Developer Reference

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

DGESDD 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. * ============================================================================= * * DGESDD Example. * ============== * * Program computes the singular value decomposition of a general * rectangular matrix A using a divide and conquer method, where A is: * * 7.52 -1.10 -7.95 1.08 * -0.76 0.62 9.34 -7.10 * 5.13 6.62 -5.66 0.87 * -4.75 8.52 5.75 5.30 * 1.33 4.91 -5.49 -3.52 * -2.40 -6.77 2.34 3.95 * * 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. If singular vectors are desired, it uses a divide and conquer * algorithm. 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. * ======================== * * DGESDD Example Program Results * * Singular values * 18.37 13.63 10.85 4.49 * * Left singular vectors (stored columnwise) * -0.57 0.18 0.01 0.53 * 0.46 -0.11 -0.72 0.42 * -0.45 -0.41 0.00 0.36 * 0.33 -0.69 0.49 0.19 * -0.32 -0.31 -0.28 -0.61 * 0.21 0.46 0.39 0.09 * * Right singular vectors (stored rowwise) * -0.52 -0.12 0.85 -0.03 * 0.08 -0.99 -0.09 -0.01 * -0.28 -0.02 -0.14 0.95 * 0.81 0.01 0.50 0.31 * ============================================================================= * * .. Parameters .. INTEGER M, N PARAMETER ( M = 6, 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 .. * IWORK dimension should be at least 8*MIN(M,N) INTEGER IWORK( 8*N ) DOUBLE PRECISION A( LDA, N ), U( LDU, M ), VT( LDVT, N ), S( N ), $ WORK( LWMAX ) DATA A/ $ 7.52,-0.76, 5.13,-4.75, 1.33,-2.40, $ -1.10, 0.62, 6.62, 8.52, 4.91,-6.77, $ -7.95, 9.34,-5.66, 5.75,-5.49, 2.34, $ 1.08,-7.10, 0.87, 5.30,-3.52, 3.95 $ / * * .. External Subroutines .. EXTERNAL DGESDD EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'DGESDD Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL DGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT, $ LDVT, WORK, LWORK, IWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Compute SVD. * CALL DGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT, $ LDVT, WORK, LWORK, IWORK, 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 DGESDD 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

Product and Performance Information

1

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