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

.in +1c
.ti -1c
.RI "subroutine \fBztpqrt\fP (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)"
.br
.RI "\fBZTPQRT\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztpqrt (integer m, integer n, integer l, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)"

.PP
\fBZTPQRT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZTPQRT computes a blocked QR factorization of a complex
 'triangular-pentagonal' 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 number of rows of the matrix B\&.
          M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.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 
.PP
.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
\fINB\fP 
.PP
.nf
          NB is INTEGER
          The block size to be used in the blocked QR\&.  N >= NB >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.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 
.PP
.nf
          T is COMPLEX*16 array, dimension (LDT,N)
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.  See Further Details\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (NB*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 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
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 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
.PP
 
.RE
.PP

.PP
Definition at line \fB187\fP of file \fBztpqrt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.