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template<typename T>
void poequ(integer *n, T *a, integer *lda, T *s, T *scond, T *amax, integer *info)# POEQU computes row and column scalings.
Purpose:
POEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A 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:
N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
A – [in]
A is REAL array, dimension (LDA,N)
The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
LDA – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,N).
S – [out]
S is REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND – [out]
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 – [out]
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 – [out]
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.