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  • 12/20/2021
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SGELSD 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. * ============================================================================= * * SGELSD Example. * ============== * * Program computes the minimum norm-solution to a real linear least squares * problem using the singular value decomposition of A, * where A is the coefficient matrix: * * 0.12 -8.19 7.69 -2.26 -4.71 * -6.91 2.22 -5.12 -9.08 9.96 * -3.33 -8.94 -6.72 -4.40 -9.98 * 3.97 3.33 -2.74 -7.92 -3.20 * * and B is the right-hand side matrix: * * 7.30 0.47 -6.28 * 1.33 6.58 -3.42 * 2.68 -1.71 3.46 * -9.62 -0.79 0.41 * * Description. * ============ * * The routine computes the minimum-norm solution to a real linear least * squares problem: minimize ||b - A*x|| using the singular value * decomposition (SVD) of A. A is an m-by-n matrix which may be rank-deficient. * * Several right hand side vectors b and solution vectors x can be handled * in a single call; they are stored as the columns of the m-by-nrhs right * hand side matrix B and the n-by-nrhs solution matrix X. * * The effective rank of A is determined by treating as zero those singular * values which are less than rcond times the largest singular value. * * Example Program Results. * ======================== * * SGELSD Example Program Results * * Minimum norm solution * -0.69 -0.24 0.06 * -0.80 -0.08 0.21 * 0.38 0.12 -0.65 * 0.29 -0.24 0.42 * 0.29 0.35 -0.30 * * Effective rank = 4 * * Singular values * 18.66 15.99 10.01 8.51 * ============================================================================= * * .. Parameters .. INTEGER M, N, NRHS PARAMETER ( M = 4, N = 5, NRHS = 3 ) INTEGER LDA, LDB PARAMETER ( LDA = M, LDB = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK, RANK REAL RCOND * * .. Local Arrays .. * IWORK dimension should be at least 3*MIN(M,N)*NLVL + 11*MIN(M,N), * where NLVL = MAX( 0, INT( LOG_2( MIN(M,N)/(SMLSIZ+1) ) )+1 ) * and SMLSIZ = 25 INTEGER IWORK( 3*M*0+11*M ) REAL A( LDA, N ), B( LDB, NRHS ), S( M ), $ WORK( LWMAX ) DATA A/ $ 0.12,-6.91,-3.33, 3.97, $ -8.19, 2.22,-8.94, 3.33, $ 7.69,-5.12,-6.72,-2.74, $ -2.26,-9.08,-4.40,-7.92, $ -4.71, 9.96,-9.98,-3.20 $ / DATA B/ $ 7.30, 1.33, 2.68,-9.62, 0.00, $ 0.47, 6.58,-1.71,-0.79, 0.00, $ -6.28,-3.42, 3.46, 0.41, 0.00 $ / * * .. External Subroutines .. EXTERNAL SGELSD EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'SGELSD Example Program Results' * Negative RCOND means using default (machine precision) value RCOND = -1.0 * * Query the optimal workspace. * LWORK = -1 CALL SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, $ LWORK, IWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve the equations A*X = B. * CALL SGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, $ LWORK, IWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm computing SVD failed to converge;' WRITE(*,*)'the least squares solution could not be computed.' STOP END IF * * Print minimum norm solution. * CALL PRINT_MATRIX( 'Minimum norm solution', N, NRHS, B, LDB ) * * Print effective rank. * WRITE(*,'(/A,I6)')' Effective rank = ', RANK * * Print singular values. * CALL PRINT_MATRIX( 'Singular values', 1, M, S, 1 ) STOP END * * End of SGELSD 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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