cher2k(3S)
CHER2K, ZHER2K - Performs Hermitian rank 2k update of a complex Hermitian matrix
As shipped in IRIX 6.5.19. Added in IRIX 6.5.15.
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 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 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). 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]) 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), 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.