
NAMEztzrzf.f SYNOPSISFunctions/Subroutinessubroutine ztzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO) Function/Subroutine Documentationsubroutine ztzrzf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, integerINFO)ZTZRZF Purpose:ZTZRZF 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. M
Author:
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 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.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 ith argument had an illegal value Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 2012
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn.,
Knoxville, USA
Further Details:
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. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Visit the GSP FreeBSD Man Page Interface. 