DSPCO(3)

SYNOPSIS
SUBROUTINE DSPCO (AP, N, KPVT, RCOND, Z)

NAME
dspco - Factor a real symmetric matrix stored in packed form by elimination with symmetric pivoting and estimate the condition number of the matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2B1A

TYPE
DOUBLE PRECISION (SSPCO-S, DSPCO-D, CHPCO-C, CSPCO-C)

KEYWORDS
CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION, PACKED, SYMMETRIC

AUTHOR
Moler, C. B., (U. of New Mexico)

DESCRIPTION
DSPCO factors a double precision symmetric matrix stored in packed form by elimination with symmetric pivoting and estimates the condition of the matrix. IF RCOND is not needed, DSPFA is slightly faster. To solve A*X = B , follow DSPCO by DSPSL. To compute INVERSE(A)*C , follow DSPCO by DSPSL. To compute INVERSE(A) , follow DSPCO by DSPDI. To compute DETERMINANT(A) , follow DSPCO by DSPDI. To compute INERTIA(A), follow DSPCO by DSPDI. On Entry AP DOUBLE PRECISION (N*(N+1)/2) the packed form of a symmetric 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*TRANS(U) where U is a product of permutation and unit upper triangular matrices , TRANS(U) is the transpose of U , and D is block diagonal with 1 by 1 and 2 by 2 blocks. KPVT INTEGER(N) an integer vector of pivot indices. RCOND DOUBLE PRECISION 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 DOUBLE PRECISION(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 NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . Packed Storage The following program segment will pack the upper triangle of a symmetric 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

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
DASUM, DAXPY, DDOT, DSCAL, DSPFA

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
891107 Modified routine equivalence list. (WRB)
891107 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)