dppequ (l) - Linux Manuals

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)

NAME

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)

SYNOPSIS

SUBROUTINE DPPEQU(
UPLO, N, AP, S, SCOND, AMAX, INFO )

    
CHARACTER UPLO

    
INTEGER INFO, N

    
DOUBLE PRECISION AMAX, SCOND

    
DOUBLE PRECISION AP( * ), S( * )

PURPOSE

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.

ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) 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 = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
S (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND (output) 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 (output) 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 (output) 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.

Pages related to dppequ

  • dppequ (3)
  • dppcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
  • dpprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
  • dppsv (l) - computes the solution to a real system of linear equations A * X = B,
  • dppsvx (l) - uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,
  • dpptrf (l) - computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
  • dpptri (l) - computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF
  • dpptrs (l) - solves a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF