# CentOS 7.0 - man page for dpbequ (centos section 3)

dpbequ.f(3) LAPACK dpbequ.f(3)dpbequ.fNAME-Functions/Subroutines subroutine dpbequ (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO) DPBEQUSYNOPSISFunction/Subroutine Documentation subroutine dpbequ (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO) DPBEQU Purpose: DPBEQU 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. Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. N N is INTEGER The order of the matrix A. N >= 0. 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. AB AB is DOUBLE PRECISION 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). LDAB LDAB is INTEGER The leading dimension of the array A. LDAB >= KD+1. S S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND SCOND is 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 AMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value. > 0: if INFO = i, the i-th diagonal element is nonpositive. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 130 of file dpbequ.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dpbequ.f(3)