDVT PARAMETER ( LDA = M, LDU = M, LDVT = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. * RWORK dimension should be at least MAX( 1, 5*MIN(M,N) ) DOUBLE PRECISION S( M ), RWORK( 5*M ) COMPLEX*16 A( LDA, N ), U( LDU, M ), VT( LDVT, N ), $ WORK( LWMAX ) DATA A/ $ ( 5.91,-5.69),(-3.15,-4.08),(-4.89, 4.20), $ ( 7.09, 2.72),(-1.89, 3.27),( 4.10,-6.70), $ ( 7.78,-4.06),( 4.57,-2.07),( 3.28,-3.84), $ (-0.79,-7.21),(-3.88,-3.30),( 3.84, 1.19) $ / * * .. External Subroutines .. EXTERNAL ZGESVD EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'ZGESVD Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL ZGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LWORK, RWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Compute SVD. * CALL ZGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LWORK, RWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm computing SVD failed to converge.' STOP END IF * * Print singular values. * CALL PRINT_RMATRIX( 'Singular values', 1, M, S, 1 ) * * Print left singular vectors. * CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)', $ M, M, U, LDU ) * * Print right singular vectors. * CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)', $ M, N, VT, LDVT ) STOP END * * End of ZGESVD 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 real matrix. * SUBROUTINE PRINT_RMATRIX( 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

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