her2k(3)

NAME
her2k - {he,sy}r2k: Hermitian/symmetric rank-2k update

SYNOPSIS

  Functions
subroutine cher2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CHER2K
subroutine csyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CSYR2K
subroutine dsyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DSYR2K
subroutine ssyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SSYR2K
subroutine zher2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZHER2K
subroutine zsyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZSYR2K

Detailed Description

Function Documentation

  subroutine cher2k (character uplo, character trans, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, real beta, complex, dimension(ldc,*) c, integer ldc)

CHER2K

Purpose:

     CHER2K  performs one of the hermitian rank 2k operations
        C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
     or
        C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
     where  alpha and beta  are scalars with  beta  real,  C is an  n by n
     hermitian matrix and  A and B  are  n by k matrices in the first case
     and  k by n  matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'    C := alpha*A*B**H          +
                                             conjg( alpha )*B*A**H +
                                             beta*C.
                  TRANS = 'C' or 'c'    C := alpha*A**H*B          +
                                             conjg( alpha )*B**H*A +
                                             beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'C' or 'c',  K  specifies  the number of rows of the
               matrices  A and B.  K must be at least zero.

    ALPHA

              ALPHA is COMPLEX
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is COMPLEX array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta.

    C

              C is COMPLEX array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  hermitian matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  hermitian matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set,  they are assumed to be zero,  and on exit they
               are set to zero.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.
      -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
         Ed Anderson, Cray Research Inc.

Definition at line 196 of file cher2k.f.

  subroutine csyr2k (character uplo, character trans, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

CSYR2K

Purpose:

     CSYR2K  performs one of the symmetric rank 2k operations
        C := alpha*A*B**T + alpha*B*A**T + beta*C,
     or
        C := alpha*A**T*B + alpha*B**T*A + beta*C,
     where  alpha and beta  are scalars,  C is an  n by n symmetric matrix
     and  A and B  are  n by k  matrices  in the  first  case  and  k by n
     matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'    C := alpha*A*B**T + alpha*B*A**T +
                                             beta*C.
                  TRANS = 'T' or 't'    C := alpha*A**T*B + alpha*B**T*A +
                                             beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'T' or 't',  K  specifies  the number of rows of the
               matrices  A and B.  K must be at least zero.

    ALPHA

              ALPHA is COMPLEX
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is COMPLEX array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is COMPLEX
               On entry, BETA specifies the scalar beta.

    C

              C is COMPLEX array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 187 of file csyr2k.f.

  subroutine dsyr2k (character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYR2K

Purpose:

     DSYR2K  performs one of the symmetric rank 2k operations
        C := alpha*A*B**T + alpha*B*A**T + beta*C,
     or
        C := alpha*A**T*B + alpha*B**T*A + beta*C,
     where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
     and  A and B  are  n by k  matrices  in the  first  case  and  k by n
     matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +
                                            beta*C.
                  TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.
                  TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
               of rows of the matrices  A and B.  K must be at least  zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is DOUBLE PRECISION.
               On entry, BETA specifies the scalar beta.

    C

              C is DOUBLE PRECISION array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 191 of file dsyr2k.f.

  subroutine ssyr2k (character uplo, character trans, integer n, integer k, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)

SSYR2K

Purpose:

     SSYR2K  performs one of the symmetric rank 2k operations
        C := alpha*A*B**T + alpha*B*A**T + beta*C,
     or
        C := alpha*A**T*B + alpha*B**T*A + beta*C,
     where  alpha and beta  are scalars, C is an  n by n  symmetric matrix
     and  A and B  are  n by k  matrices  in the  first  case  and  k by n
     matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +
                                            beta*C.
                  TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.
                  TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +
                                            beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'T' or 't' or 'C' or 'c',  K  specifies  the  number
               of rows of the matrices  A and B.  K must be at least  zero.

    ALPHA

              ALPHA is REAL
               On entry, ALPHA specifies the scalar alpha.

    A

              A is REAL array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is REAL array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is REAL
               On entry, BETA specifies the scalar beta.

