.TH "sgelqt3.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
sgelqt3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "recursive subroutine \fBsgelqt3\fP (M, \fBN\fP, A, \fBLDA\fP, T, LDT, INFO)"
.br
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "recursive subroutine sgelqt3 (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, integer INFO)"

.PP
\fBPurpose:\fP
.RS 4

.RE
.PP
DGELQT3 recursively computes a LQ factorization of a real M-by-N matrix A, using the compact WY representation of Q\&.
.PP
Based on the algorithm of Elmroth and Gustavson, IBM J\&. Res\&. Develop\&. Vol 44 No\&. 4 July 2000\&.  
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\fBParameters:\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A.  M =< N.
.fi
.PP
.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 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          On entry, the real 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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.nf
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is REAL 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
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.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 
.PP
Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
.PP
\fBDate:\fP
.RS 4
November 2017 
.RE
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\fBFurther Details:\fP
.RS 4

.RE
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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
.PP
V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 v3 )
.PP
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
.PP
H = I - V * T * V**T
.PP
where V**T is the transpose of V\&.
.PP
For details of the algorithm, see Elmroth and Gustavson (cited above)\&.  
.PP
Definition at line 116 of file sgelqt3\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
