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/* dptcon.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
/* Subroutine */ int dptcon_(integer *n, doublereal *d__, doublereal *e,
doublereal *anorm, doublereal *rcond, doublereal *work, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Local variables */
integer i__, ix;
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal ainvnm;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DPTCON computes the reciprocal of the condition number (in the */
/* 1-norm) of a real symmetric positive definite tridiagonal matrix */
/* using the factorization A = L*D*L**T or A = U**T*D*U computed by */
/* DPTTRF. */
/* Norm(inv(A)) is computed by a direct method, and the reciprocal of */
/* the condition number is computed as */
/* RCOND = 1 / (ANORM * norm(inv(A))). */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* The n diagonal elements of the diagonal matrix D from the */
/* factorization of A, as computed by DPTTRF. */
/* E (input) DOUBLE PRECISION array, dimension (N-1) */
/* The (n-1) off-diagonal elements of the unit bidiagonal factor */
/* U or L from the factorization of A, as computed by DPTTRF. */
/* ANORM (input) DOUBLE PRECISION */
/* The 1-norm of the original matrix A. */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the */
/* 1-norm of inv(A) computed in this routine. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The method used is described in Nicholas J. Higham, "Efficient */
/* Algorithms for Computing the Condition Number of a Tridiagonal */
/* Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments. */
/* Parameter adjustments */
--work;
--e;
--d__;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*anorm < 0.) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DPTCON", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm == 0.) {
return 0;
}
/* Check that D(1:N) is positive. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (d__[i__] <= 0.) {
return 0;
}
/* L10: */
}
/* Solve M(A) * x = e, where M(A) = (m(i,j)) is given by */
/* m(i,j) = abs(A(i,j)), i = j, */
/* m(i,j) = -abs(A(i,j)), i .ne. j, */
/* and e = [ 1, 1, ..., 1 ]'. Note M(A) = M(L)*D*M(L)'. */
/* Solve M(L) * x = e. */
work[1] = 1.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
work[i__] = work[i__ - 1] * (d__1 = e[i__ - 1], abs(d__1)) + 1.;
/* L20: */
}
/* Solve D * M(L)' * x = b. */
work[*n] /= d__[*n];
for (i__ = *n - 1; i__ >= 1; --i__) {
work[i__] = work[i__] / d__[i__] + work[i__ + 1] * (d__1 = e[i__],
abs(d__1));
/* L30: */
}
/* Compute AINVNM = max(x(i)), 1<=i<=n. */
ix = idamax_(n, &work[1], &c__1);
ainvnm = (d__1 = work[ix], abs(d__1));
/* Compute the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
return 0;
/* End of DPTCON */
} /* dptcon_ */
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