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

.in +1c
.ti -1c
.RI "subroutine \fBdtpqrt\fP (M, \fBN\fP, L, NB, A, \fBLDA\fP, B, \fBLDB\fP, T, LDT, WORK, INFO)"
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.RI "\fBDTPQRT\fP "
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.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dtpqrt (integer M, integer N, integer L, integer NB, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( * ) WORK, integer INFO)"

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\fBDTPQRT\fP  
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\fBPurpose: \fP
.RS 4

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.nf
 DTPQRT computes a blocked QR factorization of a real
 "triangular-pentagonal" matrix C, which is composed of a
 triangular block A and pentagonal block B, using the compact
 WY representation for Q.
.fi
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.RE
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\fBParameters:\fP
.RS 4
\fIM\fP 
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          M is INTEGER
          The number of rows of the matrix B.
          M >= 0.
.fi
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\fIN\fP 
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          N is INTEGER
          The number of columns of the matrix B, and the order of the
          triangular matrix A.
          N >= 0.
.fi
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\fIL\fP 
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.nf
          L is INTEGER
          The number of rows of the upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.
.fi
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\fINB\fP 
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          NB is INTEGER
          The block size to be used in the blocked QR.  N >= NB >= 1.
.fi
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\fIA\fP 
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          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the upper triangular N-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the upper triangular matrix R.
.fi
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.br
\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
.fi
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\fIB\fP 
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          B is DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the pentagonal M-by-N matrix B.  The first M-L rows
          are rectangular, and the last L rows are upper trapezoidal.
          On exit, B contains the pentagonal matrix V.  See Further Details.
.fi
.PP
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\fILDB\fP 
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          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
.fi
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\fIT\fP 
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          T is DOUBLE PRECISION array, dimension (LDT,N)
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See Further Details.
.fi
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\fILDT\fP 
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          LDT is INTEGER
          The leading dimension of the array T.  LDT >= NB.
.fi
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\fIWORK\fP 
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          WORK is DOUBLE PRECISION array, dimension (NB*N)
.fi
.PP
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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
.PP
 
.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
December 2016 
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\fBFurther Details: \fP
.RS 4

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.nf
  The input matrix C is a (N+M)-by-N matrix

               C = [ A ]
                   [ B ]

  where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
  matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
  upper trapezoidal matrix B2:

               B = [ B1 ]  <- (M-L)-by-N rectangular
                   [ B2 ]  <-     L-by-N upper trapezoidal.

  The upper trapezoidal matrix B2 consists of the first L rows of a
  N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
  B is rectangular M-by-N; if M=L=N, B is upper triangular.

  The matrix W stores the elementary reflectors H(i) in the i-th column
  below the diagonal (of A) in the (N+M)-by-N input matrix C

               C = [ A ]  <- upper triangular N-by-N
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as

               W = [ I ]  <- identity, N-by-N
                   [ V ]  <- M-by-N, same form as B.

  Thus, all of information needed for W is contained on exit in B, which
  we call V above.  Note that V has the same form as B; that is,

               V = [ V1 ] <- (M-L)-by-N rectangular
                   [ V2 ] <-     L-by-N upper trapezoidal.

  The columns of V represent the vectors which define the H(i)'s.

  The number of blocks is B = ceiling(N/NB), where each
  block is of order NB except for the last block, which is of order
  IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
  for the last block) T's are stored in the NB-by-N matrix T as

               T = [T1 T2 ... TB].
.fi
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.RE
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Definition at line 191 of file dtpqrt\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.
