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template<typename T>
void geequb(integer *m, integer *n, T *a, integer *lda, T *r, T *c, T *rowcnd, T *colcnd, T *amax, integer *info)# GEEQUB - computes row and column scaling to reduce condition number of matrix.
Purpose:
GEEQUB computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix. R(i) and C(j) are restricted to be a power of the radix between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice. This routine differs from SGEEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).
- Parameters:
M – [in]
M is INTEGER
The number of rows of the matrix A. M >= 0.
N – [in]
N is INTEGER
The number of columns of the matrix A. N >= 0.
A – [in]
A is REAL array, dimension (LDA,N)
The M-by-N matrix whose equilibration factors are to be computed.
LDA – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,M).
R – [out]
R is REAL array, dimension (M)
If INFO = 0 or INFO > M, R contains the row scale factors for A.
C – [out]
C is REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND – [out]
ROWCND is REAL
If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R.
COLCND – [out]
COLCND is REAL
If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C.
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, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero