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

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

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

.PP
.nf
!>
!> ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
!> using the compact WY representation of Q\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The block size to be used in the blocked QR\&.  MIN(M,N) >= NB >= 1\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit, the elements on and above the diagonal of the array
!>          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
!>          upper triangular if M >= N); the elements below the diagonal
!>          are the columns of V\&.
!> 
.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*16 array, dimension (LDT,MIN(M,N))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks\&.  See below
!>          for 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 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\&.
!>
!>  Let K=MIN(M,N)\&.  The number of blocks is B = ceiling(K/NB), where each
!>  block is of order NB except for the last block, which is of order
!>  IB = K - (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-K matrix T as
!>
!>               T = (T1 T2 \&.\&.\&. TB)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB140\fP of file \fBzgeqrt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.