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CHER2K(3S)							    CHER2K(3S)

NAME
     CHER2K, ZHER2K - Performs Hermitian rank 2k update of a complex Hermitian
     matrix

SYNOPSIS
     Single precision complex

	  Fortran:
	       CALL CHER2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

	  C/C++:
	       #include <scsl_blas.h>
	       void cher2k (char *uplo, char *trans, int n, int k,
	       scsl_complex *alpha, scsl_complex *a, int lda, scsl_complex *b,
	       int ldb, float *beta, scsl_complex *c, int ldc);

	  C++ STL:
	       #include <complex.h>
	       void cher2k (char *uplo, char *trans, int n, int k,
	       complex<float> *alpha, scsl_complex *a, int lda, complex<float>
	       *b, int ldb, float *beta, complex<float> *c, int ldc);

     Double precision complex

	  Fortran:
	       CALL ZHER2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

	  C/C++:
	       #include <scsl_blas.h>
	       void zher2k (char *uplo, char *trans, int n, int k,
	       scsl_zomplex *alpha, scsl_zomplex *a, int lda, scsl_zomplex *b,
	       int ldb, double *beta, scsl_zomplex *c, int ldc);

	  C++ STL:
	       #include <complex.h>
	       void zher2k (char *uplo, char *trans, int n, int k,
	       complex<double> *alpha, complex<double> *a, int lda,
	       complex<double> *b, int ldb, double *beta, complex<double> *c,
	       int ldc);

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use

									Page 1

CHER2K(3S)							    CHER2K(3S)

     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

     The C and C++ prototypes shown above are appropriate for the 4-byte
     integer version of SCSL. When using the 8-byte integer version, the
     variables of type int become long long and the <scsl_blas_i8.h> header
     file should be included.

DESCRIPTION
     These routines perform a Hermitian rank 2k update of a complex Hermitian
     matrix.  They perform one of the following Hermitian rank 2k operations:

	  C <- alpha ABH + conj(alpha) BAH + beta*C

	  C <- alpha AHB + conj(alpha) BHA + beta*C

     where the following is true:

     *	 AH and BH are the conjugate transposes of A and B, respectively;

     *	 alpha and beta are scalars;

     *	 C is an n-by-n Hermitian matrix,

     *	 A and B are n-by-k matrices in the first operation listed previously,
	 and k-by-n matrices in the second.

     See the NOTES section of this man page for information about the
     interpretation of the data types described in the following arguments.

     These routines have the following arguments:

     uplo      Character.  (input)
	       Specifies whether the upper or lower triangular part of array c
	       is referenced, as follows:

	       uplo = 'U' or 'u': only the upper triangular part of c is
	       referenced.
	       uplo = 'L' or 'l': only the lower triangular part of c is
	       referenced.

	       For C/C++, a pointer to this character is passed.

     trans     Character.  (input)
	       Specifies the operation to be performed, as follows:

	       trans = 'N' or 'n':  C <- alpha ABH + conj(alpha) BAH + beta*C

	       trans = 'C' or 'c':  C <- alpha AHB + conj(alpha) BHA + beta*C

									Page 2

CHER2K(3S)							    CHER2K(3S)

     n	       Integer.	 (input)
	       Specifies the order of matrix C.	 n must be >= 0.

     k	       Integer.	 (input)

	       On entry with trans = 'N' or 'n', k specifies the number of
	       columns of matrices A and B.

	       On entry with trans = 'C' or 'c', k specifies the number of
	       rows of matrices A and B.

	       k must be >= 0.

     alpha     First scalar factor.  (input)
	       CHER2K: Single precision complex.
	       ZHER2K: Double precision complex.

	       For C/C++, a pointer to this scalar is passed.

     a	       Array of dimension (lda,ka).  (input)
	       CHER2K: Single precision complex array.
	       ZHER2K: Double precision complex array.
	       When trans = 'N' or 'n', ka is k; otherwise, it is n.  Contains
	       matrix A.

