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Updated: June 2017
 
 

zsytrf (3p)

Name

zsytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

Synopsis

SUBROUTINE ZSYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER N, LDA, LDWORK, INFO
INTEGER IPIVOT(*)

SUBROUTINE ZSYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, LDA, LDWORK, INFO
INTEGER*8 IPIVOT(*)




F95 INTERFACE
SUBROUTINE SYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, LDA, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT

SUBROUTINE SYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK,
INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT




C INTERFACE
#include <sunperf.h>

void zsytrf(char uplo, int n, doublecomplex *a, int lda,  int  *ipivot,
int *info);

void  zsytrf_64(char  uplo,  long  n,  doublecomplex *a, long lda, long
*ipivot, long *info);

Description

Oracle Solaris Studio Performance Library                           zsytrf(3P)



NAME
       zsytrf  -  compute  the  factorization  of a complex symmetric matrix A
       using the Bunch-Kaufman diagonal pivoting method


SYNOPSIS
       SUBROUTINE ZSYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*), WORK(*)
       INTEGER N, LDA, LDWORK, INFO
       INTEGER IPIVOT(*)

       SUBROUTINE ZSYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*), WORK(*)
       INTEGER*8 N, LDA, LDWORK, INFO
       INTEGER*8 IPIVOT(*)




   F95 INTERFACE
       SUBROUTINE SYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:) :: WORK
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER :: N, LDA, LDWORK, INFO
       INTEGER, DIMENSION(:) :: IPIVOT

       SUBROUTINE SYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK,
              INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:) :: WORK
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER(8) :: N, LDA, LDWORK, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT




   C INTERFACE
       #include <sunperf.h>

       void zsytrf(char uplo, int n, doublecomplex *a, int lda,  int  *ipivot,
                 int *info);

       void  zsytrf_64(char  uplo,  long  n,  doublecomplex *a, long lda, long
                 *ipivot, long *info);



PURPOSE
       zsytrf computes the factorization of a complex symmetric matrix A using
       the Bunch-Kaufman diagonal pivoting method.  The form of the factoriza-
       tion is

          A = U*D*U**T  or  A = L*D*L**T

       where U (or L) is a product of permutation and unit upper (lower)  tri-
       angular  matrices,  and  D  is  symmetric  and block diagonal with with
       1-by-1 and 2-by-2 diagonal blocks.

       This is the blocked version of the algorithm, calling Level 3 BLAS.


ARGUMENTS
       UPLO (input)
                 = 'U':  Upper triangle of A is stored;
                 = 'L':  Lower triangle of A is stored.


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


       A (input/output)
                 On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                 N-by-N upper triangular part of A contains the upper triangu-
                 lar 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)
                 The leading dimension of the array A.  LDA >= max(1,N).


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


       WORK (workspace)
                 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.


       LDWORK (input)
                 The length of WORK.  LDWORK >=1.  For best performance LDWORK
                 >= N*NB, where NB is the block size returned by ILAENV.

                 If  LDWORK  = -1, then a workspace query is assumed; the rou-
                 tine 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 LDWORK is issued by XERBLA.


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value
                 > 0:  if INFO = i, D(i,i) 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', 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 IPIVOT(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', 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 IPIVOT(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                        zsytrf(3P)