sptt01.c

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/* sptt01.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"

/* Subroutine */ int sptt01_(integer *n, real *d__, real *e, real *df, real *
        ef, real *work, real *resid)
{
    /* System generated locals */
    integer i__1;
    real r__1, r__2, r__3, r__4, r__5;

    /* Local variables */
    integer i__;
    real de, eps, anorm;
    extern doublereal slamch_(char *);


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SPTT01 reconstructs a tridiagonal matrix A from its L*D*L' */
/*  factorization and computes the residual */
/*     norm(L*D*L' - A) / ( n * norm(A) * EPS ), */
/*  where EPS is the machine epsilon. */

/*  Arguments */
/*  ========= */

/*  N       (input) INTEGTER */
/*          The order of the matrix A. */

/*  D       (input) REAL array, dimension (N) */
/*          The n diagonal elements of the tridiagonal matrix A. */

/*  E       (input) REAL array, dimension (N-1) */
/*          The (n-1) subdiagonal elements of the tridiagonal matrix A. */

/*  DF      (input) REAL array, dimension (N) */
/*          The n diagonal elements of the factor L from the L*D*L' */
/*          factorization of A. */

/*  EF      (input) REAL array, dimension (N-1) */
/*          The (n-1) subdiagonal elements of the factor L from the */
/*          L*D*L' factorization of A. */

/*  WORK    (workspace) REAL array, dimension (2*N) */

/*  RESID   (output) REAL */
/*          norm(L*D*L' - A) / (n * norm(A) * EPS) */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick return if possible */

    /* Parameter adjustments */
    --work;
    --ef;
    --df;
    --e;
    --d__;

    /* Function Body */
    if (*n <= 0) {
        *resid = 0.f;
        return 0;
    }

    eps = slamch_("Epsilon");

/*     Construct the difference L*D*L' - A. */

    work[1] = df[1] - d__[1];
    i__1 = *n - 1;
    for (i__ = 1; i__ <= i__1; ++i__) {
        de = df[i__] * ef[i__];
        work[*n + i__] = de - e[i__];
        work[i__ + 1] = de * ef[i__] + df[i__ + 1] - d__[i__ + 1];
/* L10: */
    }

/*     Compute the 1-norms of the tridiagonal matrices A and WORK. */

    if (*n == 1) {
        anorm = d__[1];
        *resid = dabs(work[1]);
    } else {
/* Computing MAX */
        r__2 = d__[1] + dabs(e[1]), r__3 = d__[*n] + (r__1 = e[*n - 1], dabs(
                r__1));
        anorm = dmax(r__2,r__3);
/* Computing MAX */
        r__4 = dabs(work[1]) + (r__1 = work[*n + 1], dabs(r__1)), r__5 = (
                r__2 = work[*n], dabs(r__2)) + (r__3 = work[(*n << 1) - 1], 
                dabs(r__3));
        *resid = dmax(r__4,r__5);
        i__1 = *n - 1;
        for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
            r__3 = anorm, r__4 = d__[i__] + (r__1 = e[i__], dabs(r__1)) + (
                    r__2 = e[i__ - 1], dabs(r__2));
            anorm = dmax(r__3,r__4);
/* Computing MAX */
            r__4 = *resid, r__5 = (r__1 = work[i__], dabs(r__1)) + (r__2 = 
                    work[*n + i__ - 1], dabs(r__2)) + (r__3 = work[*n + i__], 
                    dabs(r__3));
            *resid = dmax(r__4,r__5);
/* L20: */
        }
    }

/*     Compute norm(L*D*L' - A) / (n * norm(A) * EPS) */

    if (anorm <= 0.f) {
        if (*resid != 0.f) {
            *resid = 1.f / eps;
        }
    } else {
        *resid = *resid / (real) (*n) / anorm / eps;
    }

    return 0;

/*     End of SPTT01 */

} /* sptt01_ */