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template<typename T>
void pbequ(char *uplo, integer *n, integer *kd, T *ab, integer *ldab, T *s, T *scond, T *amax, integer *info)# PBEQU computes row and column scalings.
Purpose:
PBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band 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:
UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangular of A is stored;
= ‘L’: Lower triangular of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
KD – [in]
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.
AB – [in]
AB is REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = ‘U’, AB(kd+1+i-j,j) = A(i,j) for fla_max(1,j-kd)<=i<=j;
if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB – [in]
LDAB is INTEGER
The leading dimension of the array A. LDAB >= KD+1.
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.