    C

              C is REAL array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 191 of file ssyr2k.f.

  subroutine zher2k (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, double precision beta, complex*16, dimension(ldc,*) c, integer ldc)

ZHER2K

Purpose:

     ZHER2K  performs one of the hermitian rank 2k operations
        C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
     or
        C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
     where  alpha and beta  are scalars with  beta  real,  C is an  n by n
     hermitian matrix and  A and B  are  n by k matrices in the first case
     and  k by n  matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'    C := alpha*A*B**H          +
                                             conjg( alpha )*B*A**H +
                                             beta*C.
                  TRANS = 'C' or 'c'    C := alpha*A**H*B          +
                                             conjg( alpha )*B**H*A +
                                             beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'C' or 'c',  K  specifies  the number of rows of the
               matrices  A and B.  K must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16 .
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).
               Unchanged on exit.

    BETA

              BETA is DOUBLE PRECISION .
               On entry, BETA specifies the scalar beta.

    C

              C is COMPLEX*16 array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  hermitian matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  hermitian matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set,  they are assumed to be zero,  and on exit they
               are set to zero.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.
      -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
         Ed Anderson, Cray Research Inc.

Definition at line 197 of file zher2k.f.

  subroutine zsyr2k (character uplo, character trans, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)

ZSYR2K

Purpose:

     ZSYR2K  performs one of the symmetric rank 2k operations
        C := alpha*A*B**T + alpha*B*A**T + beta*C,
     or
        C := alpha*A**T*B + alpha*B**T*A + beta*C,
     where  alpha and beta  are scalars,  C is an  n by n symmetric matrix
     and  A and B  are  n by k  matrices  in the  first  case  and  k by n
     matrices in the second case.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On  entry,   UPLO  specifies  whether  the  upper  or  lower
               triangular  part  of the  array  C  is to be  referenced  as
               follows:
                  UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                                      is to be referenced.

    TRANS

              TRANS is CHARACTER*1
               On entry,  TRANS  specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'    C := alpha*A*B**T + alpha*B*A**T +
                                             beta*C.
                  TRANS = 'T' or 't'    C := alpha*A**T*B + alpha*B**T*A +
                                             beta*C.

    N

              N is INTEGER
               On entry,  N specifies the order of the matrix C.  N must be
               at least zero.

    K

              K is INTEGER
               On entry with  TRANS = 'N' or 'n',  K  specifies  the number
               of  columns  of the  matrices  A and B,  and on  entry  with
               TRANS = 'T' or 't',  K  specifies  the number of rows of the
               matrices  A and B.  K must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  A  must contain the matrix  A,  otherwise
               the leading  k by n  part of the array  A  must contain  the
               matrix A.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDA must be at least  max( 1, n ), otherwise  LDA must
               be at least  max( 1, k ).

    B

              B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is
               k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
               Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
               part of the array  B  must contain the matrix  B,  otherwise
               the leading  k by n  part of the array  B  must contain  the
               matrix B.

    LDB

              LDB is INTEGER
               On entry, LDB specifies the first dimension of B as declared
               in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
               then  LDB must be at least  max( 1, n ), otherwise  LDB must
               be at least  max( 1, k ).

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta.

    C

              C is COMPLEX*16 array, dimension ( LDC, N )
               Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
               upper triangular part of the array C must contain the upper
               triangular part  of the  symmetric matrix  and the strictly
               lower triangular part of C is not referenced.  On exit, the
               upper triangular part of the array  C is overwritten by the
               upper triangular part of the updated matrix.
               Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
               lower triangular part of the array C must contain the lower
               triangular part  of the  symmetric matrix  and the strictly
               upper triangular part of C is not referenced.  On exit, the
               lower triangular part of the array  C is overwritten by the
               lower triangular part of the updated matrix.

    LDC

              LDC is INTEGER
               On entry, LDC specifies the first dimension of C as declared
               in  the  calling  (sub)  program.   LDC  must  be  at  least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 3 Blas routine.
      -- Written on 8-February-1989.
         Jack Dongarra, Argonne National Laboratory.
         Iain Duff, AERE Harwell.
         Jeremy Du Croz, Numerical Algorithms Group Ltd.
         Sven Hammarling, Numerical Algorithms Group Ltd.

Definition at line 187 of file zsyr2k.f.

Author

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