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SGBEQU(l)) SGBEQU(l)SGBEQU - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condi- tion numberNAMESUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO ) INTEGER INFO, KL, KU, LDAB, M, N REAL AMAX, COLCND, ROWCND REAL AB( LDAB, * ), C( * ), R( * )SYNOPSISSGBEQU computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condi- tion 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.PURPOSEM (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. AB (input) REAL 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 (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. R (output) REAL array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A. C (output) REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND (output) 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 (output) 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 (output) REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to under- flow, the matrix should be scaled. INFO (output) INTEGER = 0: successful exit < 0: if INFO =ARGUMENTS, 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-iLAPACK version 3.015 June 2000 SGBEQU(l)

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