text: /* sptcon.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 sptcon_(integer *n, real *d__, real *e, real *anorm, 
  	real *rcond, real *work, integer *info)
  {
      /* System generated locals */
      integer i__1;
      real r__1;
  
      /* Local variables */
      integer i__, ix;
      extern /* Subroutine */ int xerbla_(char *, integer *);
      extern integer isamax_(integer *, real *, integer *);
      real ainvnm;
  
  
  /*  -- LAPACK routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SPTCON 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 */
  /*  SPTTRF. */
  
  /*  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) REAL array, dimension (N) */
  /*          The n diagonal elements of the diagonal matrix D from the */
  /*          factorization of A, as computed by SPTTRF. */
  
  /*  E       (input) REAL 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 SPTTRF. */
  
  /*  ANORM   (input) REAL */
  /*          The 1-norm of the original matrix A. */
  
  /*  RCOND   (output) REAL */
  /*          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) REAL 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.f) {
  	*info = -4;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SPTCON", &i__1);
  	return 0;
      }
  
  /*     Quick return if possible */
  
      *rcond = 0.f;
      if (*n == 0) {
  	*rcond = 1.f;
  	return 0;
      } else if (*anorm == 0.f) {
  	return 0;
      }
  
  /*     Check that D(1:N) is positive. */
  
      i__1 = *n;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	if (d__[i__] <= 0.f) {
  	    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.f;
      i__1 = *n;
      for (i__ = 2; i__ <= i__1; ++i__) {
  	work[i__] = work[i__ - 1] * (r__1 = e[i__ - 1], dabs(r__1)) + 1.f;
  /* 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] * (r__1 = e[i__], 
  		dabs(r__1));
  /* L30: */
      }
  
  /*     Compute AINVNM = max(x(i)), 1<=i<=n. */
  
      ix = isamax_(n, &work[1], &c__1);
      ainvnm = (r__1 = work[ix], dabs(r__1));
  
  /*     Compute the reciprocal condition number. */
  
      if (ainvnm != 0.f) {
  	*rcond = 1.f / ainvnm / *anorm;
      }
  
      return 0;
  
  /*     End of SPTCON */
  
  } /* sptcon_ */
  