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Updated: June 2017
 
 

zhetf2_rook (3p)

Name

zhetf2_rook - nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm)

Synopsis

SUBROUTINE ZHETF2_ROOK(UPLO, N, A, LDA, IPIV, INFO)


CHARACTER*1 UPLO

INTEGER INFO, LDA, N

INTEGER IPIV(*)

DOUBLE COMPLEX A(LDA,*)


SUBROUTINE ZHETF2_ROOK_64(UPLO, N, A, LDA, IPIV, INFO)


CHARACTER*1 UPLO

INTEGER*8 INFO, LDA, N

INTEGER*8 IPIV(*)

DOUBLE COMPLEX A(LDA,*)


F95 INTERFACE
SUBROUTINE HETF2_ROOK(UPLO, N, A, LDA, IPIV, INFO)


INTEGER :: N, LDA, INFO

CHARACTER(LEN=1) :: UPLO

INTEGER, DIMENSION(:) :: IPIV

COMPLEX(8), DIMENSION(:,:) :: A


SUBROUTINE HETF2_ROOK_64(UPLO, N, A, LDA, IPIV, INFO)


INTEGER(8) :: N, LDA, INFO

CHARACTER(LEN=1) :: UPLO

INTEGER(8), DIMENSION(:) :: IPIV

COMPLEX(8), DIMENSION(:,:) :: A


C INTERFACE
#include <sunperf.h>

void  zhetf2_rook  (char  uplo,  int  n, doublecomplex *a, int lda, int
*ipiv, int *info);


void zhetf2_rook_64 (char uplo, long n,  doublecomplex  *a,  long  lda,
long *ipiv, long *info);

Description

Oracle Solaris Studio Performance Library                      zhetf2_rook(3P)



NAME
       zhetf2_rook  - compute the factorization of a complex Hermitian indefi-
       nite matrix using the bounded Bunch-Kaufman ("rook") diagonal  pivoting
       method (unblocked algorithm)


SYNOPSIS
       SUBROUTINE ZHETF2_ROOK(UPLO, N, A, LDA, IPIV, INFO)


       CHARACTER*1 UPLO

       INTEGER INFO, LDA, N

       INTEGER IPIV(*)

       DOUBLE COMPLEX A(LDA,*)


       SUBROUTINE ZHETF2_ROOK_64(UPLO, N, A, LDA, IPIV, INFO)


       CHARACTER*1 UPLO

       INTEGER*8 INFO, LDA, N

       INTEGER*8 IPIV(*)

       DOUBLE COMPLEX A(LDA,*)


   F95 INTERFACE
       SUBROUTINE HETF2_ROOK(UPLO, N, A, LDA, IPIV, INFO)


       INTEGER :: N, LDA, INFO

       CHARACTER(LEN=1) :: UPLO

       INTEGER, DIMENSION(:) :: IPIV

       COMPLEX(8), DIMENSION(:,:) :: A


       SUBROUTINE HETF2_ROOK_64(UPLO, N, A, LDA, IPIV, INFO)


       INTEGER(8) :: N, LDA, INFO

       CHARACTER(LEN=1) :: UPLO

       INTEGER(8), DIMENSION(:) :: IPIV

       COMPLEX(8), DIMENSION(:,:) :: A


   C INTERFACE
       #include <sunperf.h>

       void  zhetf2_rook  (char  uplo,  int  n, doublecomplex *a, int lda, int
                 *ipiv, int *info);


       void zhetf2_rook_64 (char uplo, long n,  doublecomplex  *a,  long  lda,
                 long *ipiv, long *info);


PURPOSE
       zhetf2_rook  computes the factorization of a complex Hermitian matrix A
       using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:

       A = U*D*U**H  or  A = L*D*L**H

       where U (or L) is a product of permutation and unit upper (lower)  tri-
       angular matrices, U**H is the conjugate transpose of U, and D is Hermi-
       tian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

       This is the unblocked version of the algorithm, calling Level 2 BLAS.


ARGUMENTS
       UPLO (input)
                 UPLO is CHARACTER*1
                 Specifies whether the upper or lower triangular part  of  the
                 Hermitian matrix A is stored:
                 = 'U':  Upper triangular;
                 = 'L':  Lower triangular.


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


       A (input/output)
                 A is COMPLEX*16 array, dimension (LDA,N)
                 On entry, the Hermitian matrix A.
                 If  UPLO = 'U', the leading n-by-n upper triangular part of A
                 contains the upper triangular part of the matrix A,  and  the
                 strictly lower triangular part of A is not referenced.
                 If  UPLO = 'L', the leading n-by-n lower triangular part of A
                 contains the lower triangular part of the matrix A,  and  the
                 strictly upper triangular part of A is not referenced.
                 On exit, the block diagonal matrix D and the multipliers used
                 to obtain the factor U or L (see below for further  details).


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


       IPIV (output)
                 IPIV is INTEGER array, dimension (N)
                 Details of the interchanges and the block structure of D.
                 If UPLO = 'U':
                 If  IPIV(k)  >  0,  then  rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and
                 -IPIV(k)  were  interchanged  and  rows  and  columns k-1 and
                 -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diago-
                 nal block.
                 If UPLO = 'L':
                 If  IPIV(k)  >  0,  then  rows and columns k and IPIV(k) were
                 interchanged and D(k,k) is a 1-by-1 diagonal block.
                 If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and
                 -IPIV(k)  were  interchanged  and  rows  and  columns k+1 and
                 -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diago-
                 nal block.


       INFO (output)
                 INFO is INTEGER
                 = 0: successful exit;
                 < 0: if INFO = -k, the k-th argument had an illegal value;
                 >  0:  if INFO = k, D(k,k) is exactly zero. The factorization
                 has been completed,  but  the  block  diagonal  matrix  D  is
                 exactly  singular,  and  division by zero will occur if it is
                 used to solve a system of equations.


FURTHER DETAILS
       If UPLO = 'U', then A = U*D*U**H, where
          U = P(n)*U(n)* ... *P(k)U(k)* ...,
       i.e., U is a product of terms P(k)*U(k), where k decreases from n to  1
       in  steps  of  1 or 2, and D is a block diagonal matrix with 1-by-1 and
       2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix  as  defined
       by  IPIV(k),  and  U(k) is a unit upper triangular matrix, such that if
       the diagonal block D(k) is of order s (s = 1 or 2), then
                    (   I    v    0   )   k-s
            U(k) =  (   0    I    0   )   s
                    (   0    0    I   )   n-k
                       k-s   s   n-k


   If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
       If s = 2, the upper triangle of D(k) overwrites  A(k-1,k-1),  A(k-1,k),
       and A(k,k), and v overwrites A(1:k-2,k-1:k).

       If  UPLO = 'L', then A = L*D*L**H, where L = P(1)*L(1)* ... *P(k)*L(k)*
       ..., i.e., L is a product of terms P(k)*L(k), where k increases from  1
       to  n  in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
       and 2-by-2 diagonal blocks D(k).   P(k)  is  a  permutation  matrix  as
       defined  by  IPIV(k),  and L(k) is a unit lower triangular matrix, such
       that if the diagonal block D(k) is of order s (s = 1 or 2), then

                    (   I    0     0   )  k-1
            L(k) =  (   0    I     0   )  s
                    (   0    v     I   )  n-k-s+1
                       k-1   s  n-k-s+1


   If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
       If s = 2, the lower triangle of D(k) overwrites A(k,k),  A(k+1,k),  and
       A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).



                                  7 Nov 2015                   zhetf2_rook(3P)