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## Intel® oneAPI Math Kernel Library LAPACK Examples

ID 766877
Date 3/31/2023
Public

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## DGESVD Example Program in Fortran

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*  =============================================================================
*
*  DGESVD Example.
*  ==============
*
*  Program computes the singular value decomposition of a general
*  rectangular matrix A:
*
*    8.79   9.93   9.83   5.45   3.16
*    6.11   6.91   5.04  -0.27   7.98
*   -9.15  -7.93   4.86   4.85   3.01
*    9.57   1.64   8.83   0.74   5.80
*   -3.49   4.02   9.80  10.00   4.27
*    9.84   0.15  -8.99  -6.02  -5.31
*
*  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. 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.
*  ========================
*
* DGESVD Example Program Results
*
* Singular values
*  27.47  22.64   8.56   5.99   2.01
*
* Left singular vectors (stored columnwise)
*  -0.59   0.26   0.36   0.31   0.23
*  -0.40   0.24  -0.22  -0.75  -0.36
*  -0.03  -0.60  -0.45   0.23  -0.31
*  -0.43   0.24  -0.69   0.33   0.16
*  -0.47  -0.35   0.39   0.16  -0.52
*   0.29   0.58  -0.02   0.38  -0.65
*
* Right singular vectors (stored rowwise)
*  -0.25  -0.40  -0.69  -0.37  -0.41
*   0.81   0.36  -0.25  -0.37  -0.10
*  -0.26   0.70  -0.22   0.39  -0.49
*   0.40  -0.45   0.25   0.43  -0.62
*  -0.22   0.14   0.59  -0.63  -0.44
*  =============================================================================
*
*     .. Parameters ..
INTEGER          M, N
PARAMETER        ( M = 6, N = 5 )
INTEGER          LDA, LDU, LDVT
PARAMETER        ( LDA = M, LDU = M, LDVT = N )
INTEGER          LWMAX
PARAMETER        ( LWMAX = 1000 )
*
*     .. Local Scalars ..
INTEGER          INFO, LWORK
*
*     .. Local Arrays ..
DOUBLE PRECISION A( LDA, N ), U( LDU, M ), VT( LDVT, N ), S( N ),
$WORK( LWMAX ) DATA A/$  8.79, 6.11,-9.15, 9.57,-3.49, 9.84,
$9.93, 6.91,-7.93, 1.64, 4.02, 0.15,$  9.83, 5.04, 4.86, 8.83, 9.80,-8.99,
$5.45,-0.27, 4.85, 0.74,10.00,-6.02,$  3.16, 7.98, 3.01, 5.80, 4.27,-5.31
$/ * * .. External Subroutines .. EXTERNAL DGESVD EXTERNAL PRINT_MATRIX * * .. Intrinsic Functions .. INTRINSIC INT, MIN * * .. Executable Statements .. WRITE(*,*)'DGESVD Example Program Results' * * Query the optimal workspace. * LWORK = -1 CALL DGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT,$             WORK, LWORK, INFO )
LWORK = MIN( LWMAX, INT( WORK( 1 ) ) )
*
*     Compute SVD.
*
CALL DGESVD( 'All', 'All', M, N, A, LDA, S, U, LDU, VT, LDVT,
$WORK, LWORK, INFO ) * * Check for convergence. * IF( INFO.GT.0 ) THEN WRITE(*,*)'The algorithm computing SVD failed to converge.' STOP END IF * * Print singular values. * CALL PRINT_MATRIX( 'Singular values', 1, N, S, 1 ) * * Print left singular vectors. * CALL PRINT_MATRIX( 'Left singular vectors (stored columnwise)',$                   M, N, U, LDU )
*
*     Print right singular vectors.
*
CALL PRINT_MATRIX( 'Right singular vectors (stored rowwise)',
\$                   N, N, VT, LDVT )
STOP
END
*
*     End of DGESVD 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