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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine spbequ | ( | character | UPLO, |
integer | N, | ||
integer | KD, | ||
real, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
real, dimension( * ) | S, | ||
real | SCOND, | ||
real | AMAX, | ||
integer | INFO | ||
) |
SPBEQU
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SPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.
[in] | UPLO | UPLO is CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in] | KD | KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
[in] | AB | AB is REAL array, dimension (LDAB,N) The upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
[in] | LDAB | LDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1. |
[out] | S | S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. |
[out] | SCOND | SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. |
[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, the i-th diagonal element is nonpositive. |
Definition at line 131 of file spbequ.f.