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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 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. 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 |