SSPCO(3F)SSPCO(3F)NAMESSPCO - SSPCO factors a real symmetric matrix stored in packed form by
elimination with symmetric pivoting and estimates the condition of the
matrix.
If RCOND is not needed, SSPFA is slightly faster. To solve A*X = B ,
follow SSPCO by SSPSL. To compute INVERSE(A)*C , follow SSPCO by SSPSL.
To compute INVERSE(A) , follow SSPCO by SSPDI. To compute
DETERMINANT(A) , follow SSPCO by SSPDI. To compute INERTIA(A), follow
SSPCO by SSPDI.
SYNOPSYS
SUBROUTINE SSPCO(AP,N,KPVT,RCOND,Z)
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 . Output
AP a block diagonal matrix and the multipliers which
were used to obtain it stored in packed form.
The factorization can be written A = U*D*TRANS(U)
where U is a product of permutation and unit
upper triangular matrices , TRANS(U) is the
transpose of U , and D is block diagonal
with 1 by 1 and 2 by 2 blocks.
KPVT INTEGER(N)
an integer vector of pivot indices.
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.
Z REAL(N)
a work vector whose contents are usually unimportant.
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SSPCO(3F)SSPCO(3F)
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) . Packed Storage The following
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 SSPFA BLAS SAXPY,SDOT,SSCAL,SASUM Fortran
ABS,AMAX1,IABS,SIGN
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