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RedHat 9 (Linux i386) - man page for zpbequ (redhat section l)

ZPBEQU(l)						  )						    ZPBEQU(l)

NAME
ZPBEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
SYNOPSIS
SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N DOUBLE PRECISION AMAX, SCOND DOUBLE PRECISION S( * ) COMPLEX*16 AB( LDAB, * )
PURPOSE
ZPBEQU computes row and column scalings intended to equilibrate a Hermitian 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 condi- tion number over all possible diagonal scalings.
ARGUMENTS
UPLO (input) CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input) COMPLEX*16 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 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). LDAB (input) INTEGER The leading dimension of the array A. LDAB >= KD+1. S (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) DOUBLE PRECISION 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. AMAX (output) DOUBLE PRECISION 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 = -i, the i-th argument had an illegal value. > 0: if INFO = i, the i-th diagonal element is nonpositive. LAPACK version 3.0 15 June 2000 ZPBEQU(l)


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