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---
:name: ctzrzf
:md5sum: 0236521a4c727d201e0d3d1786f9f82b
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: complex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- tau:
:type: complex
:intent: output
:dims:
- m
- work:
:type: complex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: m
- info:
:type: integer
:intent: output
:substitutions:
m: lda
:fortran_help: " SUBROUTINE CTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A\n\
* to upper triangular form by means of unitary transformations.\n\
*\n\
* The upper trapezoidal matrix A is factored as\n\
*\n\
* A = ( R 0 ) * Z,\n\
*\n\
* where Z is an N-by-N unitary matrix and R is an M-by-M upper\n\
* triangular matrix.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= M.\n\
*\n\
* A (input/output) COMPLEX array, dimension (LDA,N)\n\
* On entry, the leading M-by-N upper trapezoidal part of the\n\
* array A must contain the matrix to be factorized.\n\
* On exit, the leading M-by-M upper triangular part of A\n\
* contains the upper triangular matrix R, and elements M+1 to\n\
* N of the first M rows of A, with the array TAU, represent the\n\
* unitary matrix Z as a product of M elementary reflectors.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* TAU (output) COMPLEX array, dimension (M)\n\
* The scalar factors of the elementary reflectors.\n\
*\n\
* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,M).\n\
* For optimum performance LWORK >= M*NB, where NB is\n\
* the optimal blocksize.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA\n\
*\n\
* The factorization is obtained by Householder's method. The kth\n\
* transformation matrix, Z( k ), which is used to introduce zeros into\n\
* the ( m - k + 1 )th row of A, is given in the form\n\
*\n\
* Z( k ) = ( I 0 ),\n\
* ( 0 T( k ) )\n\
*\n\
* where\n\
*\n\
* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),\n\
* ( 0 )\n\
* ( z( k ) )\n\
*\n\
* tau is a scalar and z( k ) is an ( n - m ) element vector.\n\
* tau and z( k ) are chosen to annihilate the elements of the kth row\n\
* of X.\n\
*\n\
* The scalar tau is returned in the kth element of TAU and the vector\n\
* u( k ) in the kth row of A, such that the elements of z( k ) are\n\
* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in\n\
* the upper triangular part of A.\n\
*\n\
* Z is given by\n\
*\n\
* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).\n\
*\n\
* =====================================================================\n\
*\n"
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