cgbequ (3) - Linux Man Pages
subroutine cgbequ (integerM, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)
CGBEQU computes row and column scalings intended to equilibrate an M-by-N band 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 absolute value 1. R(i) and C(j) are restricted to be 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.
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.
KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
AB is COMPLEX array, dimension (LDAB,N) The band matrix A, stored 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(m,j+kl).
LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
R is REAL array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A.
C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A.
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 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 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 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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- November 2011
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