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

.in +1c
.ti -1c
.RI "subroutine \fBztplqt\fP (m, n, l, mb, a, lda, b, ldb, t, ldt, work, info)"
.br
.RI "\fBZTPLQT\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztplqt (integer m, integer n, integer l, integer mb, 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
\fBZTPLQT\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZTPLQT computes a blocked LQ 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, and the order of the
          triangular matrix A\&.
          M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix B\&.
          N >= 0\&.
.fi
.PP
.br
\fIL\fP 
.PP
.nf
          L is INTEGER
          The number of rows of the lower trapezoidal part of B\&.
          MIN(M,N) >= L >= 0\&.  See Further Details\&.
.fi
.PP
.br
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The block size to be used in the blocked QR\&.  M >= MB >= 1\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,M)
          On entry, the lower triangular M-by-M matrix A\&.
          On exit, the elements on and below the diagonal of the array
          contain the lower triangular matrix L\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.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 N-L columns
          are rectangular, and the last L columns are lower 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 lower 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 >= MB\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (MB*M)
.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 M-by-(M+N) matrix

               C = [ A ] [ B ]


  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
  upper trapezoidal matrix B2:
          [ B ] = [ B1 ] [ B2 ]
                   [ B1 ]  <- M-by-(N-L) rectangular
                   [ B2 ]  <-     M-by-L lower trapezoidal\&.

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

  The matrix W stores the elementary reflectors H(i) in the i-th row
  above the diagonal (of A) in the M-by-(M+N) input matrix C
            [ C ] = [ A ] [ B ]
                   [ A ]  <- lower triangular M-by-M
                   [ B ]  <- M-by-N pentagonal

  so that W can be represented as
            [ W ] = [ I ] [ V ]
                   [ I ]  <- identity, M-by-M
                   [ 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 ] [ V2 ]
                   [ V1 ] <- M-by-(N-L) rectangular
                   [ V2 ] <-     M-by-L lower trapezoidal\&.

  The rows of V represent the vectors which define the H(i)'s\&.

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

               T = [T1 T2 \&.\&.\&. TB]\&.
.fi
.PP
 
.RE
.PP

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