cppequ-f(3)

cppequ.f –

Synopsis

Functions/Subroutines

subroutine cppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
CPPEQU

Function/Subroutine Documentation

subroutine cppequ (characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )S, realSCOND, realAMAX, integerINFO)

CPPEQU

Purpose:

 CPPEQU 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.

Parameters:

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangle of A is stored;
 = 'L': Lower triangle of A is stored.

 N is INTEGER
 The order of the matrix A. N >= 0.

 AP is COMPLEX 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 is REAL array, dimension (N)
 If INFO = 0, S contains the scale factors for A.

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.

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.

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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 118 of file cppequ.f.

Author

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