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SUBROUTINE SQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
$ RANK, NORMA, NORMB, ISEED, WORK, LWORK )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
REAL NORMA, NORMB
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
* ..
*
* Purpose
* =======
*
* SQRT15 generates a matrix with full or deficient rank and of various
* norms.
*
* Arguments
* =========
*
* SCALE (input) INTEGER
* SCALE = 1: normally scaled matrix
* SCALE = 2: matrix scaled up
* SCALE = 3: matrix scaled down
*
* RKSEL (input) INTEGER
* RKSEL = 1: full rank matrix
* RKSEL = 2: rank-deficient matrix
*
* M (input) INTEGER
* The number of rows of the matrix A.
*
* N (input) INTEGER
* The number of columns of A.
*
* NRHS (input) INTEGER
* The number of columns of B.
*
* A (output) REAL array, dimension (LDA,N)
* The M-by-N matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A.
*
* B (output) REAL array, dimension (LDB, NRHS)
* A matrix that is in the range space of matrix A.
*
* LDB (input) INTEGER
* The leading dimension of the array B.
*
* S (output) REAL array, dimension MIN(M,N)
* Singular values of A.
*
* RANK (output) INTEGER
* number of nonzero singular values of A.
*
* NORMA (output) REAL
* one-norm of A.
*
* NORMB (output) REAL
* one-norm of B.
*
* ISEED (input/output) integer array, dimension (4)
* seed for random number generator.
*
* WORK (workspace) REAL array, dimension (LWORK)
*
* LWORK (input) INTEGER
* length of work space required.
* LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TWO, SVMIN
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
$ SVMIN = 0.1E0 )
* ..
* .. Local Scalars ..
INTEGER INFO, J, MN
REAL BIGNUM, EPS, SMLNUM, TEMP
* ..
* .. Local Arrays ..
REAL DUMMY( 1 )
* ..
* .. External Functions ..
REAL SASUM, SLAMCH, SLANGE, SLARND, SNRM2
EXTERNAL SASUM, SLAMCH, SLANGE, SLARND, SNRM2
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLAORD, SLARF, SLARNV, SLAROR, SLASCL,
$ SLASET, SSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. Executable Statements ..
*
MN = MIN( M, N )
IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN
CALL XERBLA( 'SQRT15', 16 )
RETURN
END IF
*
SMLNUM = SLAMCH( 'Safe minimum' )
BIGNUM = ONE / SMLNUM
EPS = SLAMCH( 'Epsilon' )
SMLNUM = ( SMLNUM / EPS ) / EPS
BIGNUM = ONE / SMLNUM
*
* Determine rank and (unscaled) singular values
*
IF( RKSEL.EQ.1 ) THEN
RANK = MN
ELSE IF( RKSEL.EQ.2 ) THEN
RANK = ( 3*MN ) / 4
DO 10 J = RANK + 1, MN
S( J ) = ZERO
10 CONTINUE
ELSE
CALL XERBLA( 'SQRT15', 2 )
END IF
*
IF( RANK.GT.0 ) THEN
*
* Nontrivial case
*
S( 1 ) = ONE
DO 30 J = 2, RANK
20 CONTINUE
TEMP = SLARND( 1, ISEED )
IF( TEMP.GT.SVMIN ) THEN
S( J ) = ABS( TEMP )
ELSE
GO TO 20
END IF
30 CONTINUE
CALL SLAORD( 'Decreasing', RANK, S, 1 )
*
* Generate 'rank' columns of a random orthogonal matrix in A
*
CALL SLARNV( 2, ISEED, M, WORK )
CALL SSCAL( M, ONE / SNRM2( M, WORK, 1 ), WORK, 1 )
CALL SLASET( 'Full', M, RANK, ZERO, ONE, A, LDA )
CALL SLARF( 'Left', M, RANK, WORK, 1, TWO, A, LDA,
$ WORK( M+1 ) )
*
* workspace used: m+mn
*
* Generate consistent rhs in the range space of A
*
CALL SLARNV( 2, ISEED, RANK*NRHS, WORK )
CALL SGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, ONE,
$ A, LDA, WORK, RANK, ZERO, B, LDB )
*
* work space used: <= mn *nrhs
*
* generate (unscaled) matrix A
*
DO 40 J = 1, RANK
CALL SSCAL( M, S( J ), A( 1, J ), 1 )
40 CONTINUE
IF( RANK.LT.N )
$ CALL SLASET( 'Full', M, N-RANK, ZERO, ZERO, A( 1, RANK+1 ),
$ LDA )
CALL SLAROR( 'Right', 'No initialization', M, N, A, LDA, ISEED,
$ WORK, INFO )
*
ELSE
*
* work space used 2*n+m
*
* Generate null matrix and rhs
*
DO 50 J = 1, MN
S( J ) = ZERO
50 CONTINUE
CALL SLASET( 'Full', M, N, ZERO, ZERO, A, LDA )
CALL SLASET( 'Full', M, NRHS, ZERO, ZERO, B, LDB )
*
END IF
*
* Scale the matrix
*
IF( SCALE.NE.1 ) THEN
NORMA = SLANGE( 'Max', M, N, A, LDA, DUMMY )
IF( NORMA.NE.ZERO ) THEN
IF( SCALE.EQ.2 ) THEN
*
* matrix scaled up
*
CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A,
$ LDA, INFO )
CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S,
$ MN, INFO )
CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B,
$ LDB, INFO )
ELSE IF( SCALE.EQ.3 ) THEN
*
* matrix scaled down
*
CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A,
$ LDA, INFO )
CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S,
$ MN, INFO )
CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B,
$ LDB, INFO )
ELSE
CALL XERBLA( 'SQRT15', 1 )
RETURN
END IF
END IF
END IF
*
NORMA = SASUM( MN, S, 1 )
NORMB = SLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY )
*
RETURN
*
* End of SQRT15
*
END
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