Developer Reference

ID 766877
Date 12/20/2021
Public

## DGESDD Example Program in Fortran

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*  in writing.
*  =============================================================================
*
*  DGESDD Example.
*  ==============
*
*  Program computes the singular value decomposition of a general
*  rectangular matrix A using a divide and conquer method, where A is:
*
*    7.52  -1.10  -7.95   1.08
*   -0.76   0.62   9.34  -7.10
*    5.13   6.62  -5.66   0.87
*   -4.75   8.52   5.75   5.30
*    1.33   4.91  -5.49  -3.52
*   -2.40  -6.77   2.34   3.95
*
*  Description.
*  ============
*
*  The routine computes the singular value decomposition (SVD) of a real
*  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*VT
*
*  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 orthogonal matrix and VT (V transposed)
*  is an n-by-n orthogonal 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 VT, not V.
*
*  Example Program Results.
*  ========================
*
* DGESDD Example Program Results
*
* Singular values
*  18.37  13.63  10.85   4.49
*
* Left singular vectors (stored columnwise)
*  -0.57   0.18   0.01   0.53
*   0.46  -0.11  -0.72   0.42
*  -0.45  -0.41   0.00   0.36
*   0.33  -0.69   0.49   0.19
*  -0.32  -0.31  -0.28  -0.61
*   0.21   0.46   0.39   0.09
*
* Right singular vectors (stored rowwise)
*  -0.52  -0.12   0.85  -0.03
*   0.08  -0.99  -0.09  -0.01
*  -0.28  -0.02  -0.14   0.95
*   0.81   0.01   0.50   0.31
*  =============================================================================
*
*     .. Parameters ..
INTEGER          M, N
PARAMETER        ( M = 6, 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*N )
DOUBLE PRECISION A( LDA, N ), U( LDU, M ), VT( LDVT, N ), S( N ),
$WORK( LWMAX ) DATA A/$  7.52,-0.76, 5.13,-4.75, 1.33,-2.40,
$-1.10, 0.62, 6.62, 8.52, 4.91,-6.77,$ -7.95, 9.34,-5.66, 5.75,-5.49, 2.34,
$1.08,-7.10, 0.87, 5.30,-3.52, 3.95$                  /
*
*     .. External Subroutines ..
EXTERNAL         DGESDD
EXTERNAL         PRINT_MATRIX
*
*     .. Intrinsic Functions ..
INTRINSIC        INT, MIN
*
*     .. Executable Statements ..
WRITE(*,*)'DGESDD Example Program Results'
*
*     Query the optimal workspace.
*
LWORK = -1
CALL DGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT,
$LDVT, WORK, LWORK, IWORK, INFO ) LWORK = MIN( LWMAX, INT( WORK( 1 ) ) ) * * Compute SVD. * CALL DGESDD( 'Singular vectors', M, N, A, LDA, S, U, LDU, VT,$             LDVT, WORK, LWORK, 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_MATRIX( 'Singular values', 1, N, S, 1 )
*
*     Print left singular vectors.
*
CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)',
$M, N, U, LDU ) * * Print right singular vectors. * CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)',$                   N, N, VT, LDVT )
STOP
END
*
*     End of DGESDD 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