CHICO(3F)CHICO(3F)NAMECHICO - CHICO factors a complex Hermitian matrix by elimination with
symmetric pivoting and estimates the condition of the matrix.
If RCOND is not needed, CHIFA is slightly faster. To solve A*X = B ,
follow CHICO by CHISL. To compute INVERSE(A)*C , follow CHICO by CHISL.
To compute INVERSE(A) , follow CHICO by CHIDI. To compute
DETERMINANT(A) , follow CHICO by CHIDI. To compute INERTIA(A), follow
CHICO by CHIDI.
SYNOPSYS
SUBROUTINE CHICO(A,LDA,N,KPVT,RCOND,Z)
DESCRIPTION
On Entry
A COMPLEX(LDA, N)
the Hermitian 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 . Output
A a block diagonal matrix and the multipliers which
were used to obtain it.
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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CHICO(3F)CHICO(3F)
NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . LINPACK. This version dated
08/14/78 . Cleve Moler, University of New Mexico, Argonne National Lab.
Subroutines and Functions LINPACK CHIFA BLAS CAXPY,CDOTC,CSSCAL,SCASUM
Fortran ABS,AIMAG,AMAX1,CMPLX,CONJG,IABS,REAL
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