LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  ctzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO) 
CTZRZF 
subroutine ctzrzf  (  integer  M, 
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
complex, dimension( * )  TAU,  
complex, dimension( * )  WORK,  
integer  LWORK,  
integer  INFO  
) 
CTZRZF
Download CTZRZF + dependencies [TGZ] [ZIP] [TXT]CTZRZF reduces the MbyN ( 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 NbyN unitary matrix and R is an MbyM upper triangular matrix.
[in]  M  M is INTEGER The number of rows of the matrix A. M >= 0. 
[in]  N  N is INTEGER The number of columns of the matrix A. N >= M. 
[in,out]  A  A is COMPLEX 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 unitary matrix Z as a product of M elementary reflectors. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  TAU  TAU is COMPLEX array, dimension (M) The scalar factors of the elementary reflectors. 
[out]  WORK  WORK is COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  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. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
The NbyN matrix Z can be computed by Z = Z(1)*Z(2)* ... *Z(M) where each NbyN 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 MbyN matrix V = ( I A(:,M+1:N) ) I is the MbyM 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.
Definition at line 152 of file ctzrzf.f.