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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/clatrz.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
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diff --git a/SRC/clatrz.f b/SRC/clatrz.f index 31713e53..bdccf4f7 100644 --- a/SRC/clatrz.f +++ b/SRC/clatrz.f @@ -1,84 +1,148 @@ - SUBROUTINE CLATRZ( M, N, L, A, LDA, TAU, WORK ) +*> \brief \b CLATRZ * -* -- LAPACK routine (version 3.3.1) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* =========== DOCUMENTATION =========== * -* .. Scalar Arguments .. - INTEGER L, LDA, M, N -* .. -* .. Array Arguments .. - COMPLEX A( LDA, * ), TAU( * ), WORK( * ) -* .. +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== * +* SUBROUTINE CLATRZ( M, N, L, A, LDA, TAU, WORK ) +* +* .. Scalar Arguments .. +* INTEGER L, LDA, M, N +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ), TAU( * ), WORK( * ) +* .. +* * Purpose * ======= * -* CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix -* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means -* of unitary transformations, where Z is an (M+L)-by-(M+L) unitary -* matrix and, R and A1 are M-by-M upper triangular matrices. +*>\details \b Purpose: +*>\verbatim +*> +*> CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix +*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means +*> of unitary transformations, where Z is an (M+L)-by-(M+L) unitary +*> matrix and, R and A1 are M-by-M upper triangular matrices. +*> +*>\endverbatim * * Arguments * ========= * -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* L (input) INTEGER -* The number of columns of the matrix A containing the -* meaningful part of the Householder vectors. N-M >= L >= 0. +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] L +*> \verbatim +*> L is INTEGER +*> The number of columns of the matrix A containing the +*> meaningful part of the Householder vectors. N-M >= L >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> On entry, the leading M-by-N upper trapezoidal part of the +*> array A must contain the matrix to be factorized. +*> On exit, the leading M-by-M upper triangular part of A +*> contains the upper triangular matrix R, and elements N-L+1 to +*> N of the first M rows of A, with the array TAU, represent the +*> unitary matrix Z as a product of M elementary reflectors. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX array, dimension (M) +*> The scalar factors of the elementary reflectors. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension (M) +*> \endverbatim +*> +* +* Authors +* ======= * -* A (input/output) COMPLEX array, dimension (LDA,N) -* On entry, the leading M-by-N upper trapezoidal part of the -* array A must contain the matrix to be factorized. -* On exit, the leading M-by-M upper triangular part of A -* contains the upper triangular matrix R, and elements N-L+1 to -* N of the first M rows of A, with the array TAU, represent the -* unitary matrix Z as a product of M elementary reflectors. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). +*> \date November 2011 * -* TAU (output) COMPLEX array, dimension (M) -* The scalar factors of the elementary reflectors. +*> \ingroup complexOTHERcomputational * -* WORK (workspace) COMPLEX array, dimension (M) * * Further Details * =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Based on contributions by +*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA +*> +*> The factorization is obtained by Householder's method. The kth +*> transformation matrix, Z( k ), which is used to introduce zeros into +*> the ( m - k + 1 )th row of A, is given in the form +*> +*> Z( k ) = ( I 0 ), +*> ( 0 T( k ) ) +*> +*> where +*> +*> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), +*> ( 0 ) +*> ( z( k ) ) +*> +*> tau is a scalar and z( k ) is an l element vector. tau and z( k ) +*> are chosen to annihilate the elements of the kth row of A2. +*> +*> The scalar tau is returned in the kth element of TAU and the vector +*> u( k ) in the kth row of A2, such that the elements of z( k ) are +*> in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in +*> the upper triangular part of A1. +*> +*> Z is given by +*> +*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE CLATRZ( M, N, L, A, LDA, TAU, WORK ) * -* Based on contributions by -* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA -* -* The factorization is obtained by Householder's method. The kth -* transformation matrix, Z( k ), which is used to introduce zeros into -* the ( m - k + 1 )th row of A, is given in the form -* -* Z( k ) = ( I 0 ), -* ( 0 T( k ) ) -* -* where -* -* T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ), -* ( 0 ) -* ( z( k ) ) -* -* tau is a scalar and z( k ) is an l element vector. tau and z( k ) -* are chosen to annihilate the elements of the kth row of A2. -* -* The scalar tau is returned in the kth element of TAU and the vector -* u( k ) in the kth row of A2, such that the elements of z( k ) are -* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in -* the upper triangular part of A1. -* -* Z is given by +* -- LAPACK computational routine (version 3.3.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * -* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). +* .. Scalar Arguments .. + INTEGER L, LDA, M, N +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ), TAU( * ), WORK( * ) +* .. * * ===================================================================== * |