her2k - Man Page

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

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

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

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

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

          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 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 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 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, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, double precision beta, complex16, 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 is INTEGER
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.

          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 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 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 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, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, complex16 beta, complex16, 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 is INTEGER
           On entry,  N specifies the order of the matrix C.  N must be
           at least zero.

          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 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 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 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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Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK

her2k - Man Page

Synopsis

Functions

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)

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)

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)

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)

subroutine zher2k (character uplo, character trans, integer n, integer k, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, double precision beta, complex16, dimension(ldc,*) c, integer ldc)

subroutine zsyr2k (character uplo, character trans, integer n, integer k, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, complex16 beta, complex16, dimension(ldc,) c, integer ldc)

Author

Info

Synopsis

Functions

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)

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)

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)

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)

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)

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)

Author

Info

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)

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)

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)

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)

subroutine zher2k (character uplo, character trans, integer n, integer k, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, double precision beta, complex16, dimension(ldc,*) c, integer ldc)

subroutine zsyr2k (character uplo, character trans, integer n, integer k, complex16 alpha, complex16, dimension(lda,) a, integer lda, complex16, dimension(ldb,) b, integer ldb, complex16 beta, complex16, dimension(ldc,) c, integer ldc)