ssyr2k(3S)
SSYR2K, DSYR2K, CSYR2K, ZSYR2K - Performs symmetric rank 2k update of a real or complex symmetric matrix
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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) 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 * 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. 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. 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++: 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.