.TH "SRC/ztpqrt2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/ztpqrt2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBztpqrt2\fP (m, n, l, a, lda, b, ldb, t, ldt, info)"
.br
.RI "\fBZTPQRT2\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 ztpqrt2 (integer m, integer n, integer l, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, integer info)"

.PP
\fBZTPQRT2\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
.RS 4

.PP
.nf
!>
!> ZTPQRT2 computes a QR factorization of a complex 
!> matrix C, which is composed of a triangular block A and pentagonal block B,
!> using the compact WY representation for Q\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The total number of rows of the matrix B\&.
!>          M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
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.nf
!>          N is INTEGER
!>          The number of columns of the matrix B, and the order of
!>          the triangular matrix A\&.
!>          N >= 0\&.
!> 
.fi
.PP
.br
\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
.PP
.br
\fIA\fP 
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.nf
!>          A is COMPLEX*16 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
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 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
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIT\fP 
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.nf
!>          T is COMPLEX*16 array, dimension (LDT,N)
!>          The N-by-N upper triangular factor T of the block reflector\&.
!>          See Further Details\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= max(1,N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.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 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.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 (M+N)-by-(M+N) block reflector H is then given by
!>
!>               H = I - W * T * W**H
!>
!>  where W**H is the conjugate transpose of W and T is the upper triangular
!>  factor of the block reflector\&.
!> 
.fi
.PP
 
.RE
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Definition at line \fB172\fP of file \fBztpqrt2\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.