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  4. zgeqr(3)

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zgeqr.f(3) LAPACK zgeqr.f(3)

NAME

zgeqr.f

SYNOPSIS

Functions/Subroutines


subroutine zgeqr (M, N, A, LDA, T, TSIZE, WORK, LWORK, INFO)

Function/Subroutine Documentation

subroutine zgeqr (integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) T, integer TSIZE, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

ZGEQR computes a QR factorization of an M-by-N matrix A.

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.

A



          A is COMPLEX*16 array, dimension (LDA,N)


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


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


          contain the min(M,N)-by-N upper trapezoidal matrix R


          (R is upper triangular if M >= N);


          the elements below the diagonal are used to store part of the 


          data structure to represent Q.

LDA



          LDA is INTEGER


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

T



          T is COMPLEX*16 array, dimension (MAX(5,TSIZE))


          On exit, if INFO = 0, T(1) returns optimal (or either minimal 


          or optimal, if query is assumed) TSIZE. See TSIZE for details.


          Remaining T contains part of the data structure used to represent Q.


          If one wants to apply or construct Q, then one needs to keep T 


          (in addition to A) and pass it to further subroutines.

TSIZE



          TSIZE is INTEGER


          If TSIZE >= 5, the dimension of the array T.


          If TSIZE = -1 or -2, then a workspace query is assumed. The routine


          only calculates the sizes of the T and WORK arrays, returns these


          values as the first entries of the T and WORK arrays, and no error


          message related to T or WORK is issued by XERBLA.


          If TSIZE = -1, the routine calculates optimal size of T for the 


          optimum performance and returns this value in T(1).


          If TSIZE = -2, the routine calculates minimal size of T and 


          returns this value in T(1).

WORK



          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal


          or optimal, if query was assumed) LWORK.


          See LWORK for details.

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.


          If LWORK = -1 or -2, then a workspace query is assumed. The routine


          only calculates the sizes of the T and WORK arrays, returns these


          values as the first entries of the T and WORK arrays, and no error


          message related to T or WORK is issued by XERBLA.


          If LWORK = -1, the routine calculates optimal size of WORK for the


          optimal performance and returns this value in WORK(1).


          If LWORK = -2, the routine calculates minimal size of WORK and 


          returns this value in WORK(1).

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.

Further Details

The goal of the interface is to give maximum freedom to the developers for creating any QR factorization algorithm they wish. The triangular (trapezoidal) R has to be stored in the upper part of A. The lower part of A and the array T can be used to store any relevant information for applying or constructing the Q factor. The WORK array can safely be discarded after exit.

Caution: One should not expect the sizes of T and WORK to be the same from one LAPACK implementation to the other, or even from one execution to the other. A workspace query (for T and WORK) is needed at each execution. However, for a given execution, the size of T and WORK are fixed and will not change from one query to the next.

Further Details particular to this LAPACK implementation:

These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are unlikely not true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface.

In this version,

T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by ZLATSQR or ZGEQRT

Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, ZGEQR will use either ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute the QR factorization.

Definition at line 162 of file zgeqr.f.

Author

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Tue Nov 14 2017 Version 3.8.0