SPPCO(3F)SPPCO(3F)NAMESPPCO - SPPCO factors a real symmetric positive definite matrix stored
in packed form and estimates the condition of the matrix.
If RCOND is not needed, SPPFA is slightly faster. To solve A*X = B ,
follow SPPCO by SPPSL. To compute INVERSE(A)*C , follow SPPCO by SPPSL.
To compute DETERMINANT(A) , follow SPPCO by SPPDI. To compute
INVERSE(A) , follow SPPCO by SPPDI.
SYNOPSYS
SUBROUTINE SPPCO(AP,N,RCOND,Z,INFO)
DESCRIPTION
On Entry
AP REAL (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 REAL
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 REAL(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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SPPCO(3F)SPPCO(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 SPPFA BLAS SAXPY,SDOT,SSCAL,SASUM Fortran
ABS,AMAX1,REAL,SIGN
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