Developer Reference

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

CGELS 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. * ============================================================================= * * CGELS Example. * ============== * * Program computes the minimum norm solution to the underdetermined linear * system A*X = B with full rank matrix A using LQ factorization, * where A is the coefficient matrix: * * ( -4.20, -3.44) ( -3.35, 1.52) ( 1.73, 8.85) ( 2.35, 0.34) * ( -5.43, -8.81) ( -4.53, -8.47) ( 5.93, 3.75) ( -3.75, -5.66) * ( -5.56, 3.39) ( 2.90, -9.22) ( 8.03, 9.37) ( 5.69, -0.47) * * and B is the right-hand side matrix: * * ( -7.02, 4.80) ( 3.88, -2.59) * ( 0.62, -2.40) ( 1.57, 3.24) * ( 3.10, -2.19) ( -6.93, -5.99) * * Description. * ============ * * The routine solves overdetermined or underdetermined complex linear systems * involving an m-by-n matrix A, or its transpose, using a QR or LQ * factorization of A. It is assumed that A has full rank. * * 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. * * Example Program Results. * ======================== * * CGELS Example Program Results * * Minimum norm solution * ( -0.25, -0.04) ( -0.21, 0.42) * ( 0.99, 0.27) ( -0.21, -0.43) * ( 0.25, 0.43) ( -0.24, -0.13) * ( -0.32, 0.14) ( -0.23, -0.09) * * Details of LQ factorization * ( 11.40, 0.00) ( 0.18, -0.14) ( -0.23, -0.52) ( -0.15, 0.01) * ( 7.73, -0.39) ( 15.32, 0.00) ( -0.22, 0.42) ( 0.45, 0.17) * ( 8.60, -5.68) ( 3.96, 6.46) ( 12.54, 0.00) ( -0.02, -0.47) * ============================================================================= * * .. Parameters .. INTEGER M, N, NRHS PARAMETER ( M = 3, N = 4, NRHS = 2 ) INTEGER LDA, LDB PARAMETER ( LDA = M, LDB = N ) INTEGER LWMAX PARAMETER ( LWMAX = 100 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. COMPLEX A( LDA, N ), B( LDB, NRHS ), WORK( LWMAX ) DATA A/ $ (-4.20,-3.44),(-5.43,-8.81),(-5.56, 3.39), $ (-3.35, 1.52),(-4.53,-8.47),( 2.90,-9.22), $ ( 1.73, 8.85),( 5.93, 3.75),( 8.03, 9.37), $ ( 2.35, 0.34),(-3.75,-5.66),( 5.69,-0.47) $ / DATA B/ $ (-7.02, 4.80),( 0.62,-2.40),( 3.10,-2.19),( 0.00, 0.00), $ ( 3.88,-2.59),( 1.57, 3.24),(-6.93,-5.99),( 0.00, 0.00) $ / * * .. External Subroutines .. EXTERNAL CGELS EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CGELS Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL CGELS( 'No transpose', M, N, NRHS, A, LDA, B, LDB, WORK, $ LWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve the equations A*X = B. * CALL CGELS( 'No transpose', M, N, NRHS, A, LDA, B, LDB, WORK, $ LWORK, INFO ) * * Check for the full rank. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The diagonal element ',INFO,' of the triangular ' WRITE(*,*)'factor of A is zero, so that A does not have full ' WRITE(*,*)'rank; the minimum norm solution could not be ' WRITE(*,*)'computed.' STOP END IF * * Print minimum norm solution. * CALL PRINT_MATRIX( 'Minimum norm solution', N, NRHS, B, LDB ) * * Print details of LQ factorization. * CALL PRINT_MATRIX( 'Details of LQ factorization', M, N, A, LDA ) STOP END * * End of CGELS Example. * * ============================================================================= * * Auxiliary routine: printing a matrix. * SUBROUTINE PRINT_MATRIX( DESC, M, N, A, LDA ) CHARACTER*(*) DESC INTEGER M, N, LDA COMPLEX 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

Product and Performance Information

1

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