ztzrzf (l) - Linux Man Pages
ztzrzf: reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
NAMEZTZRZF - reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
- SUBROUTINE ZTZRZF(
- M, N, A, LDA, TAU, WORK, LWORK, INFO )
- INTEGER INFO, LDA, LWORK, M, N
- COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
PURPOSEZTZRZF 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
where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.
- 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) 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 (input) INTEGER
- The leading dimension of the array A. LDA >= max(1,M).
- TAU (output) COMPLEX*16 array, dimension (M)
- The scalar factors of the elementary reflectors.
- WORK (workspace/output) COMPLEX*16 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 i-th argument had an illegal value
FURTHER DETAILSBased on contributions by
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