zlatrz(3) [debian man page]
zlatrz.f(3) LAPACK zlatrz.f(3) NAME
zlatrz.f - SYNOPSIS
Functions/Subroutines subroutine zlatrz (M, N, L, A, LDA, TAU, WORK) ZLATRZ Function/Subroutine Documentation subroutine zlatrz (integerM, integerN, integerL, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK) ZLATRZ Purpose: ZLATRZ 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. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder vectors. N-M >= L >= 0. A A is COMPLEX*16 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX*16 array, dimension (M) The scalar factors of the elementary reflectors. WORK WORK is COMPLEX*16 array, dimension (M) Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: 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 ). Definition at line 141 of file zlatrz.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 zlatrz.f(3)
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zlatrz.f(3) LAPACK zlatrz.f(3) NAME
zlatrz.f - SYNOPSIS
Functions/Subroutines subroutine zlatrz (M, N, L, A, LDA, TAU, WORK) ZLATRZ Function/Subroutine Documentation subroutine zlatrz (integerM, integerN, integerL, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK) ZLATRZ Purpose: ZLATRZ 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. Parameters: M M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0. L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder vectors. N-M >= L >= 0. A A is COMPLEX*16 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX*16 array, dimension (M) The scalar factors of the elementary reflectors. WORK WORK is COMPLEX*16 array, dimension (M) Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Contributors: A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA Further Details: 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 ). Definition at line 141 of file zlatrz.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 zlatrz.f(3)