numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/dorbdb5.f | 8130B | -rw-r--r-- |
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*> \brief \b DORBDB5 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORBDB5 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb5.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb5.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb5.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, * LDQ2, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2, * $ N * .. * .. Array Arguments .. * DOUBLE PRECISION Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*) * .. * * *> \par Purpose: * ============= *> *>\verbatim *> *> DORBDB5 orthogonalizes the column vector *> X = [ X1 ] *> [ X2 ] *> with respect to the columns of *> Q = [ Q1 ] . *> [ Q2 ] *> The columns of Q must be orthonormal. *> *> If the projection is zero according to Kahan's "twice is enough" *> criterion, then some other vector from the orthogonal complement *> is returned. This vector is chosen in an arbitrary but deterministic *> way. *> *>\endverbatim * * Arguments: * ========== * *> \param[in] M1 *> \verbatim *> M1 is INTEGER *> The dimension of X1 and the number of rows in Q1. 0 <= M1. *> \endverbatim *> *> \param[in] M2 *> \verbatim *> M2 is INTEGER *> The dimension of X2 and the number of rows in Q2. 0 <= M2. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns in Q1 and Q2. 0 <= N. *> \endverbatim *> *> \param[in,out] X1 *> \verbatim *> X1 is DOUBLE PRECISION array, dimension (M1) *> On entry, the top part of the vector to be orthogonalized. *> On exit, the top part of the projected vector. *> \endverbatim *> *> \param[in] INCX1 *> \verbatim *> INCX1 is INTEGER *> Increment for entries of X1. *> \endverbatim *> *> \param[in,out] X2 *> \verbatim *> X2 is DOUBLE PRECISION array, dimension (M2) *> On entry, the bottom part of the vector to be *> orthogonalized. On exit, the bottom part of the projected *> vector. *> \endverbatim *> *> \param[in] INCX2 *> \verbatim *> INCX2 is INTEGER *> Increment for entries of X2. *> \endverbatim *> *> \param[in] Q1 *> \verbatim *> Q1 is DOUBLE PRECISION array, dimension (LDQ1, N) *> The top part of the orthonormal basis matrix. *> \endverbatim *> *> \param[in] LDQ1 *> \verbatim *> LDQ1 is INTEGER *> The leading dimension of Q1. LDQ1 >= M1. *> \endverbatim *> *> \param[in] Q2 *> \verbatim *> Q2 is DOUBLE PRECISION array, dimension (LDQ2, N) *> The bottom part of the orthonormal basis matrix. *> \endverbatim *> *> \param[in] LDQ2 *> \verbatim *> LDQ2 is INTEGER *> The leading dimension of Q2. LDQ2 >= M2. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= N. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup unbdb5 * * ===================================================================== SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, $ Q2, $ LDQ2, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2, $ N * .. * .. Array Arguments .. DOUBLE PRECISION Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION REALZERO PARAMETER ( REALZERO = 0.0D0 ) DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER CHILDINFO, I, J DOUBLE PRECISION EPS, NORM, SCL, SSQ * .. * .. External Subroutines .. EXTERNAL DLASSQ, DORBDB6, DSCAL, XERBLA * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DNRM2 EXTERNAL DLAMCH, DNRM2 * .. * .. Intrinsic Function .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test input arguments * INFO = 0 IF( M1 .LT. 0 ) THEN INFO = -1 ELSE IF( M2 .LT. 0 ) THEN INFO = -2 ELSE IF( N .LT. 0 ) THEN INFO = -3 ELSE IF( INCX1 .LT. 1 ) THEN INFO = -5 ELSE IF( INCX2 .LT. 1 ) THEN INFO = -7 ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN INFO = -9 ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN INFO = -11 ELSE IF( LWORK .LT. N ) THEN INFO = -13 END IF * IF( INFO .NE. 0 ) THEN CALL XERBLA( 'DORBDB5', -INFO ) RETURN END IF * EPS = DLAMCH( 'Precision' ) * * Project X onto the orthogonal complement of Q if X is nonzero * SCL = REALZERO SSQ = REALZERO CALL DLASSQ( M1, X1, INCX1, SCL, SSQ ) CALL DLASSQ( M2, X2, INCX2, SCL, SSQ ) NORM = SCL * SQRT( SSQ ) * IF( NORM .GT. N * EPS ) THEN * Scale vector to unit norm to avoid problems in the caller code. * Computing the reciprocal is undesirable but * * xLASCL cannot be used because of the vector increments and * * the round-off error has a negligible impact on * orthogonalization. CALL DSCAL( M1, ONE / NORM, X1, INCX1 ) CALL DSCAL( M2, ONE / NORM, X2, INCX2 ) CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) * * If the projection is nonzero, then return * IF( DNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. DNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END IF * * Project each standard basis vector e_1,...,e_M1 in turn, stopping * when a nonzero projection is found * DO I = 1, M1 DO J = 1, M1 X1(J) = ZERO END DO X1(I) = ONE DO J = 1, M2 X2(J) = ZERO END DO CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) IF( DNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. DNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END DO * * Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn, * stopping when a nonzero projection is found * DO I = 1, M2 DO J = 1, M1 X1(J) = ZERO END DO DO J = 1, M2 X2(J) = ZERO END DO X2(I) = ONE CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) IF( DNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. DNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END DO * RETURN * * End of DORBDB5 * END