# ?spr

Performs a rank-1 update of a symmetric packed matrix.

## Syntax

FORTRAN 77:

call sspr(uplo, n, alpha, x, incx, ap )

call dspr(uplo, n, alpha, x, incx, ap )

Fortran 95:

call spr(a, x [,uplo] [, alpha])

## Description

The ?spr routines perform a matrix-vector operation defined as
`a:= alpha*x*x'+ A,`

where:

alpha is a real scalar,

x is an n-element vector,

A is an n-by-n symmetric matrix, supplied in packed form.

## Input Parameters

uplo

  CHARACTER*1. Specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array ap.

  If `uplo = 'U'` or 'u', then the upper triangular part of the matrix A is supplied in the packed array ap .

  If `uplo = 'L'` or 'l', then the low triangular part of the matrix A is supplied in the packed array ap .

n

  INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

alpha

  REAL for sspr

  DOUBLE PRECISION for dspr

  Specifies the scalar alpha.

x

  REAL for sspr

  DOUBLE PRECISION for dspr

  Array, DIMENSION at least `(1 + (n - 1)*abs(incx))`. Before entry, the incremented array x must contain the n-element vector x.

incx

  INTEGER. Specifies the increment for the elements of x.

  The value of incx must not be zero.

ap

  REAL for sspr

  DOUBLE PRECISION for dspr

  Array, DIMENSION at least `((n*(n + 1))/2)`. Before entry with `uplo = 'U'` or 'u', the array ap must contain the upper triangular part of the symmetric matrix packed sequentially, column-by-column, so that `ap(1)` contains `a(1,1)`, `ap(2)` and `ap(3)` contain `a(1,2)` and `a(2,2)` respectively, and so on.

  Before entry with `uplo = 'L'` or 'l', the array ap must contain the lower triangular part of the symmetric matrix packed sequentially, column-by-column, so that `ap(1)` contains `a(1,1)`, `ap(2)` and `ap(3)` contain `a(2,1)` and `a(3,1)` respectively, and so on.

## Output Parameters

ap

  With `uplo = 'U'` or 'u', overwritten by the upper triangular part of the updated matrix.

  With `uplo = 'L'` or 'l', overwritten by the lower triangular part of the updated matrix.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine spr interface are the following:

a

  Holds the array a of size (n*(n+1)/2).

x

  Holds the vector of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

alpha

  The default value is 1.

Parent topic: BLAS Level 2 Routines