subroutine ztzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
subroutine ztzrzf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, integerINFO)ZTZRZF Purpose:
ZTZRZF 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 triangular matrix.
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 >= M.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 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
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 (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK
LWORK is 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
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USAFurther Details:
The N-by-N matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each N-by-N Z(k) is given by Z(k) = I - tau(k)*v(k)*v(k)**H with v(k) is the kth row vector of the M-by-N matrix V = ( I A(:,M+1:N) ) I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from DTZRZF, and tau(k) is the kth element of the array TAU.