cgehrd (3p)

Name

cgehrd - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

Synopsis

SUBROUTINE CGEHRD(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, INFO)

COMPLEX A(LDA,*), TAU(*), WORKIN(*)
INTEGER N, ILO, IHI, LDA, LWORKIN, INFO

SUBROUTINE CGEHRD_64(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, INFO)

COMPLEX A(LDA,*), TAU(*), WORKIN(*)
INTEGER*8 N, ILO, IHI, LDA, LWORKIN, INFO




F95 INTERFACE
SUBROUTINE GEHRD(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN,
INFO)

COMPLEX, DIMENSION(:) :: TAU, WORKIN
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, ILO, IHI, LDA, LWORKIN, INFO

SUBROUTINE GEHRD_64(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN,
INFO)

COMPLEX, DIMENSION(:) :: TAU, WORKIN
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, ILO, IHI, LDA, LWORKIN, INFO




C INTERFACE
#include <sunperf.h>

void cgehrd(int n, int ilo, int ihi, complex *a, int lda, complex *tau,
int *info);

void  cgehrd_64(long  n, long ilo, long ihi, complex *a, long lda, com-
plex *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           cgehrd(3P)



NAME
       cgehrd  -  reduce a complex general matrix A to upper Hessenberg form H
       by a unitary similarity transformation


SYNOPSIS
       SUBROUTINE CGEHRD(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, INFO)

       COMPLEX A(LDA,*), TAU(*), WORKIN(*)
       INTEGER N, ILO, IHI, LDA, LWORKIN, INFO

       SUBROUTINE CGEHRD_64(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN, INFO)

       COMPLEX A(LDA,*), TAU(*), WORKIN(*)
       INTEGER*8 N, ILO, IHI, LDA, LWORKIN, INFO




   F95 INTERFACE
       SUBROUTINE GEHRD(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN,
              INFO)

       COMPLEX, DIMENSION(:) :: TAU, WORKIN
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER :: N, ILO, IHI, LDA, LWORKIN, INFO

       SUBROUTINE GEHRD_64(N, ILO, IHI, A, LDA, TAU, WORKIN, LWORKIN,
              INFO)

       COMPLEX, DIMENSION(:) :: TAU, WORKIN
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER(8) :: N, ILO, IHI, LDA, LWORKIN, INFO




   C INTERFACE
       #include <sunperf.h>

       void cgehrd(int n, int ilo, int ihi, complex *a, int lda, complex *tau,
                 int *info);

       void  cgehrd_64(long  n, long ilo, long ihi, complex *a, long lda, com-
                 plex *tau, long *info);



PURPOSE
       cgehrd reduces a complex general matrix A to upper Hessenberg form H by
       a unitary similarity transformation:  Q**H * A * Q = H .


ARGUMENTS
       N (input) The order of the matrix A.  N >= 0.


       ILO (input)
                 It  is assumed that A is already upper triangular in rows and
                 columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set  by
                 a  previous call to CGEBAL; otherwise they should be set to 1
                 and N respectively. See Further Details.


       IHI (input)
                 See the description of ILO.


       A (input/output)
                 On entry, the N-by-N general matrix to be reduced.  On  exit,
                 the  upper  triangle and the first subdiagonal of A are over-
                 written with the upper Hessenberg matrix H, and the  elements
                 below  the  first  subdiagonal, with the array TAU, represent
                 the unitary matrix Q as a product of  elementary  reflectors.
                 See Further Details.


       LDA (input)
                 The leading dimension of the array A. LDA >= max(1,N).


       TAU (output) COMPLEX array, dimension (N-1)
                 The  scalar factors of the elementary reflectors (see Further
                 Details). Elements 1:ILO-1 and IHI:N-1  of  TAU  are  set  to
                 zero.


       WORKIN (workspace)
                 On  exit, if INFO = 0, WORKIN(1) returns the optimal LWORKIN.


       LWORKIN (input)
                 The length of the array WORKIN.  LWORKIN  >=  max(1,N).   For
                 optimum  performance LWORKIN >= N*NB, where NB is the optimal
                 blocksize.

                 If LWORKIN = -1, then a workspace query is assumed; the  rou-
                 tine  only  calculates  the optimal size of the WORKIN array,
                 returns this value as the first entry of  the  WORKIN  array,
                 and  no error message related to LWORKIN is issued by XERBLA.


       INFO (output)
                 = 0:  successful exit;
                 < 0:  if INFO = -i, the i-th argument had an illegal value.


FURTHER DETAILS
       The matrix Q is  represented  as  a  product  of  (ihi-ilo)  elementary
       reflectors

          Q = H(ilo) H(ilo+1) . . . H(ihi-1).

       Each H(i) has the form

          H(i) = I - tau * v * v**H

       where  tau is a complex scalar, and v is a complex vector with v(1:i) =
       0, v(i+1) = 1 and v(ihi+1:n) = 0;  v(i+2:ihi)  is  stored  on  exit  in
       A(i+2:ihi,i), and tau in TAU(i).

       The contents of A are illustrated by the following example, with n = 7,
       ilo = 2 and ihi = 6:

       on entry,                on exit,

       (a  a  a  a  a  a  a)    (a  a   h   h   h  h  a)
       (   a  a  a  a  a  a)    (   a   h   h   h  h  a)
       (   a  a  a  a  a  a)    (   h   h   h   h  h  h)
       (   a  a  a  a  a  a)    (   v2  h   h   h  h  h)
       (   a  a  a  a  a  a)    (   v2  v3  h   h  h  h)
       (   a  a  a  a  a  a)    (   v2  v3  v4  h  h  h)
       (                  a)    (                     a)

       where a denotes an element of the original matrix A, h denotes a  modi-
       fied  element  of the upper Hessenberg matrix H, and vi denotes an ele-
       ment of the vector defining H(i).




                                  7 Nov 2015                        cgehrd(3P)