SPPEQU - compute row and column scalings intended to equi
librate a symmetric positive definite matrix A in packed
storage and reduce its condition number (with respect to
the two-norm)
SYNOPSIS
SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
CHARACTER UPLO
INTEGER INFO, N
REAL AMAX, SCOND
REAL AP( * ), S( * )
PURPOSE
SPPEQU computes row and column scalings intended to equi
librate 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 num
ber over all possible diagonal scalings.
ARGUMENTS
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 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 (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 by S.
Absolute value of largest matrix element. If AMAX
is very close to overflow or very close to under
flow, the matrix should be scaled.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: if INFO = i, the i-th diagonal element is
nonpositive.
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