stpt01.c

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/* stpt01.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 stpt01_(char *uplo, char *diag, integer *n, real *ap, 
        real *ainvp, real *rcond, real *work, real *resid)
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    integer j, jc;
    real eps;
    extern logical lsame_(char *, char *);
    real anorm;
    logical unitd;
    extern /* Subroutine */ int stpmv_(char *, char *, char *, integer *, 
            real *, real *, integer *);
    extern doublereal slamch_(char *);
    real ainvnm;
    extern doublereal slantp_(char *, char *, char *, integer *, real *, real 
            *);


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

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

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

/*  STPT01 computes the residual for a triangular matrix A times its */
/*  inverse when A is stored in packed format: */
/*     RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), */
/*  where EPS is the machine epsilon. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the matrix A is upper or lower triangular. */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  DIAG    (input) CHARACTER*1 */
/*          Specifies whether or not the matrix A is unit triangular. */
/*          = 'N':  Non-unit triangular */
/*          = 'U':  Unit triangular */

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

/*  AP      (input) REAL array, dimension (N*(N+1)/2) */
/*          The original upper or lower triangular matrix A, packed */
/*          columnwise in a linear array.  The j-th column of A is stored */
/*          in the array AP as follows: */
/*          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; */
/*          if UPLO = 'L', */
/*             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. */

/*  AINVP   (input/output) REAL array, dimension (N*(N+1)/2) */
/*          On entry, the (triangular) inverse of the matrix A, packed */
/*          columnwise in a linear array as in AP. */
/*          On exit, the contents of AINVP are destroyed. */

/*  RCOND   (output) REAL */
/*          The reciprocal condition number of A, computed as */
/*          1/(norm(A) * norm(AINV)). */

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

/*  RESID   (output) REAL */
/*          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) */

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

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

/*     Quick exit if N = 0. */

    /* Parameter adjustments */
    --work;
    --ainvp;
    --ap;

    /* Function Body */
    if (*n <= 0) {
        *rcond = 1.f;
        *resid = 0.f;
        return 0;
    }

/*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */

    eps = slamch_("Epsilon");
    anorm = slantp_("1", uplo, diag, n, &ap[1], &work[1]);
    ainvnm = slantp_("1", uplo, diag, n, &ainvp[1], &work[1]);
    if (anorm <= 0.f || ainvnm <= 0.f) {
        *rcond = 0.f;
        *resid = 1.f / eps;
        return 0;
    }
    *rcond = 1.f / anorm / ainvnm;

/*     Compute A * AINV, overwriting AINV. */

    unitd = lsame_(diag, "U");
    if (lsame_(uplo, "U")) {
        jc = 1;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (unitd) {
                ainvp[jc + j - 1] = 1.f;
            }

/*           Form the j-th column of A*AINV */

            stpmv_("Upper", "No transpose", diag, &j, &ap[1], &ainvp[jc], &
                    c__1);

/*           Subtract 1 from the diagonal */

            ainvp[jc + j - 1] += -1.f;
            jc += j;
/* L10: */
        }
    } else {
        jc = 1;
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (unitd) {
                ainvp[jc] = 1.f;
            }

/*           Form the j-th column of A*AINV */

            i__2 = *n - j + 1;
            stpmv_("Lower", "No transpose", diag, &i__2, &ap[jc], &ainvp[jc], 
                    &c__1);

/*           Subtract 1 from the diagonal */

            ainvp[jc] += -1.f;
            jc = jc + *n - j + 1;
/* L20: */
        }
    }

/*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) */

    *resid = slantp_("1", uplo, "Non-unit", n, &ainvp[1], &work[1]);

    *resid = *resid * *rcond / (real) (*n) / eps;

    return 0;

/*     End of STPT01 */

} /* stpt01_ */