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cpoequb.f - Man Page




subroutine cpoequb (n, a, lda, s, scond, amax, info)

Function/Subroutine Documentation

subroutine cpoequb (integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real scond, real amax, integer info)



 CPOEQUB computes row and column scalings intended to equilibrate a
 Hermitian positive definite 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

 This routine differs from CPOEQU by restricting the scaling factors
 to a power of the radix.  Barring over- and underflow, scaling by
 these factors introduces no additional rounding errors.  However, the
 scaled diagonal entries are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix).


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


          A is COMPLEX array, dimension (LDA,N)
          The N-by-N Hermitian positive definite matrix whose scaling
          factors are to be computed.  Only the diagonal elements of A
          are referenced.


          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).


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


          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 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 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.

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Definition at line 118 of file cpoequb.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page cpoequb(3) is an alias of cpoequb.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK