numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/zupgtr.f | 6023B | -rw-r--r-- |
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*> \brief \b ZUPGTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUPGTR + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zupgtr.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zupgtr.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zupgtr.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDQ, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUPGTR generates a complex unitary matrix Q which is defined as the *> product of n-1 elementary reflectors H(i) of order n, as returned by *> ZHPTRD using packed storage: *> *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular packed storage used in previous *> call to ZHPTRD; *> = 'L': Lower triangular packed storage used in previous *> call to ZHPTRD. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix Q. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> The vectors which define the elementary reflectors, as *> returned by ZHPTRD. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZHPTRD. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> The N-by-N unitary matrix Q. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N-1) *> \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 upgtr * * ===================================================================== SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, 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 .. CHARACTER UPLO INTEGER INFO, LDQ, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IINFO, IJ, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNG2L, ZUNG2R * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUPGTR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Q was determined by a call to ZHPTRD with UPLO = 'U' * * Unpack the vectors which define the elementary reflectors and * set the last row and column of Q equal to those of the unit * matrix * IJ = 2 DO 20 J = 1, N - 1 DO 10 I = 1, J - 1 Q( I, J ) = AP( IJ ) IJ = IJ + 1 10 CONTINUE IJ = IJ + 2 Q( N, J ) = CZERO 20 CONTINUE DO 30 I = 1, N - 1 Q( I, N ) = CZERO 30 CONTINUE Q( N, N ) = CONE * * Generate Q(1:n-1,1:n-1) * CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO ) * ELSE * * Q was determined by a call to ZHPTRD with UPLO = 'L'. * * Unpack the vectors which define the elementary reflectors and * set the first row and column of Q equal to those of the unit * matrix * Q( 1, 1 ) = CONE DO 40 I = 2, N Q( I, 1 ) = CZERO 40 CONTINUE IJ = 3 DO 60 J = 2, N Q( 1, J ) = CZERO DO 50 I = J + 1, N Q( I, J ) = AP( IJ ) IJ = IJ + 1 50 CONTINUE IJ = IJ + 2 60 CONTINUE IF( N.GT.1 ) THEN * * Generate Q(2:n,2:n) * CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK, $ IINFO ) END IF END IF RETURN * * End of ZUPGTR * END