LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  spbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO) 
SPBEQU 
subroutine spbequ  (  character  UPLO, 
integer  N,  
integer  KD,  
real, dimension( ldab, * )  AB,  
integer  LDAB,  
real, dimension( * )  S,  
real  SCOND,  
real  AMAX,  
integer  INFO  
) 
SPBEQU
Download SPBEQU + dependencies [TGZ] [ZIP] [TXT]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 twonorm). 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 jth column of A is stored in the jth column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,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 ith argument had an illegal value. > 0: if INFO = i, the ith diagonal element is nonpositive. 
Definition at line 130 of file spbequ.f.