LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine sgeequb | ( | integer | M, |
integer | N, | ||
real, dimension( lda, * ) | A, | ||
integer | LDA, | ||
real, dimension( * ) | R, | ||
real, dimension( * ) | C, | ||
real | ROWCND, | ||
real | COLCND, | ||
real | AMAX, | ||
integer | INFO | ||
) |
SGEEQUB
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SGEEQUB 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. Baring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitured are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).
[in] | M | M is INTEGER The number of rows of the matrix A. M >= 0. |
[in] | N | N is INTEGER The number of columns of the matrix A. N >= 0. |
[in] | A | A is REAL array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). |
[out] | R | R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A. |
[out] | C | C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. |
[out] | ROWCND | 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. |
[out] | COLCND | 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. |
[out] | AMAX | 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. |
[out] | INFO | 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 |
Definition at line 148 of file sgeequb.f.