subroutine zppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
subroutine zppequ (characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, integerINFO)ZPPEQU Purpose:
ZPPEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage 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.
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.N
N is INTEGER The order of the matrix A. N >= 0.AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.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 = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
November 2011Definition at line 118 of file zppequ.f.