SSYR(3S)SSYR(3S)NAME
SSYR, DSYR, CSYR, ZSYR - Performs symmetric rank 1 update of a real or
complex symmetric matrix
SYNOPSIS
Single precision
Fortran:
CALL SSYR (uplo, n, alpha, x, incx, a, lda)
C/C++:
#include <scsl_blas.h>
void ssyr (char *uplo, int n, float alpha, float *x, int incx,
float *a, int lda);
Double precision
Fortran:
CALL DSYR (uplo, n, alpha, x, incx, a, lda)
C/C++:
#include <scsl_blas.h>
void dsyr (char *uplo, int n, double alpha, double *x, int
incx, double *a, int lda);
Single precision complex
Fortran:
CALL CSYR (uplo, n, alpha, x, incx, a, lda)
C/C++:
#include <scsl_blas.h>
void csyr (char *uplo, int n, scsl_complex *alpha, scsl_complex
*x, int incx, scsl_complex *a, int lda);
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void csyr (char *uplo, int n, complex<float> *alpha,
complex<float> *x, int incx, complex<float> *a, int lda);
Double precision complex
Fortran:
CALL ZSYR (uplo, n, alpha, x, incx, a, lda)
C/C++:
#include <scsl_blas.h>
void zsyr (char *uplo, int n, scsl_zomplex *alpha, scsl_zomplex
*x, int incx, scsl_zomplex *a, int lda);
Page 1
SSYR(3S)SSYR(3S)
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void zsyr (char *uplo, int n, complex<double> *alpha,
complex<double> *x, int incx, complex<double> *a, int lda);
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 the following symmetric rank 1 operation:
A <- alpha xxT + A
where xT is the transpose of x, alpha is a real or complex scalar, x is
an n-element vector, and A is an n-by-n symmetric matrix.
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 a
is referenced, as follows:
uplo= 'U' or 'u': only the upper triangular part of a is
referenced.
uplo= 'L' or 'l': only the lower triangular part of a is
referenced.
For C/C++, a pointer to this character is passed.
n Integer. (input)
Specifies the order of matrix A. n >= 0.
Page 2
SSYR(3S)SSYR(3S)
alpha Scalar alpha. (input)
SSYR: Single precision.
DSYR: Double precision.
CSYR: Single precision complex.
ZSYR: Double precision complex.
For C/C++, a pointer to this scalar is passed when alpha is
complex; otherwise, alpha is passed by value.
x Array of dimension 1+(n-1) * |incx|. (input)
SSYR: Single precision array.
DSYR: Double precision array.
CSYR: Single precision complex array.
ZSYR: Double precision complex array.
Contains vector x.
incx Integer. (input)
Specifies the increment for the elements of x. incx must not
be 0.
a Array of dimension (lda,n). (input and output)
SSYR: Single precision array.
DSYR: Double precision array.
CSYR: Single precision complex array.
ZSYR: Double precision complex array.
Before entry with uplo = 'U' or 'u', the leading n-by-n upper
triangular part of array a must contain the upper triangular
part of the symmetric matrix. The strictly lower triangular
part of a is not referenced. On exit, the upper triangular
part of the updated matrix overwrites the upper triangular part
of array a.
Before entry with uplo = 'L' or 'l', the leading n-by-n lower
triangular part of array a must contain the lower triangular
part of the symmetric matrix. The strictly upper triangular
part of a is not referenced. On exit, the lower triangular
part of the updated matrix overwrites the lower triangular part
of array a.
lda Integer. (input)
Specifies the first dimension of a as declared in the calling
program. lda >= MAX(1,n).
NOTES
SSYR/DSYR is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).
CSYR/ZSYR is an extension to Level 2 BLAS.
When working backward (incx < 0), each routine starts at the end of the
vector and moves backward, as follows:
Page 3
SSYR(3S)SSYR(3S)
x(1-incx * (n-1)), x(1-incx * (n-2)), ..., x(1)
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]
Page 4
SSYR(3S)SSYR(3S)
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 ALSOINTRO_SCSL(3S), INTRO_BLAS2(3S), CHER(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 5