LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  zheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) 
ZHEEQUB 
subroutine zheequb  (  character  UPLO, 
integer  N,  
complex*16, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( * )  S,  
double precision  SCOND,  
double precision  AMAX,  
complex*16, dimension( * )  WORK,  
integer  INFO  
) 
ZHEEQUB
Download ZHEEQUB + dependencies [TGZ] [ZIP] [TXT]ZHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A 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.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  A  A is COMPLEX*16 array, dimension (LDA,N) The NbyN Hermitian matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  S  S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. 
[out]  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. 
[out]  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. 
[out]  WORK  WORK is COMPLEX*16 array, dimension (3*N) 
[out]  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. 
Definition at line 127 of file zheequb.f.