LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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sppequ.f File Reference

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subroutine sppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)

Function/Subroutine Documentation

subroutine sppequ ( character  UPLO,
integer  N,
real, dimension( * )  AP,
real, dimension( * )  S,
real  SCOND,
real  AMAX,
integer  INFO 


Download SPPEQU + dependencies [TGZ] [ZIP] [TXT]
 SPPEQU computes row and column scalings intended to equilibrate a
 symmetric 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
          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 REAL array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric 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 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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 117 of file sppequ.f.

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