CHPCO(3F)CHPCO(3F)NAMECHPCO - CHPCO factors a complex Hermitian matrix stored in packed form
by elimination with symmetric pivoting and estimates the condition of the
matrix.
if RCOND is not needed, CHPFA is slightly faster. To solve A*X = B ,
follow CHPCO by CHPSL. To compute INVERSE(A)*C , follow CHPCO by CHPSL.
To compute INVERSE(A) , follow CHPCO by CHPDI. To compute
DETERMINANT(A) , follow CHPCO by CHPDI. To compute INERTIA(A), follow
CHPCO by CHPDI.
SYNOPSYS
SUBROUTINE CHPCO(AP,N,KPVT,RCOND,Z)
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.
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 COMPLEX(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
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CHPCO(3F)CHPCO(3F)
NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . 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 . Cleve Moler,
University of New Mexico, Argonne National Lab. Subroutines and
Functions LINPACK CHPFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM Fortran
ABS,AIMAG,AMAX1,CMPLX,CONJG,IABS,REAL
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