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  • 2022.1
  • 12/20/2021
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CHEEVX 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. * ============================================================================= * * CHEEVX Example. * ============== * * Program computes eigenvalues specified by a selected range of values * and corresponding eigenvectors of a complex Hermitian matrix A: * * ( 6.51, 0.00) ( -5.92, 9.53) ( -2.46, 2.91) ( 8.84, 3.21) * ( -5.92, -9.53) ( -1.73, 0.00) ( 6.50, 2.09) ( 1.32, 8.81) * ( -2.46, -2.91) ( 6.50, -2.09) ( 6.90, 0.00) ( -0.59, 2.47) * ( 8.84, -3.21) ( 1.32, -8.81) ( -0.59, -2.47) ( -2.85, 0.00) * * Description. * ============ * * The routine computes selected eigenvalues and, optionally, eigenvectors of * an n-by-n complex Hermitian 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. * ======================== * * CHEEVX Example Program Results * * The total number of eigenvalues found: 3 * * Selected eigenvalues * 0.09 9.53 18.75 * * Selected eigenvectors (stored columnwise) * ( 0.18, 0.00) ( -0.54, 0.00) ( 0.67, 0.00) * ( -0.40, -0.31) ( -0.21, -0.17) ( -0.30, -0.43) * ( 0.60, 0.40) ( -0.35, -0.28) ( -0.39, -0.34) * ( -0.34, 0.26) ( -0.57, 0.35) ( 0.05, 0.05) * ============================================================================= * * .. Parameters .. INTEGER N PARAMETER ( N = 4 ) INTEGER LDA, LDZ PARAMETER ( LDA = N, LDZ = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK, IL, IU, M REAL ABSTOL, VL, VU * * .. Local Arrays .. * IWORK dimension should be at least 5*N INTEGER IWORK( 5*N ), IFAIL( N ) * RWORK dimension should be at least 7*N REAL W( N ), RWORK( 7*N ) COMPLEX A( LDA, N ), Z( LDZ, N ), WORK( LWMAX ) DATA A/ $ ( 6.51, 0.00),(-5.92,-9.53),(-2.46,-2.91),( 8.84,-3.21), $ ( 0.00, 0.00),(-1.73, 0.00),( 6.50,-2.09),( 1.32,-8.81), $ ( 0.00, 0.00),( 0.00, 0.00),( 6.90, 0.00),(-0.59,-2.47), $ ( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),(-2.85, 0.00) $ / * * .. External Subroutines .. EXTERNAL CHEEVX EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CHEEVX Example Program Results' * Negative ABSTOL means using the default value ABSTOL = -1.0 * Set VL, VU to compute eigenvalues in half-open (VL,VU] interval VL = 0.0 VU = 100.0 * * Query the optimal workspace. * LWORK = -1 CALL CHEEVX( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL, $ IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, $ IFAIL, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL CHEEVX( 'Vectors', 'Values', 'Lower', N, A, LDA, VL, VU, IL, $ IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, $ IFAIL, 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_RMATRIX( 'Selected eigenvalues', 1, M, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Selected eigenvectors (stored columnwise)', $ N, M, Z, LDZ ) STOP END * * End of CHEEVX 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 * * Auxiliary routine: printing a real matrix. * SUBROUTINE PRINT_RMATRIX( 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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