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
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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
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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).
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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])
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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.
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CHER2K(3S)CHER2K(3S)SEE ALSOINTRO_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.
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