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SSYR2K(3S)							    SSYR2K(3S)

NAME
     SSYR2K, DSYR2K, CSYR2K, ZSYR2K - Performs symmetric rank 2k update of a
     real or complex symmetric matrix

SYNOPSIS
     Single precision

	  Fortran:
	       CALL SSYR2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

	  C/C++:
	       #include <scsl_blas.h>
	       void ssyr2k (char *uplo, char *trans, int n, int k, float
	       alpha, float *a, int lda, float *b, int ldb, float beta, float
	       *c, int ldc);

     Double precision

	  Fortran:
	       CALL DSYR2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

	  C/C++:
	       #include <scsl_blas.h>
	       void dsyr2k (char *uplo, char *trans, int n, int k, double
	       alpha, double *a, int lda, double *b, int ldb, double beta,
	       double *c, int ldc);

     Single precision complex

	  Fortran:
	       CALL CSYR2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

	  C/C++:
	       #include <scsl_blas.h>
	       void csyr2k (char *uplo, char *trans, int n, int k,
	       scsl_complex *alpha, scsl_complex *a, int lda, scsl_complex *b,
	       int ldb, scsl_complex *beta, scsl_complex *c, int ldc);

	  C++ STL:
	       #include <complex.h>
	       void csyr2k (char *uplo, char *trans, int n, int k,
	       complex<float> *alpha, scsl_complex *a, int lda, complex<float>
	       *b, int ldb, complex<float> *beta, complex<float> *c, int ldc);

     Double precision complex

	  Fortran:
	       CALL ZSYR2K (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
	       ldc)

									Page 1

SSYR2K(3S)							    SSYR2K(3S)

	  C/C++:
	       #include <scsl_blas.h>
	       void zsyr2k (char *uplo, char *trans, int n, int k,
	       scsl_zomplex *alpha, scsl_zomplex *a, int lda, scsl_zomplex *b,
	       int ldb, scsl_zomplex *beta, scsl_zomplex *c, int ldc);

	  C++ STL:
	       #include <complex.h>
	       void zsyr2k (char *uplo, char *trans, int n, int k,
	       complex<double> *alpha, complex<double> *a, int lda,
	       complex<double> *b, int ldb, complex<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
     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
     SSYR2K and DSYR2K performs a symmetric rank 2k update of a real symmetric
     matrix.

     CSYR2K and ZSYR2K performs a symmetric rank 2k update of a complex
     symmetric matrix.

     These routines perform one of the following symmetric rank 2k operations:

	  C <- alpha ABT + alpha BAT + beta C

	  or

	  C <- alpha ATB + alpha BTA + beta C

     where

     *	 alpha and beta are scalars

									Page 2

SSYR2K(3S)							    SSYR2K(3S)

     *	 C is an n-by-n symmetric matrix

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

     *	 AT and BT are transposes of A and B, respectively

     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 ABT + alpha BAT + beta C

	       trans = 'T' or 't':  C <- alpha ATB + alpha BTA + beta C

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

     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 = 'T' or 't', k specifies the number of
	       rows of matrices A and B.

	       k must be >= 0.

     alpha     Scalar factor.  (input)
	       SSYR2K: Single precision.
	       DSYR2K: Double precision.
	       CSYR2K: Single precision complex.
	       ZSYR2K: Double precision complex.

									Page 3

SSYR2K(3S)							    SSYR2K(3S)

	       For C/C++, a pointer to this scalar is passed when alpha is
	       complex; otherwise, alpha is passed by value.

     a	       Array of dimension (lda,ka).  (input)
	       SSYR2K: Single precision array.
	       DSYR2K: Double precision array.
	       CSYR2K: Single precision complex array.
	       ZSYR2K: Double precision complex array.
	       When trans = 'N' or 'n', ka is k; otherwise, it is n.  Contains
	       the 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)
	       SSYR2K: Single precision array.
	       DSYR2K: Double precision array.
	       CSYR2K: Single precision complex array.
	       ZSYR2K:	Double precision complex array.

	       When trans = 'N' or 'n', kb is k; otherwise, it is n.  Contains
	       the 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).

     beta      Scalar factor.  (input)
	       SSYR2K: Single precision.
	       DSYR2K: Double precision.
	       CSYR2K: Single precision complex.
	       ZSYR2K: Double precision complex.

	       For C/C++, a pointer to this scalar is passed when beta is
	       complex; otherwise, beta is passed by value.

     c	       Array of dimension (ldc,n).  (input and output)
	       SSYR2K: Single precision array.
	       DSYR2K: Double precision array.
	       CSYR2K: Single precision complex array.
	       ZSYR2K: Double precision complex array.

									Page 4

SSYR2K(3S)							    SSYR2K(3S)

	       Contains the 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 symmetric 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 symmetric 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.

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

NOTES
     These routines are Level 3 Basic Linear Algebra Subprograms (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])

	  Single precision		REAL

	  Double precision		DOUBLE PRECISION

	  Single precision complex	COMPLEX

	  Double precision complex	DOUBLE COMPLEX

     C/C++:

									Page 5

SSYR2K(3S)							    SSYR2K(3S)

	  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.

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS3(3S), CHER2K(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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