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Updated: June 2017
 
 

csytf2 (3p)

Name

csytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

Synopsis

SUBROUTINE CSYTF2(UPLO, N, A, LDA, IPIV, INFO)

CHARACTER*1 UPLO
COMPLEX A(LDA,*)
INTEGER N, LDA, INFO
INTEGER IPIV(*)

SUBROUTINE CSYTF2_64(UPLO, N, A, LDA, IPIV, INFO)

CHARACTER*1 UPLO
COMPLEX A(LDA,*)
INTEGER*8 N, LDA, INFO
INTEGER*8 IPIV(*)




F95 INTERFACE
SUBROUTINE SYTF2(UPLO, N, A, LDA, IPIV, INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, LDA, INFO
INTEGER, DIMENSION(:) :: IPIV

SUBROUTINE SYTF2_64(UPLO, N, A, LDA, IPIV, INFO)

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




C INTERFACE
#include <sunperf.h>

void csytf2(char uplo, int n, complex  *a,  int  lda,  int  *ipiv,  int
*info);

void  csytf2_64(char  uplo,  long  n, complex *a, long lda, long *ipiv,
long *info);

Description

Oracle Solaris Studio Performance Library                           csytf2(3P)



NAME
       csytf2  -  compute  the  factorization  of a complex symmetric matrix A
       using the Bunch-Kaufman diagonal pivoting method


SYNOPSIS
       SUBROUTINE CSYTF2(UPLO, N, A, LDA, IPIV, INFO)

       CHARACTER*1 UPLO
       COMPLEX A(LDA,*)
       INTEGER N, LDA, INFO
       INTEGER IPIV(*)

       SUBROUTINE CSYTF2_64(UPLO, N, A, LDA, IPIV, INFO)

       CHARACTER*1 UPLO
       COMPLEX A(LDA,*)
       INTEGER*8 N, LDA, INFO
       INTEGER*8 IPIV(*)




   F95 INTERFACE
       SUBROUTINE SYTF2(UPLO, N, A, LDA, IPIV, INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:,:) :: A
       INTEGER :: N, LDA, INFO
       INTEGER, DIMENSION(:) :: IPIV

       SUBROUTINE SYTF2_64(UPLO, N, A, LDA, IPIV, INFO)

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




   C INTERFACE
       #include <sunperf.h>

       void csytf2(char uplo, int n, complex  *a,  int  lda,  int  *ipiv,  int
                 *info);

       void  csytf2_64(char  uplo,  long  n, complex *a, long lda, long *ipiv,
                 long *info);



PURPOSE
       csytf2 computes the factorization of a complex symmetric matrix A using
       the Bunch-Kaufman diagonal pivoting method:

          A = U*D*U'  or  A = L*D*L'

       where  U (or L) is a product of permutation and unit upper (lower) tri-
       angular matrices, U' is the transpose of U,  and  D  is  symmetric  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)
                 Specifies  whether  the upper or lower triangular part of the
                 symmetric matrix A is stored:
                 = 'U':  Upper triangular
                 = 'L':  Lower triangular


       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).


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


       INFO (output)
                 = 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
       1-96 - Based on modifications by J. Lewis, Boeing Computer Services
              Company

       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  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', 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                        csytf2(3P)