computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
- SUBROUTINE ZPPEQU(
UPLO, N, AP, S, SCOND, AMAX, INFO )
PRECISION AMAX, SCOND
PRECISION S( * )
AP( * )
ZPPEQU computes row and column scalings intended to equilibrate a
Hermitian 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
- 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) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
- SCOND (output) DOUBLE PRECISION
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 (output) DOUBLE PRECISION
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.