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*AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2*

## SSYMV or DSYMV Subroutine

### Purpose

Performs matrix-vector operations using a symmetric matrix.

### Library

BLAS Library (**libblas.a**)

### FORTRAN Syntax

**SUBROUTINE SSYMV(***UPLO***, ***N***, ***ALPHA***, ***A***, ***LDA***,**
*X***, ***INCX***, ***BETA***, ***Y***, ***INCY***)**
**REAL** *ALPHA***,***BETA*
**INTEGER** *INCX***,***INCY***,***LDA***,***N*
**CHARACTER*1** *UPLO*
**REAL** *A***(***LDA***,*), ***X***(*), ***Y***(*)**

**SUBROUTINE DSYMV(***UPLO***, ***N***, ***ALPHA***, ***A***, ***LDA***,**
*X***, ***INCX***, ***BETA***, ***Y***, ***INCY***)**
**DOUBLE PRECISION** *ALPHA***,***BETA*
**INTEGER** *INCX***,***INCY***,***LDA***,***N*
**CHARACTER*1** *UPLO*
**DOUBLE PRECISION** *A***(***LDA***,*), ***X***(*), ***Y***(*)**

### Description

The **SSYMV** or **DSYMV** subroutine performs the matrix-vector operation:

`y := alpha * ``A ``* x + beta * y`

where alpha and beta are scalars, x and y are *N* element vectors and *A* is an *N* by *N* symmetric matrix.

### Parameters

*UPLO* |
On entry, *UPLO* specifies whether the upper or lower triangular part of the array *A* is to be referenced as follows:
*UPLO* = 'U' or 'u' |
Only the upper triangular part of *A* is to be referenced. |
*UPLO* = 'L' or 'l' |
Only the lower triangular part of *A* is to be referenced. |
Unchanged on exit. |

*N* |
On entry, *N *specifies the order of the matrix *A*; *N* must be at least 0; unchanged on exit. |

*ALPHA* |
On entry, *ALPHA* specifies the scalar alpha; unchanged on exit. |

*A* |
An array of dimension ( *LDA*, *N *); on entry with *UPLO *= 'U' or 'u', the leading *N* by *N* upper triangular part of the array *A* must contain the upper triangular part of the symmetric matrix; the strictly lower triangular part of *A* is not referenced; on entry with *UPLO *= 'L' or 'l', the leading *N* by *N* lower triangular part of the array* A *must contain the lower triangular part of the symmetric matrix; the strictly upper triangular part of *A* is not referenced; unchanged on exit. |

*LDA* |
On entry, *LDA* specifies the first dimension of *A *as declared in the calling (sub) program; *LDA *must be at least max( 1, *N* ); unchanged on exit. |

*X* |
A vector of dimension at least (1 + (*N*-1) * abs( *INCX* ) ); on entry, the incremented array *X* must contain the *N* element vector x; unchanged on exit. |

*INCX* |
On entry, *INCX* specifies the increment for the elements of *X*; *INCX* must not be 0; unchanged on exit. |

*BETA* |
On entry, *BETA* specifies the scalar beta; when* BETA* is supplied as 0 then *Y* need not be set on input; unchanged on exit. |

*Y* |
A vector of dimension at least (1 + (*N*-1) * abs( *INCY* ) ); on entry, the incremented array *Y* must contain the *N* element vector y; on exit,* Y* is overwritten by the updated vector y. |

*INCY* |
On entry, *INCY* specifies the increment for the elements of *Y*; *INCY* must not be 0; unchanged on exit. |

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