ztzrqf.f man page
ztzrqf.f — ZTZRQF Purpose: Parameters: M N A LDA TAU INFO Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Further Details: Definition at line 139 of file ztzrqf.f. Generated automatically by Doxygen for LAPACK from the source code. ztzrqf(3) is an alias of ztzrqf.f(3).
subroutine ztzrqf (M, N, A, LDA, TAU, INFO)
subroutine ztzrqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, integerINFO)
This routine is deprecated and has been replaced by routine ZTZRZF.
ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
to upper triangular form by means of unitary transformations.
The upper trapezoidal matrix A is factored as
A = ( R 0 ) * Z,
where Z is an N-by-N unitary matrix and R is an M-by-M upper
M is INTEGER
The number of rows of the matrix A. M >= 0.
N is INTEGER
The number of columns of the matrix A. N >= M.
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 M+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 is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU is COMPLEX*16 array, dimension (M)
The scalar factors of the elementary reflectors.
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
The factorization is obtained by Householder's method. The kth
transformation matrix, Z( k ), whose conjugate transpose 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 ) )
T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ),
( 0 )
( z( k ) )
tau is a scalar and z( k ) is an ( n - m ) element vector.
tau and z( k ) are chosen to annihilate the elements of the kth row
The scalar tau is returned in the kth element of TAU and the vector
u( k ) in the kth row of A, such that the elements of z( k ) are
in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
the upper triangular part of A.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Definition at line 139 of file ztzrqf.f.
Generated automatically by Doxygen for LAPACK from the source code.
ztzrqf(3) is an alias of ztzrqf.f(3).