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  4. cgelqt(3)

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cgelqt.f(3) LAPACK cgelqt.f(3)

NAME

cgelqt.f

SYNOPSIS

Functions/Subroutines


subroutine cgelqt (M, N, MB, A, LDA, T, LDT, WORK, INFO)

Function/Subroutine Documentation

subroutine cgelqt (integer M, integer N, integer MB, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( * ) WORK, integer INFO)

Purpose:

CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q.

Parameters:

M 



          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 >= 0.

MB



          MB is INTEGER


          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

A



          A is COMPLEX array, dimension (LDA,N)


          On entry, the M-by-N matrix A.


          On exit, the elements on and below the diagonal of the array


          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is


          lower triangular if M <= N); the elements above the diagonal


          are the rows of V.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,M).

T



          T is COMPLEX array, dimension (LDT,MIN(M,N))


          The upper triangular block reflectors stored in compact form


          as a sequence of upper triangular blocks.  See below


          for further details.

LDT



          LDT is INTEGER


          The leading dimension of the array T.  LDT >= MB.

WORK



          WORK is COMPLEX array, dimension (MB*N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

June 2017

Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 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. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).

Definition at line 125 of file cgelqt.f.

Author

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Tue Nov 14 2017 Version 3.8.0