DGEEQUB 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 DGEEQU 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).
M is INTEGER The number of rows of the matrix A. M >= 0.
N is INTEGER The number of columns of the matrix A. N >= 0.
A is DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
R is DOUBLE PRECISION array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A.
C is DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A.
ROWCND is DOUBLE PRECISION 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 is DOUBLE PRECISION 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 is 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 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
Univ. of California Berkeley
Univ. of Colorado Denver
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