dtzrzf (l)  Linux Manuals
dtzrzf: reduces the MbyN ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
NAME
DTZRZF  reduces the MbyN ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformationsSYNOPSIS
 SUBROUTINE DTZRZF(
 M, N, A, LDA, TAU, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LWORK, M, N
 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
DTZRZF reduces the MbyN ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. The upper trapezoidal matrix A is factored asA
where Z is an NbyN orthogonal matrix and R is an MbyM upper triangular matrix.
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 >= M.
 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 On entry, the leading MbyN upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading MbyM 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 orthogonal matrix Z as a product of M elementary reflectors.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 TAU (output) DOUBLE PRECISION array, dimension (M)
 The scalar factors of the elementary reflectors.
 WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 LWORK (input) INTEGER
 The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
Based on contributions byZ(
where
T(
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