DPPCO(3F)DPPCO(3F)NAMEDPPCO - DPPCO factors a double precision symmetric positive definite
matrix stored in packed form and estimates the condition of the matrix.
If RCOND is not needed, DPPFA is slightly faster. To solve A*X = B ,
follow DPPCO by DPPSL. To compute INVERSE(A)*C , follow DPPCO by DPPSL.
To compute DETERMINANT(A) , follow DPPCO by DPPDI. To compute
INVERSE(A) , follow DPPCO by DPPDI.
SYNOPSYS
SUBROUTINE DPPCO(AP,N,RCOND,Z,INFO)
DESCRIPTION
On Entry
AP DOUBLE PRECISION (N*(N+1)/2)
the packed form of a symmetric matrix A . The
columns of the upper triangle are stored sequentially
in a one-dimensional array of length N*(N+1)/2 .
See comments below for details.
N INTEGER
the order of the matrix A . On Return
AP an upper triangular matrix R , stored in packed
form, so that A = TRANS(R)*R .
If INFO .NE. 0 , the factorization is not complete.
RCOND DOUBLE PRECISION
an estimate of the reciprocal condition of A .
For the system A*X = B , relative perturbations
in A and B of size EPSILON may cause
relative perturbations in X of size EPSILON/RCOND .
If RCOND is so small that the logical expression
1.0 + RCOND .EQ. 1.0
is true, then A may be singular to working
precision. In particular, RCOND is zero if
exact singularity is detected or the estimate
underflows. If INFO .NE. 0 , RCOND is unchanged.
Z DOUBLE PRECISION(N)
a work vector whose contents are usually unimportant.
If A is singular to working precision, then Z is
an approximate null vector in the sense that
NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
If INFO .NE. 0 , Z is unchanged.
INFO INTEGER
= 0 for normal return.
= K signals an error condition. The leading minor
of order K is not positive definite. Packed Storage The following
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DPPCO(3F)DPPCO(3F)
program segment will pack the upper triangle of a symmetric matrix.
K = 0
DO 20 J = 1, N
DO 10 I = 1, J
K = K + 1
AP(K) = A(I,J)
10 CONTINUE
20 CONTINUE LINPACK. This version dated 08/14/78 . Cleve Moler,
University of New Mexico, Argonne National Lab. Subroutines and
Functions LINPACK DPPFA BLAS DAXPY,DDOT,DSCAL,DASUM Fortran
DABS,DMAX1,DREAL,DSIGN
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