	       Before entry with trans = 'N' or 'n', the leading n-by-k part
	       of array a must contain matrix A; otherwise, the leading k-by-n
	       part of array a must contain matrix A.

     lda       Integer.	 (input)
	       Specifies the first dimension of a as declared in the calling
	       program.

	       If trans = 'N' or 'n', lda >= MAX(1,n); otherwise, lda >=
	       MAX(1,k).

     b	       Array of dimension (ldb,kb).  (input)
	       CHER2K: Single precision complex array.
	       ZHER2K: Double precision complex array.
	       When trans = 'N' or 'n', kb is k; otherwise, it is n.  Contains
	       matrix B.

	       Before entry with trans = 'N' or 'n', the leading n-by-k part
	       of array b must contain matrix B; otherwise, the leading k-by-n
	       part of array b must contain matrix B.

     ldb       Integer.	 (input)
	       Specifies the first dimension of b as declared in the calling
	       program.	 If trans = 'N' or 'n', ldb >= MAX(1,n); otherwise,
	       ldb >= MAX(1,k).

									Page 3

CHER2K(3S)							    CHER2K(3S)

     beta      First scalar factor.  (input)
	       CHER2K: Single precision.
	       ZHER2K: Double precision.

     c	       Array of dimension (ldc,n).  (input)
	       CHER2K: Single precision complex array.
	       ZHER2K: Double precision complex array.
	       Contains matrix C.

	       Before entry with uplo = 'U' or 'u', the leading n-by-n upper
	       triangular part of array c must contain the upper triangular
	       part of the Hermitian matrix.  The strictly lower triangular
	       part of c is not referenced.  On exit, the upper triangular
	       part of the updated matrix overwrites the upper triangular part
	       of array c.

	       Before entry with uplo = 'L' or 'l', the leading n-by-n lower
	       triangular part of array c must contain the lower triangular
	       part of the Hermitian matrix.  The strictly upper triangular
	       part of c is not referenced.  On exit, the lower triangular
	       part of the updated matrix overwrites the lower triangular part
	       of array c.

	       The imaginary parts of the diagonal elements need not be set
	       and are assumed to be 0.	 On exit, they are set to 0.

     ldc       Integer.	 (input)
	       Specifies the first dimension of c as declared in the calling
	       program.	 ldc >= MAX(1,n).

NOTES
     CHER2K/ZHER2K is a Level 3 Basic Linear Algebra Subprogram (Level 3
     BLAS).

   Data Types
     The following data types are described in this documentation:

	  Term Used			Data type

     Fortran:

	  Array dimensioned n		x(n)

	  Array of dimensions (m,n)	x(m,n)

	  Character			CHARACTER

	  Integer			INTEGER (INTEGER*8 for -lscs_i8[_mp])

									Page 4

CHER2K(3S)							    CHER2K(3S)

	  Single precision		REAL

	  Double precision		DOUBLE PRECISION

	  Single precision complex	COMPLEX

	  Double precision complex	DOUBLE COMPLEX

     C/C++:

	  Array dimensioned n		x[n]

	  Array of dimensions (m,n)	x[m*n]

	  Character			char

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	scsl_complex

	  Double precision complex	scsl_zomplex

     C++ STL:

	  Array dimensioned n		x[n]

	  Array of dimensions (m,n)	x[m*n]

	  Character			char

	  Integer			int (long long for -lscs_i8[_mp])

	  Single precision		float

	  Double precision		double

	  Single precision complex	complex<float>

	  Double precision complex	complex<double>

     Note that you can explicitly declare multidimensional C/C++ arrays
     provided that the array dimensions are swapped with respect to the
     Fortran declaration (e.g., x[n][m] in C/C++ versus x(m,n) in Fortran).
     To avoid a compiler type mismatch error in C++ (or a compiler warning
     message in C), however, the array should be cast to a pointer of the
     appropriate type when passed as an argument to a SCSL routine.

									Page 5

CHER2K(3S)							    CHER2K(3S)

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS3(3S), SSYR2K(3S)

     INTRO_CBLAS(3S) for information about using the C interface to Fortran 77
     Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic
     Linear Algebra Subprograms Technical Forum.

									Page 6

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