chpco.f
SUBROUTINE CHPCO (AP, N, KPVT, RCOND, Z)
C***BEGIN PROLOGUE CHPCO
C***PURPOSE Factor a complex Hermitian matrix stored in packed form by
C elimination with symmetric pivoting and estimate the
C condition number of the matrix.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2D1A
C***TYPE COMPLEX (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C)
C***KEYWORDS CONDITION NUMBER, HERMITIAN, LINEAR ALGEBRA, LINPACK,
C MATRIX FACTORIZATION, PACKED
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C CHPCO factors a complex Hermitian matrix stored in packed
C form by elimination with symmetric pivoting and estimates
C the condition of the matrix.
C
C if RCOND is not needed, CHPFA is slightly faster.
C To solve A*X = B , follow CHPCO by CHPSL.
C To compute INVERSE(A)*C , follow CHPCO by CHPSL.
C To compute INVERSE(A) , follow CHPCO by CHPDI.
C To compute DETERMINANT(A) , follow CHPCO by CHPDI.
C To compute INERTIA(A), follow CHPCO by CHPDI.
C
C On Entry
C
C AP COMPLEX (N*(N+1)/2)
C the packed form of a Hermitian matrix A . The
C columns of the upper triangle are stored sequentially
C in a one-dimensional array of length N*(N+1)/2 .
C See comments below for details.
C
C N INTEGER
C the order of the matrix A .
C
C Output
C
C AP a block diagonal matrix and the multipliers which
C were used to obtain it stored in packed form.
C The factorization can be written A = U*D*CTRANS(U)
C where U is a product of permutation and unit
C upper triangular matrices , CTRANS(U) is the
C conjugate transpose of U , and D is block diagonal
C with 1 by 1 and 2 by 2 blocks.
C
C KVPT INTEGER(N)
C an integer vector of pivot indices.
C
C RCOND REAL
C an estimate of the reciprocal condition of A .
C For the system A*X = B , relative perturbations
C in A and B of size EPSILON may cause
C relative perturbations in X of size EPSILON/RCOND .
C If RCOND is so small that the logical expression
C 1.0 + RCOND .EQ. 1.0
C is true, then A may be singular to working
C precision. In particular, RCOND is zero if
C exact singularity is detected or the estimate
C underflows.
C
C Z COMPLEX(N)
C a work vector whose contents are usually unimportant.
C If A is close to a singular matrix, then Z is
C an approximate null vector in the sense that
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C
C Packed Storage
C
C The following program segment will pack the upper
C triangle of a Hermitian matrix.
C
C K = 0
C DO 20 J = 1, N
C DO 10 I = 1, J
C K = K + 1
C AP(K) = A(I,J)
C 10 CONTINUE
C 20 CONTINUE
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED CAXPY, CDOTC, CHPFA, CSSCAL, SCASUM
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891107 Modified routine equivalence list. (WRB)
C 891107 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE CHPCO