# CentOS 7.0 - man page for cgeqrt3 (centos section 3)

cgeqrt3.f(3) LAPACK cgeqrt3.f(3)cgeqrt3.fNAME-Functions/Subroutines recursive subroutine cgeqrt3 (M, N, A, LDA, T, LDT, INFO) CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.SYNOPSISFunction/Subroutine Documentation recursive subroutine cgeqrt3 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldt, * )T, integerLDT, integerINFO) CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. Purpose: CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000. Parameters: M M is INTEGER The number of rows of the matrix A. M >= N. N N is INTEGER The number of columns of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX array, dimension (LDT,N) The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by H = I - V * T * V**H where V**H is the conjugate transpose of V. For details of the algorithm, see Elmroth and Gustavson (cited above). Definition at line 133 of file cgeqrt3.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 cgeqrt3.f(3)