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

.in +1c
.ti -1c
.RI "subroutine \fBzgebrd\fP (m, n, a, lda, d, e, tauq, taup, work, lwork, info)"
.br
.RI "\fBZGEBRD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgebrd (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( * ) tauq, complex*16, dimension( * ) taup, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> ZGEBRD reduces a general complex M-by-N matrix A to upper or lower
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B\&.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows in the matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns in the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced\&.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the unitary matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the unitary matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors\&.
!>          See 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
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B:
!>          D(i) = A(i,i)\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,\&.\&.\&.,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,\&.\&.\&.,m-1\&.
!> 
.fi
.PP
.br
\fITAUQ\fP 
.PP
.nf
!>          TAUQ is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix Q\&. See Further Details\&.
!> 
.fi
.PP
.br
\fITAUP\fP 
.PP
.nf
!>          TAUP is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix P\&. See Further Details\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The length of the array WORK\&.
!>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise\&.
!>          For optimum performance LWORK >= (M+N)*NB, where NB
!>          is the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.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 matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) \&. \&. \&. H(n)  and  P = G(1) G(2) \&. \&. \&. G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i)\&.
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) \&. \&. \&. H(m-1)  and  P = G(1) G(2) \&. \&. \&. G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i)\&.
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i)\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB204\fP of file \fBzgebrd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.