.TH "dgeqrt3.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
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.SH NAME
dgeqrt3.f \- 
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.RI "recursive subroutine \fBdgeqrt3\fP (M, N, A, LDA, T, LDT, INFO)"
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.RI "\fI\fBDGEQRT3\fP recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q\&. \fP"
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.SH "Function/Subroutine Documentation"
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.SS "recursive subroutine dgeqrt3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldt, * )T, integerLDT, integerINFO)"

.PP
\fBDGEQRT3\fP recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q\&.  
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\fBPurpose: \fP
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.nf
 DGEQRT3 recursively computes a QR factorization of a real 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.
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.RE
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\fBParameters:\fP
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\fIM\fP 
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          M is INTEGER
          The number of rows of the matrix A.  M >= N.
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\fIN\fP 
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          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
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\fIA\fP 
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          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the real M-by-N matrix A.  On exit, the elements on and
          above the diagonal contain the N-by-N upper triangular matrix R; the
          elements below the diagonal are the columns of V.  See below for
          further details.
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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 DOUBLE PRECISION 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.
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\fILDT\fP 
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          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,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
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.RE
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\fBAuthor:\fP
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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\&. 
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\fBDate:\fP
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September 2012 
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\fBFurther Details: \fP
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  The matrix V stores the elementary reflectors H(i) in the i-th column
  below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 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).
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Definition at line 133 of file dgeqrt3\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.