sppco.f
SUBROUTINE SPPCO (AP, N, RCOND, Z, INFO)
C***BEGIN PROLOGUE SPPCO
C***PURPOSE Factor a symmetric positive definite matrix stored in
C packed form and estimate the condition number of the
C matrix.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2B1B
C***TYPE SINGLE PRECISION (SPPCO-S, DPPCO-D, CPPCO-C)
C***KEYWORDS CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
C MATRIX FACTORIZATION, PACKED, POSITIVE DEFINITE
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C SPPCO factors a real symmetric positive definite matrix
C stored in packed form
C and estimates the condition of the matrix.
C
C If RCOND is not needed, SPPFA is slightly faster.
C To solve A*X = B , follow SPPCO by SPPSL.
C To compute INVERSE(A)*C , follow SPPCO by SPPSL.
C To compute DETERMINANT(A) , follow SPPCO by SPPDI.
C To compute INVERSE(A) , follow SPPCO by SPPDI.
C
C On Entry
C
C AP REAL (N*(N+1)/2)
C the packed form of a symmetric 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 On Return
C
C AP an upper triangular matrix R , stored in packed
C form, so that A = TRANS(R)*R .
C If INFO .NE. 0 , the factorization is not complete.
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. If INFO .NE. 0 , RCOND is unchanged.
C
C Z REAL(N)
C a work vector whose contents are usually unimportant.
C If A is singular to working precision, then Z is
C an approximate null vector in the sense that
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C If INFO .NE. 0 , Z is unchanged.
C
C INFO INTEGER
C = 0 for normal return.
C = K signals an error condition. The leading minor
C of order K is not positive definite.
C
C Packed Storage
C
C The following program segment will pack the upper
C triangle of a symmetric 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 SASUM, SAXPY, SDOT, SPPFA, SSCAL
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 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 SPPCO