# sppequ.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **sppequ** (UPLO, **N**, AP, S, SCOND, AMAX, INFO)**SPPEQU**

## Function/Subroutine Documentation

### subroutine sppequ (character UPLO, integer N, real, dimension( * ) AP, real, dimension( * ) S, real SCOND, real AMAX, integer INFO)

**SPPEQU**

**Purpose:**

SPPEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

**Parameters:***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*AP*AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

*S*S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.

*SCOND*SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.

*AMAX*AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 118 of file sppequ.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sppequ(3) is an alias of sppequ.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK