.TH "dtpqrt2.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
dtpqrt2.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

.in +1c
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.RI "subroutine \fBdtpqrt2\fP (M, \fBN\fP, L, A, \fBLDA\fP, B, \fBLDB\fP, T, LDT, INFO)"
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.RI "\fBDTPQRT2\fP computes a QR factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dtpqrt2 (integer M, integer N, integer L, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldt, * ) T, integer LDT, integer INFO)"

.PP
\fBDTPQRT2\fP computes a QR factorization of a real or complex 'triangular-pentagonal' matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q\&.  
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\fBPurpose: \fP
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.nf
 DTPQRT2 computes a 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.
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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 total number of rows of the matrix B.
          M >= 0.
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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.
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\fIL\fP 
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          L is INTEGER
          The number of rows of the upper trapezoidal part of B.
          MIN(M,N) >= L >= 0.  See Further Details.
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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.
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\fILDA\fP 
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          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
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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
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\fILDB\fP 
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          LDB is INTEGER
          The leading dimension of the array B.  LDB >= 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 T of the block reflector.
          See 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)
.fi
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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\&. 
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\fBDate:\fP
.RS 4
December 2016 
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\fBFurther Details: \fP
.RS 4

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  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 (M+N)-by-(M+N) block reflector H is then given by

               H = I - W * T * W**T

  where W^H is the conjugate transpose of W and T is the upper triangular
  factor of the block reflector.
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.RE
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Definition at line 175 of file dtpqrt2\&.f\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.
