CPBEQU (3)  Linux Manuals
NAME
cpbequ.f 
SYNOPSIS
Functions/Subroutines
subroutine cpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO)
CPBEQU
Function/Subroutine Documentation
subroutine cpbequ (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND, realAMAX, integerINFO)
CPBEQU
Purpose:

CPBEQU computes row and column scalings intended to equilibrate a Hermitian 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.
Parameters:

UPLO
UPLO is CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored.
NN is INTEGER The order of the matrix A. N >= 0.
KDKD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
ABAB is COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the Hermitian 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).
LDABLDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1.
SS is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A.
SCONDSCOND 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.
AMAXAMAX 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.
INFOINFO 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.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Definition at line 131 of file cpbequ.f.
Author
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