LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dtzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO) 
DTZRZF 
subroutine dtzrzf  (  integer  M, 
integer  N,  
double precision, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  TAU,  
double precision, dimension( * )  WORK,  
integer  LWORK,  
integer  INFO  
) 
DTZRZF
Download DTZRZF + dependencies [TGZ] [ZIP] [TXT]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 as A = ( R 0 ) * Z, where Z is an NbyN orthogonal 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 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. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). 
[out]  TAU  TAU is DOUBLE PRECISION array, dimension (M) The scalar factors of the elementary reflectors. 
[out]  WORK  WORK is DOUBLE PRECISION 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)**T 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 dtzrzf.f.