CSPFA(3F)CSPFA(3F)NAMECSPFA - CSPFA factors a complex symmetric matrix stored in packed form
by elimination with symmetric pivoting.
To solve A*X = B , follow CSPFA by CSPSL. To compute INVERSE(A)*C ,
follow CSPFA by CSPSL. To compute DETERMINANT(A) , follow CSPFA by
CSPDI. To compute INVERSE(A) , follow CSPFA by CSPDI.
SYNOPSYS
SUBROUTINE CSPFA(AP,N,KPVT,INFO)
DESCRIPTION
On Entry
AP COMPLEX (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 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. KVPT INTEGER(N)
an integer vector of pivot indices.
INFO INTEGER
= 0 normal value.
= K if the K-th pivot block is singular. This is
not an error condition for this subroutine,
but it does indicate that CSPSL or CSPDI may
divide by zero if called. 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 . James Bunch,
Univ. Calif. San Diego, Argonne Nat. Lab. Subroutines and Functions BLAS
CAXPY,CSWAP,ICAMAX Fortran ABS,AIMAG,AMAX1,REAL,SQRT
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