
NAMEzppequ.f SYNOPSISFunctions/Subroutinessubroutine zppequ (UPLO, N, AP, S, SCOND, AMAX, INFO) Function/Subroutine Documentationsubroutine 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 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. UPLO
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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 jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/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 ith argument had an illegal value > 0: if INFO = i, the ith diagonal element is nonpositive. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 118 of file zppequ.f.
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