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  • 12/20/2021
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SGESVD 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. * ============================================================================= * * SGESVD Example. * ============== * * Program computes the singular value decomposition of a general * rectangular matrix A: * * 8.79 9.93 9.83 5.45 3.16 * 6.11 6.91 5.04 -0.27 7.98 * -9.15 -7.93 4.86 4.85 3.01 * 9.57 1.64 8.83 0.74 5.80 * -3.49 4.02 9.80 10.00 4.27 * 9.84 0.15 -8.99 -6.02 -5.31 * * Description. * ============ * * The routine computes the singular value decomposition (SVD) of a real * m-by-n matrix A, optionally computing the left and/or right singular * vectors. The SVD is written as * * A = U*SIGMA*VT * * 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 orthogonal matrix and VT (V transposed) * is an n-by-n orthogonal 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 VT, not V. * * Example Program Results. * ======================== * * SGESVD Example Program Results * * Singular values * 27.47 22.64 8.56 5.99 2.01 * * Left singular vectors (stored columnwise) * -0.59 0.26 0.36 0.31 0.23 * -0.40 0.24 -0.22 -0.75 -0.36 * -0.03 -0.60 -0.45 0.23 -0.31 * -0.43 0.24 -0.69 0.33 0.16 * -0.47 -0.35 0.39 0.16 -0.52 * 0.29 0.58 -0.02 0.38 -0.65 * * Right singular vectors (stored rowwise) * -0.25 -0.40 -0.69 -0.37 -0.41 * 0.81 0.36 -0.25 -0.37 -0.10 * -0.26 0.70 -0.22 0.39 -0.49 * 0.40 -0.45 0.25 0.43 -0.62 * -0.22 0.14 0.59 -0.63 -0.44 * ============================================================================= * * .. Parameters .. INTEGER M, N PARAMETER ( M = 6, N = 5 ) INTEGER LDA, LDU, LDVT PARAMETER ( LDA = M, LDU = M, LDVT = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. REAL A( LDA, N ), U( LDU, M ), VT( LDVT, N ), S( N ), $ WORK( LWMAX ) DATA A/ $ 8.79, 6.11,-9.15, 9.57,-3.49, 9.84, $ 9.93, 6.91,-7.93, 1.64, 4.02, 0.15, $ 9.83, 5.04, 4.86, 8.83, 9.80,-8.99, $ 5.45,-0.27, 4.85, 0.74,10.00,-6.02, $ 3.16, 7.98, 3.01, 5.80, 4.27,-5.31 $ / * * .. External Subroutines .. EXTERNAL SGESVD EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'SGESVD Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL SGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Compute SVD. * CALL SGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LWORK, 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_MATRIX( 'Singular values', 1, N, S, 1 ) * * Print left singular vectors. * CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)', $ M, N, U, LDU ) * * Print right singular vectors. * CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)', $ N, N, VT, LDVT ) STOP END * * End of SGESVD Example. * * ============================================================================= * * Auxiliary routine: printing a matrix. * SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA ) CHARACTER*(*) DESC INTEGER M, N, LDA REAL 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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