SPPEQU
November 2006
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.
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.
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. |
| 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. |