.TH "SRC/zgelq.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zgelq.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgelq\fP (m, n, a, lda, t, tsize, work, lwork, info)"
.br
.RI "\fBZGELQ\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgelq (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)"

.PP
\fBZGELQ\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZGELQ computes an LQ factorization of a complex M-by-N matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a N-by-N orthogonal matrix;
!>    L is a lower-triangular M-by-M matrix;
!>    0 is a M-by-(N-M) zero matrix, if M < N\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 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 used to store part of the 
!>          data structure to represent Q\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fITSIZE\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          (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\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK >= 1\&.
!>          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)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details\fP
.RS 4

.PP
.nf
!>
!> The goal of the interface is to give maximum freedom to the developers for
!> creating any LQ factorization algorithm they wish\&. The triangular 
!> (trapezoidal) L has to be stored in the lower 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\&.
!>
!> 
.fi
.PP
.RE
.PP
\fBFurther Details particular to this LAPACK implementation:\fP
.RS 4

.PP
.nf
!>
!> These details are particular for this LAPACK implementation\&. Users should not 
!> take them for granted\&. These details may change in the future, and are not likely
!> 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
!>                           ZLASWLQ or ZGELQT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, ZGELQ will use either
!>  ZLASWLQ (if the matrix is short-and-wide) or ZGELQT to compute
!>  the LQ factorization\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB172\fP of file \fBzgelq\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.