.TH "SRC/zgelqt3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/zgelqt3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "recursive subroutine \fBzgelqt3\fP (m, n, a, lda, t, ldt, info)"
.br
.RI "\fBZGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)"

.PP
\fBZGELQT3\fP recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZGELQT3 recursively computes a LQ 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M =< N\&.
!> 
.fi
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.br
\fIN\fP 
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.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
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.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the complex M-by-N matrix A\&.  On exit, the elements on and
!>          below the diagonal contain the N-by-N lower triangular matrix L; the
!>          elements above the diagonal are the rows of V\&.  See below for
!>          further details\&.
!> 
.fi
.PP
.br
\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
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\fIT\fP 
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!>          T is COMPLEX*16 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\&.
!> 
.fi
.PP
.br
\fILDT\fP 
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.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= max(1,N)\&.
!> 
.fi
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.br
\fIINFO\fP 
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.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 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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

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.nf
!>
!>  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 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**T
!>
!>  where V**T is the transpose of V\&.
!>
!>  For details of the algorithm, see Elmroth and Gustavson (cited above)\&.
!> 
.fi
.PP
 
.RE
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Definition at line \fB130\fP of file \fBzgelqt3\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.