SPOCO(3F) SPOCO(3F)
SPOCO - SPOCO factors a real symmetric positive definite matrix and
estimates the condition of the matrix.
If RCOND is not needed, SPOFA is slightly faster. To solve A*X = B ,
follow SPOCO by SPOSL. To compute INVERSE(A)*C , follow SPOCO by SPOSL.
To compute DETERMINANT(A) , follow SPOCO by SPODI. To compute
INVERSE(A) , follow SPOCO by SPODI.
SUBROUTINE SPOCO(A,LDA,N,RCOND,Z,INFO)
On Entry
A REAL(LDA, N)
the symmetric matrix to be factored. Only the
diagonal and upper triangle are used.
LDA INTEGER
the leading dimension of the array A .
N INTEGER
the order of the matrix A . On Return
A an upper triangular matrix R so that A = TRANS(R)*R
where TRANS(R) is the transpose.
The strict lower triangle is unaltered.
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 close to a singular matrix, 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.
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SPOCO(3F) SPOCO(3F)
= K signals an error condition. The leading minor
of order K is not positive definite. LINPACK. This version dated
08/14/78 . Cleve Moler, University of New Mexico, Argonne National Lab.
Subroutines and Functions LINPACK SPOFA BLAS SAXPY,SDOT,SSCAL,SASUM
Fortran ABS,AMAX1,REAL,SIGN
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