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  • 2022.1
  • 12/20/2021
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DSYEVR 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. * ============================================================================= * * DSYEVR Example. * ============== * * Program computes the smallest eigenvalues and the corresponding * eigenvectors of a real symmetric matrix A using the Relatively Robust * Representations, where A is: * * 0.67 -0.20 0.19 -1.06 0.46 * -0.20 3.82 -0.13 1.06 -0.48 * 0.19 -0.13 3.27 0.11 1.10 * -1.06 1.06 0.11 5.86 -0.98 * 0.46 -0.48 1.10 -0.98 3.54 * * Description. * ============ * * The routine computes selected eigenvalues and, optionally, eigenvectors of * an n-by-n real symmetric matrix A. The eigenvector v(j) of A satisfies * * A*v(j) = lambda(j)*v(j) * * where lambda(j) is its eigenvalue. The computed eigenvectors are * orthonormal. * Eigenvalues and eigenvectors can be selected by specifying either a range * of values or a range of indices for the desired eigenvalues. * * Example Program Results. * ======================== * * DSYEVR Example Program Results * * The total number of eigenvalues found: 3 * * Selected eigenvalues * 0.43 2.14 3.37 * * Selected eigenvectors (stored columnwise) * -0.98 -0.01 -0.08 * 0.01 0.02 -0.93 * 0.04 -0.69 -0.07 * -0.18 0.19 0.31 * 0.07 0.69 -0.13 * ============================================================================= * * .. Parameters .. INTEGER N, NSELECT PARAMETER ( N = 5, NSELECT = 3 ) INTEGER LDA, LDZ PARAMETER ( LDA = N, LDZ = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK, LIWORK, IL, IU, M DOUBLE PRECISION ABSTOL, VL, VU * * .. Local Arrays .. INTEGER ISUPPZ( N ), IWORK( LWMAX ) DOUBLE PRECISION A( LDA, N ), W( N ), Z( LDZ, NSELECT ), $ WORK( LWMAX ) DATA A/ $ 0.67, 0.00, 0.00, 0.00, 0.00, $ -0.20, 3.82, 0.00, 0.00, 0.00, $ 0.19,-0.13, 3.27, 0.00, 0.00, $ -1.06, 1.06, 0.11, 5.86, 0.00, $ 0.46,-0.48, 1.10,-0.98, 3.54 $ / * * .. External Subroutines .. EXTERNAL DSYEVR EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'DSYEVR Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set IL, IU to compute NSELECT smallest eigenvalues IL = 1 IU = NSELECT * * Query the optimal workspace. * LWORK = -1 LIWORK = -1 CALL DSYEVR( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL, $ IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) LIWORK = MIN( LWMAX, IWORK( 1 ) ) * * Solve eigenproblem. * CALL DSYEVR( 'Vectors', 'Indices', 'Upper', N, A, LDA, VL, VU, IL, $ IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print the number of eigenvalues found. * WRITE(*,'(/A,I2)')' The total number of eigenvalues found:', M * * Print eigenvalues. * CALL PRINT_MATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)', $ N, M, Z, LDZ ) STOP END * * End of DSYEVR 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

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