REAL FUNCTION SQRT12( M, N, A, LDA, S, WORK, LWORK ) * * -- LAPACK test routine (version 3.1.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * January 2007 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), S( * ), WORK( LWORK ) * .. * * Purpose * ======= * * SQRT12 computes the singular values `svlues' of the upper trapezoid * of A(1:M,1:N) and returns the ratio * * || s - svlues||/(||svlues||*eps*max(M,N)) * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. * * N (input) INTEGER * The number of columns of the matrix A. * * A (input) REAL array, dimension (LDA,N) * The M-by-N matrix A. Only the upper trapezoid is referenced. * * LDA (input) INTEGER * The leading dimension of the array A. * * S (input) REAL array, dimension (min(M,N)) * The singular values of the matrix A. * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= max(M*N + 4*min(M,N) + * max(M,N), M*N+2*MIN( M, N )+4*N). * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, INFO, ISCL, J, MN REAL ANRM, BIGNUM, NRMSVL, SMLNUM * .. * .. External Functions .. REAL SASUM, SLAMCH, SLANGE, SNRM2 EXTERNAL SASUM, SLAMCH, SLANGE, SNRM2 * .. * .. External Subroutines .. EXTERNAL SAXPY, SBDSQR, SGEBD2, SLABAD, SLASCL, SLASET, \$ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Local Arrays .. REAL DUMMY( 1 ) * .. * .. Executable Statements .. * SQRT12 = ZERO * * Test that enough workspace is supplied * IF( LWORK.LT.MAX( M*N+4*MIN( M, N )+MAX( M, N ), \$ M*N+2*MIN( M, N )+4*N) ) THEN CALL XERBLA( 'SQRT12', 7 ) RETURN END IF * * Quick return if possible * MN = MIN( M, N ) IF( MN.LE.ZERO ) \$ RETURN * NRMSVL = SNRM2( MN, S, 1 ) * * Copy upper triangle of A into work * CALL SLASET( 'Full', M, N, ZERO, ZERO, WORK, M ) DO 20 J = 1, N DO 10 I = 1, MIN( J, M ) WORK( ( J-1 )*M+I ) = A( I, J ) 10 CONTINUE 20 CONTINUE * * Get machine parameters * SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' ) BIGNUM = ONE / SMLNUM CALL SLABAD( SMLNUM, BIGNUM ) * * Scale work if max entry outside range [SMLNUM,BIGNUM] * ANRM = SLANGE( 'M', M, N, WORK, M, DUMMY ) ISCL = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN * * Scale matrix norm up to SMLNUM * CALL SLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO ) ISCL = 1 ELSE IF( ANRM.GT.BIGNUM ) THEN * * Scale matrix norm down to BIGNUM * CALL SLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO ) ISCL = 1 END IF * IF( ANRM.NE.ZERO ) THEN * * Compute SVD of work * CALL SGEBD2( M, N, WORK, M, WORK( M*N+1 ), WORK( M*N+MN+1 ), \$ WORK( M*N+2*MN+1 ), WORK( M*N+3*MN+1 ), \$ WORK( M*N+4*MN+1 ), INFO ) CALL SBDSQR( 'Upper', MN, 0, 0, 0, WORK( M*N+1 ), \$ WORK( M*N+MN+1 ), DUMMY, MN, DUMMY, 1, DUMMY, MN, \$ WORK( M*N+2*MN+1 ), INFO ) * IF( ISCL.EQ.1 ) THEN IF( ANRM.GT.BIGNUM ) THEN CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, \$ WORK( M*N+1 ), MN, INFO ) END IF IF( ANRM.LT.SMLNUM ) THEN CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, \$ WORK( M*N+1 ), MN, INFO ) END IF END IF * ELSE * DO 30 I = 1, MN WORK( M*N+I ) = ZERO 30 CONTINUE END IF * * Compare s and singular values of work * CALL SAXPY( MN, -ONE, S, 1, WORK( M*N+1 ), 1 ) SQRT12 = SASUM( MN, WORK( M*N+1 ), 1 ) / \$ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) IF( NRMSVL.NE.ZERO ) \$ SQRT12 = SQRT12 / NRMSVL * RETURN * * End of SQRT12 * END