SPPEQU(l) ) SPPEQU(l)
SPPEQU - compute row and column scalings intended to equilibrate a symmetric positive def-
inite matrix A in packed storage and reduce its condition number (with respect to the two-
SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
INTEGER INFO, N
REAL AMAX, SCOND
REAL AP( * ), S( * )
SPPEQU computes row and column scalings intended to equilibrate a symmetric positive defi-
nite 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.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin-
ear 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 (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND (output) 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
AMAX (output) 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 (output) 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.
LAPACK version 3.0 15 June 2000 SPPEQU(l)