DPPEQU 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


 scalings.

UPLO

          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 DOUBLE PRECISION 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

          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 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