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*> \brief \b SQRT13
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* .. Scalar Arguments ..
* INTEGER LDA, M, N, SCALE
* REAL NORMA
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* REAL A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SCALE
*> \verbatim
*> SCALE is INTEGER
*> SCALE = 1: normally scaled matrix
*> SCALE = 2: matrix scaled up
*> SCALE = 3: matrix scaled down
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of A.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> The M-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A.
*> \endverbatim
*>
*> \param[out] NORMA
*> \verbatim
*> NORMA is REAL
*> The one-norm of A.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, M, N, SCALE
REAL NORMA
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER INFO, J
REAL BIGNUM, SMLNUM
* ..
* .. External Functions ..
REAL SASUM, SLAMCH, SLANGE
EXTERNAL SASUM, SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SLABAD, SLARNV, SLASCL
* ..
* .. Intrinsic Functions ..
INTRINSIC SIGN
* ..
* .. Local Arrays ..
REAL DUMMY( 1 )
* ..
* .. Executable Statements ..
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* benign matrix
*
DO 10 J = 1, N
CALL SLARNV( 2, ISEED, M, A( 1, J ) )
IF( J.LE.M ) THEN
A( J, J ) = A( J, J ) + SIGN( SASUM( M, A( 1, J ), 1 ),
$ A( J, J ) )
END IF
10 CONTINUE
*
* scaled versions
*
IF( SCALE.NE.1 ) THEN
NORMA = SLANGE( 'Max', M, N, A, LDA, DUMMY )
SMLNUM = SLAMCH( 'Safe minimum' )
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
SMLNUM = SMLNUM / SLAMCH( 'Epsilon' )
BIGNUM = ONE / SMLNUM
*
IF( SCALE.EQ.2 ) THEN
*
* matrix scaled up
*
CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, LDA,
$ INFO )
ELSE IF( SCALE.EQ.3 ) THEN
*
* matrix scaled down
*
CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, LDA,
$ INFO )
END IF
END IF
*
NORMA = SLANGE( 'One-norm', M, N, A, LDA, DUMMY )
RETURN
*
* End of SQRT13
*
END
|
