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  • 12/20/2021
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CGESDD Example Program in Fortran

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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ============================================================================= * * CGESDD Example. * ============== * * Program computes the singular value decomposition of a general * rectangular complex matrix A using a divide and conquer method, where A is: * * ( -5.40, 7.40) ( 6.00, 6.38) ( 9.91, 0.16) ( -5.28, -4.16) * ( 1.09, 1.55) ( 2.60, 0.07) ( 3.98, -5.26) ( 2.03, 1.11) * ( 9.88, 1.91) ( 4.92, 6.31) ( -2.11, 7.39) ( -9.81, -8.98) * * Description. * ============ * * The routine computes the singular value decomposition (SVD) of a complex * m-by-n matrix A, optionally computing the left and/or right singular * vectors. If singular vectors are desired, it uses a divide and conquer * algorithm. The SVD is written as * * A = U*SIGMA*VH * * where SIGMA is an m-by-n matrix which is zero except for its min(m,n) * diagonal elements, U is an m-by-m unitary matrix and VH (V conjugate * transposed) is an n-by-n unitary matrix. The diagonal elements of SIGMA * are the singular values of A; they are real and non-negative, and are * returned in descending order. The first min(m, n) columns of U and V are * the left and right singular vectors of A. * * Note that the routine returns VH, not V. * * Example Program Results. * ======================== * * CGESDD Example Program Results * * Singular values * 21.76 16.60 3.97 * * Left singular vectors (stored columnwise) * ( 0.55, 0.00) ( 0.76, 0.00) ( -0.34, 0.00) * ( -0.04, -0.15) ( 0.27, -0.23) ( 0.55, -0.74) * ( 0.81, 0.12) ( -0.52, -0.14) ( 0.13, -0.11) * * Right singular vectors (stored rowwise) * ( 0.23, 0.21) ( 0.37, 0.39) ( 0.24, 0.33) ( -0.56, -0.37) * ( -0.58, 0.40) ( 0.11, 0.17) ( 0.60, -0.27) ( 0.16, 0.06) * ( 0.60, 0.12) ( -0.19, 0.30) ( 0.39, 0.20) ( 0.45, 0.31) * ============================================================================= * * .. Parameters .. INTEGER M, N PARAMETER ( M = 3, N = 4 ) INTEGER LDA, LDU, LDVT PARAMETER ( LDA = M, LDU = M, LDVT = N ) INTEGER LWMAX PARAMETER ( LWMAX = 1000 ) * * .. Local Scalars .. INTEGER INFO, LWORK * * .. Local Arrays .. * IWORK dimension should be at least 8*MIN(M,N) INTEGER IWORK( 8*M ) * RWORK dimension should be at least 5*(MIN(M,N))**2 + 7*MIN(M,N)) REAL S( M ), RWORK( 5*M*M + 7*M ) COMPLEX A( LDA, N ), U( LDU, M ), VT( LDVT, N ), $ WORK( LWMAX ) DATA A/ $ (-5.40, 7.40),( 1.09, 1.55),( 9.88, 1.91), $ ( 6.00, 6.38),( 2.60, 0.07),( 4.92, 6.31), $ ( 9.91, 0.16),( 3.98,-5.26),(-2.11, 7.39), $ (-5.28,-4.16),( 2.03, 1.11),(-9.81,-8.98) $ / * * .. External Subroutines .. EXTERNAL CGESDD EXTERNAL PRINT_MATRIX, PRINT_RMATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'CGESDD Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL CGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT, $ LDVT, WORK, LWORK, RWORK, IWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Compute SVD. * CALL CGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT, $ LDVT, WORK, LWORK, RWORK, IWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm computing SVD failed to converge.' STOP END IF * * Print singular values. * CALL PRINT_RMATRIX( 'Singular values', 1, M, S, 1 ) * * Print left singular vectors. * CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)', $ M, M, U, LDU ) * * Print right singular vectors. * CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)', $ M, N, VT, LDVT ) STOP END * * End of CGESDD 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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