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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine sgbequb | ( | integer | M, |
integer | N, | ||
integer | KL, | ||
integer | KU, | ||
real, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
real, dimension( * ) | R, | ||
real, dimension( * ) | C, | ||
real | ROWCND, | ||
real | COLCND, | ||
real | AMAX, | ||
integer | INFO | ||
) |
SGBEQUB
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SGBEQUB 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).
[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] | KL | KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. |
[in] | KU | KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. |
[in] | AB | AB is REAL array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array A. LDAB >= 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 162 of file sgbequb.f.