.TH "SRC/cgeqrt3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/cgeqrt3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "recursive subroutine \fBcgeqrt3\fP (m, n, a, lda, t, ldt, info)"
.br
.RI "\fB CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q\&. \fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)"

.PP
\fB CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q\&. \fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A,
 using the compact WY representation of Q\&.

 Based on the algorithm of Elmroth and Gustavson,
 IBM J\&. Res\&. Develop\&. Vol 44 No\&. 4 July 2000\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
          M is INTEGER
          The number of rows of the matrix A\&.  M >= N\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of columns of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          On entry, the complex M-by-N matrix A\&.  On exit, the elements on and
          above the diagonal contain the N-by-N upper triangular matrix R; the
          elements below the diagonal are the columns of V\&.  See below for
          further details\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector\&.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used\&.
          See below for 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 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The matrix V stores the elementary reflectors H(i) in the i-th column
  below the diagonal\&. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A\&.  The 1's along the diagonal of V are not stored in A\&.  The
  block reflector H is then given by

               H = I - V * T * V**H

  where V**H is the conjugate transpose of V\&.

  For details of the algorithm, see Elmroth and Gustavson (cited above)\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB131\fP of file \fBcgeqrt3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.