Developer Reference

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

CHEEV 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. * ============================================================================= * * CHEEV Example. * ============== * * Program computes all eigenvalues and eigenvectors of a complex Hermitian * matrix A: * * ( 9.14, 0.00) ( -4.37, -9.22) ( -1.98, -1.72) ( -8.96, -9.50) * ( -4.37, 9.22) ( -3.35, 0.00) ( 2.25, -9.51) ( 2.57, 2.40) * ( -1.98, 1.72) ( 2.25, 9.51) ( -4.82, 0.00) ( -3.24, 2.04) * ( -8.96, 9.50) ( 2.57, -2.40) ( -3.24, -2.04) ( 8.44, 0.00) * * Description. * ============ * * The routine computes all 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. * * Example Program Results. * ======================== * * CHEEV Example Program Results * * Eigenvalues * -16.00 -6.76 6.67 25.51 * * Eigenvectors (stored columnwise) * ( 0.34, 0.00) ( -0.55, 0.00) ( 0.31, 0.00) ( -0.70, 0.00) * ( 0.44, -0.54) ( 0.26, 0.18) ( 0.45, 0.29) ( 0.22, -0.28) * ( -0.48, -0.37) ( -0.52, -0.02) ( -0.05, 0.57) ( 0.15, 0.08) * ( 0.10, -0.12) ( -0.50, 0.28) ( -0.23, -0.48) ( 0.34, -0.49) * ============================================================================= * * .. Parameters .. INTEGER N PARAMETER ( N = 4 ) INTEGER LDA PARAMETER ( LDA = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. * RWORK dimension should be at least MAX(1,3*N-2) REAL W( N ), RWORK( 3*N-2 ) COMPLEX A( LDA, N ), WORK( LWMAX ) DATA A/ $ ( 9.14, 0.00),(-4.37, 9.22),(-1.98, 1.72),(-8.96, 9.50), $ ( 0.00, 0.00),(-3.35, 0.00),( 2.25, 9.51),( 2.57,-2.40), $ ( 0.00, 0.00),( 0.00, 0.00),(-4.82, 0.00),(-3.24,-2.04), $ ( 0.00, 0.00),( 0.00, 0.00),( 0.00, 0.00),( 8.44, 0.00) $ / * * .. External Subroutines .. EXTERNAL CHEEV EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CHEEV Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL CHEEV( 'Vectors', 'Lower', N, A, LDA, W, WORK, LWORK, RWORK, $ INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Solve eigenproblem. * CALL CHEEV( 'Vectors', 'Lower', N, A, LDA, W, WORK, LWORK, RWORK, $ INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm failed to compute eigenvalues.' STOP END IF * * Print eigenvalues. * CALL PRINT_RMATRIX( 'Eigenvalues', 1, N, W, 1 ) * * Print eigenvectors. * CALL PRINT_MATRIX( 'Eigenvectors (stored columnwise)', N, N, A, $ LDA ) STOP END * * End of CHEEV 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

Product and Performance Information

1

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