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DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK,
$ RWORK ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), S( * ) COMPLEX*16 A( LDA, * ), WORK( LWORK ) * .. * * Purpose * ======= * * ZQRT12 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) COMPLEX*16 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) DOUBLE PRECISION array, dimension (min(M,N)) * The singular values of the matrix A. * * WORK (workspace) COMPLEX*16 array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= M*N + 2*min(M,N) + * max(M,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (2*min(M,N)) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, INFO, ISCL, J, MN DOUBLE PRECISION ANRM, BIGNUM, NRMSVL, SMLNUM * .. * .. Local Arrays .. DOUBLE PRECISION DUMMY( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DNRM2, ZLANGE EXTERNAL DASUM, DLAMCH, DNRM2, ZLANGE * .. * .. External Subroutines .. EXTERNAL DAXPY, DBDSQR, DLABAD, DLASCL, XERBLA, ZGEBD2, $ ZLASCL, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Executable Statements .. * ZQRT12 = ZERO * * Test that enough workspace is supplied * IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN CALL XERBLA( 'ZQRT12', 7 ) RETURN END IF * * Quick return if possible * MN = MIN( M, N ) IF( MN.LE.ZERO ) $ RETURN * NRMSVL = DNRM2( MN, S, 1 ) * * Copy upper triangle of A into work * CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( 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 = DLAMCH( 'S' ) / DLAMCH( 'P' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) * * Scale work if max entry outside range [SMLNUM,BIGNUM] * ANRM = ZLANGE( 'M', M, N, WORK, M, DUMMY ) ISCL = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN * * Scale matrix norm up to SMLNUM * CALL ZLASCL( '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 ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO ) ISCL = 1 END IF * IF( ANRM.NE.ZERO ) THEN * * Compute SVD of work * CALL ZGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ), $ WORK( M*N+1 ), WORK( M*N+MN+1 ), $ WORK( M*N+2*MN+1 ), INFO ) CALL DBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ), $ DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ), $ INFO ) * IF( ISCL.EQ.1 ) THEN IF( ANRM.GT.BIGNUM ) THEN CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ), $ MN, INFO ) END IF IF( ANRM.LT.SMLNUM ) THEN CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ), $ MN, INFO ) END IF END IF * ELSE * DO 30 I = 1, MN RWORK( I ) = ZERO 30 CONTINUE END IF * * Compare s and singular values of work * CALL DAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 ) ZQRT12 = DASUM( MN, RWORK( 1 ), 1 ) / $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) ) IF( NRMSVL.NE.ZERO ) $ ZQRT12 = ZQRT12 / NRMSVL * RETURN * * End of ZQRT12 * END |