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

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.RI "subroutine \fBsgelqt\fP (M, \fBN\fP, MB, A, \fBLDA\fP, T, LDT, WORK, INFO)"
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.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgelqt (integer M, integer N, integer MB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, real, dimension( * ) WORK, integer INFO)"

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\fBPurpose:\fP
.RS 4

.RE
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DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q\&.  
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\fBParameters:\fP
.RS 4
\fIM\fP 
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          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
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\fIN\fP 
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          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
.fi
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\fIMB\fP 
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          MB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.
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\fIA\fP 
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          A is REAL 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.
.fi
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\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 REAL 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.
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\fILDT\fP 
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          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
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\fIWORK\fP 
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          WORK is REAL array, dimension (MB*N)
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\fIINFO\fP 
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          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
.fi
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.RE
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\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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\fBDate:\fP
.RS 4
November 2017 
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\fBFurther Details:\fP
.RS 4

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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
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V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 )
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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=\fBMIN(M,N)\fP\&. 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
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T = (T1 T2 \&.\&.\&. TB)\&.  
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Definition at line 124 of file sgelqt\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.
