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SSYMV(3S)							     SSYMV(3S)

NAME
     SSYMV, DSYMV, CSYMV, ZSYMV - Multiplies a real or complex vector by a
     real or complex symmetric matrix

SYNOPSIS
     Single precision

	  Fortran:
	       CALL SSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

	  C/C++:
	       #include <scsl_blas.h>
	       void ssymv (char *uplo, int n, float alpha, float *a, int lda,
	       float *x, int x, float beta, float *y, int incy);

     Double precision

	  Fortran:
	       CALL DSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

	  C/C++:
	       #include <scsl_blas.h>
	       void dsymv (char *uplo, int n, double alpha, double *a, int
	       lda, double *x, int x, double beta, double *y, int incy);

     Single precision complex

	  Fortran:
	       CALL CSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

	  C/C++:
	       #include <scsl_blas.h>
	       void csymv (char *uplo, int n, scsl_complex *alpha,
	       scsl_complex *a, int lda, scsl_complex *x, int x, scsl_complex
	       *beta, scsl_complex *y, int incy);

	  C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void csymv (char *uplo, int n, complex<float> *alpha,
	       complex<float> *a, int lda, complex<float> *x, int x,
	       complex<float> *beta, complex<float> *y, int incy);

     Double precision complex

	  Fortran:
	       CALL ZSYMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

	  C/C++:
	       #include <scsl_blas.h>
	       void zsymv (char *uplo, int n, scsl_zomplex *alpha,
	       scsl_zomplex *a, int lda, scsl_zomplex *x, int x, scsl_zomplex

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SSYMV(3S)							     SSYMV(3S)

	       *beta, scsl_zomplex *y, int incy);

	  C++ STL:
	       #include <complex.h>
	       #include <scsl_blas.h>
	       void zsymv (char *uplo, int n, complex<double> *alpha,
	       complex<double> *a, int lda, complex<double> *x, int x,
	       complex<double> *beta, complex<double> *y, int incy);

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
     SSYMV and DSYMV multiplies a real vector by a real symmetric matrix.

     CSYMV and ZSYMV multiplies a complex vector by a complex symmetric
     matrix.

     These routines perform the following matrix-vector operation:

	  y <- alpha Ax + beta y

     where alpha and beta are scalars, x and y are n-element vectors, 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 matrix
	       A is being supplied, as follows:

	       uplo= 'U' or 'u':  only the upper triangular part of A is being
	       supplied.
	       uplo= 'L' or 'l':  only the lower triangular part of A is being

									Page 2

SSYMV(3S)							     SSYMV(3S)

	       supplied.

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

     n	       Integer.	 (input)
	       Specifies the order of matrix A.	 n >= 0.

     alpha     Scalar alpha.  (input)
	       SSYMV: Single precision.
	       DSYMV: Double precision.
	       CSYMV: Single precision complex.
	       ZSYMV: 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,n).  (input)
	       SSYMV: Single precision array.
	       DSYMV: Double precision array.
	       CSYMV: Single precision complex array.
	       ZSYMV: 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.

	       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.

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

     x	       Array of dimension 1+(n-1) * |incx|.  (input)
	       SSYMV: Single precision array.
	       DSYMV: Double precision array.
	       CSYMV: Single precision complex array.
	       ZSYMV: Double precision complex array.
	       Contains the vector x.

     incx      Integer.	 (input)
	       Specifies the increment for the elements of x.  incx must not
	       be 0.

     beta      Scalar beta.  (input)
	       If beta is supplied as 0, y need not be set on input.
	       SSYMV: Single precision.
	       DSYMV: Double precision.
	       CSYMV: Single precision complex.

									Page 3

SSYMV(3S)							     SSYMV(3S)

	       ZSYMV: Double precision complex.

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

     y	       Array of dimension 1+(n-1) * |incy|.  (input and output)
	       SSYMV: Single precision array.
	       DSYMV: Double precision array.
	       CSYMV: Single precision complex array.
	       ZSYMV: Double precision complex array.
	       Contains the vector y.  On exit, the updated vector overwrites
	       array y.

     incy      Integer.	 (input)
	       Specifies the increment for the elements of y.  incy must not
	       be 0.

NOTES
     SSYMV/DSYMV is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS).
     CSYMV/ZSYMV is an extension to Level 2 BLAS.

     When working backward (incx < 0 or incy < 0), each routine starts at the
     end of the vector and moves backward, as follows:

	  x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)

	  y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(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)

	  Integer			INTEGER (INTEGER*8 for -lscs_i8[_mp])

	  Single precision		REAL

	  Double precision		DOUBLE PRECISION

	  Single precision complex	COMPLEX

	  Double precision complex	DOUBLE COMPLEX

									Page 4

SSYMV(3S)							     SSYMV(3S)

     C/C++:

	  Array dimensioned n		x[n]

	  Array of dimensions (m,n)	x[m*n]

	  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]

	  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_BLAS2(3S), CHEMV(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

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