sgtt01.c

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/* sgtt01.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 sgtt01_(integer *n, real *dl, real *d__, real *du, real *
        dlf, real *df, real *duf, real *du2, integer *ipiv, real *work, 
        integer *ldwork, real *rwork, real *resid)
{
    /* System generated locals */
    integer work_dim1, work_offset, i__1, i__2;

    /* Local variables */
    integer i__, j;
    real li;
    integer ip;
    real eps, anorm;
    integer lastj;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
            integer *), saxpy_(integer *, real *, real *, integer *, real *, 
            integer *);
    extern doublereal slamch_(char *), slangt_(char *, integer *, 
            real *, real *, real *), slanhs_(char *, integer *, real *
, integer *, real *);


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

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

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

/*  SGTT01 reconstructs a tridiagonal matrix A from its LU factorization */
/*  and computes the residual */
/*     norm(L*U - A) / ( norm(A) * EPS ), */
/*  where EPS is the machine epsilon. */

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

/*  N       (input) INTEGTER */
/*          The order of the matrix A.  N >= 0. */

/*  DL      (input) REAL array, dimension (N-1) */
/*          The (n-1) sub-diagonal elements of A. */

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

/*  DU      (input) REAL array, dimension (N-1) */
/*          The (n-1) super-diagonal elements of A. */

/*  DLF     (input) REAL array, dimension (N-1) */
/*          The (n-1) multipliers that define the matrix L from the */
/*          LU factorization of A. */

/*  DF      (input) REAL array, dimension (N) */
/*          The n diagonal elements of the upper triangular matrix U from */
/*          the LU factorization of A. */

/*  DUF     (input) REAL array, dimension (N-1) */
/*          The (n-1) elements of the first super-diagonal of U. */

/*  DU2F    (input) REAL array, dimension (N-2) */
/*          The (n-2) elements of the second super-diagonal of U. */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices; for 1 <= i <= n, row i of the matrix was */
/*          interchanged with row IPIV(i).  IPIV(i) will always be either */
/*          i or i+1; IPIV(i) = i indicates a row interchange was not */
/*          required. */

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

/*  LDWORK  (input) INTEGER */
/*          The leading dimension of the array WORK.  LDWORK >= max(1,N). */

/*  RWORK   (workspace) REAL array, dimension (N) */

/*  RESID   (output) REAL */
/*          The scaled residual:  norm(L*U - A) / (norm(A) * EPS) */

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

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

/*     Quick return if possible */

    /* Parameter adjustments */
    --dl;
    --d__;
    --du;
    --dlf;
    --df;
    --duf;
    --du2;
    --ipiv;
    work_dim1 = *ldwork;
    work_offset = 1 + work_dim1;
    work -= work_offset;
    --rwork;

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

    eps = slamch_("Epsilon");

/*     Copy the matrix U to WORK. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *n;
        for (i__ = 1; i__ <= i__2; ++i__) {
            work[i__ + j * work_dim1] = 0.f;
/* L10: */
        }
/* L20: */
    }
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        if (i__ == 1) {
            work[i__ + i__ * work_dim1] = df[i__];
            if (*n >= 2) {
                work[i__ + (i__ + 1) * work_dim1] = duf[i__];
            }
            if (*n >= 3) {
                work[i__ + (i__ + 2) * work_dim1] = du2[i__];
            }
        } else if (i__ == *n) {
            work[i__ + i__ * work_dim1] = df[i__];
        } else {
            work[i__ + i__ * work_dim1] = df[i__];
            work[i__ + (i__ + 1) * work_dim1] = duf[i__];
            if (i__ < *n - 1) {
                work[i__ + (i__ + 2) * work_dim1] = du2[i__];
            }
        }
/* L30: */
    }

/*     Multiply on the left by L. */

    lastj = *n;
    for (i__ = *n - 1; i__ >= 1; --i__) {
        li = dlf[i__];
        i__1 = lastj - i__ + 1;
        saxpy_(&i__1, &li, &work[i__ + i__ * work_dim1], ldwork, &work[i__ + 
                1 + i__ * work_dim1], ldwork);
        ip = ipiv[i__];
        if (ip == i__) {
/* Computing MIN */
            i__1 = i__ + 2;
            lastj = min(i__1,*n);
        } else {
            i__1 = lastj - i__ + 1;
            sswap_(&i__1, &work[i__ + i__ * work_dim1], ldwork, &work[i__ + 1 
                    + i__ * work_dim1], ldwork);
        }
/* L40: */
    }

/*     Subtract the matrix A. */

    work[work_dim1 + 1] -= d__[1];
    if (*n > 1) {
        work[(work_dim1 << 1) + 1] -= du[1];
        work[*n + (*n - 1) * work_dim1] -= dl[*n - 1];
        work[*n + *n * work_dim1] -= d__[*n];
        i__1 = *n - 1;
        for (i__ = 2; i__ <= i__1; ++i__) {
            work[i__ + (i__ - 1) * work_dim1] -= dl[i__ - 1];
            work[i__ + i__ * work_dim1] -= d__[i__];
            work[i__ + (i__ + 1) * work_dim1] -= du[i__];
/* L50: */
        }
    }

/*     Compute the 1-norm of the tridiagonal matrix A. */

    anorm = slangt_("1", n, &dl[1], &d__[1], &du[1]);

/*     Compute the 1-norm of WORK, which is only guaranteed to be */
/*     upper Hessenberg. */

    *resid = slanhs_("1", n, &work[work_offset], ldwork, &rwork[1])
            ;

/*     Compute norm(L*U - A) / (norm(A) * EPS) */

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

    return 0;

/*     End of SGTT01 */

} /* sgtt01_ */