CHPFA(3F)CHPFA(3F)NAMECHPFA - CHPFA factors a complex Hermitian matrix stored in packed form
by elimination with symmetric pivoting.
To solve A*X = B , follow CHPFA by CHPSL. To compute INVERSE(A)*C ,
follow CHPFA by CHPSL. To compute DETERMINANT(A) , follow CHPFA by
CHPDI. To compute INERTIA(A) , follow CHPFA by CHPDI. To compute
INVERSE(A) , follow CHPFA by CHPDI.
SYNOPSYS
SUBROUTINE CHPFA(AP,N,KPVT,INFO)
DESCRIPTION
On Entry
AP COMPLEX (N*(N+1)/2)
the packed form of a Hermitian 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*CTRANS(U)
where U is a product of permutation and unit
upper triangular matrices , CTRANS(U) is the
conjugate 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 CHPSL or CHPDI may
divide by zero if called. Packed Storage The following program
segment will pack the upper triangle of a Hermitian 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,CMPLX,CONJG,REAL,SQRT
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