dort03.c

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/* dort03.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 doublereal c_b7 = 1.;
static integer c__1 = 1;

/* Subroutine */ int dort03_(char *rc, integer *mu, integer *mv, integer *n, 
        integer *k, doublereal *u, integer *ldu, doublereal *v, integer *ldv, 
        doublereal *work, integer *lwork, doublereal *result, integer *info)
{
    /* System generated locals */
    integer u_dim1, u_offset, v_dim1, v_offset, i__1, i__2;
    doublereal d__1, d__2, d__3;

    /* Builtin functions */
    double d_sign(doublereal *, doublereal *);

    /* Local variables */
    integer i__, j;
    doublereal s;
    integer irc, lmx;
    doublereal ulp, res1, res2;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dort01_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);


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

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

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

/*  DORT03 compares two orthogonal matrices U and V to see if their */
/*  corresponding rows or columns span the same spaces.  The rows are */
/*  checked if RC = 'R', and the columns are checked if RC = 'C'. */

/*  RESULT is the maximum of */

/*     | V*V' - I | / ( MV ulp ), if RC = 'R', or */

/*     | V'*V - I | / ( MV ulp ), if RC = 'C', */

/*  and the maximum over rows (or columns) 1 to K of */

/*     | U(i) - S*V(i) |/ ( N ulp ) */

/*  where S is +-1 (chosen to minimize the expression), U(i) is the i-th */
/*  row (column) of U, and V(i) is the i-th row (column) of V. */

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

/*  RC      (input) CHARACTER*1 */
/*          If RC = 'R' the rows of U and V are to be compared. */
/*          If RC = 'C' the columns of U and V are to be compared. */

/*  MU      (input) INTEGER */
/*          The number of rows of U if RC = 'R', and the number of */
/*          columns if RC = 'C'.  If MU = 0 DORT03 does nothing. */
/*          MU must be at least zero. */

/*  MV      (input) INTEGER */
/*          The number of rows of V if RC = 'R', and the number of */
/*          columns if RC = 'C'.  If MV = 0 DORT03 does nothing. */
/*          MV must be at least zero. */

/*  N       (input) INTEGER */
/*          If RC = 'R', the number of columns in the matrices U and V, */
/*          and if RC = 'C', the number of rows in U and V.  If N = 0 */
/*          DORT03 does nothing.  N must be at least zero. */

/*  K       (input) INTEGER */
/*          The number of rows or columns of U and V to compare. */
/*          0 <= K <= max(MU,MV). */

/*  U       (input) DOUBLE PRECISION array, dimension (LDU,N) */
/*          The first matrix to compare.  If RC = 'R', U is MU by N, and */
/*          if RC = 'C', U is N by MU. */

/*  LDU     (input) INTEGER */
/*          The leading dimension of U.  If RC = 'R', LDU >= max(1,MU), */
/*          and if RC = 'C', LDU >= max(1,N). */

/*  V       (input) DOUBLE PRECISION array, dimension (LDV,N) */
/*          The second matrix to compare.  If RC = 'R', V is MV by N, and */
/*          if RC = 'C', V is N by MV. */

/*  LDV     (input) INTEGER */
/*          The leading dimension of V.  If RC = 'R', LDV >= max(1,MV), */
/*          and if RC = 'C', LDV >= max(1,N). */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK) */

/*  LWORK   (input) INTEGER */
/*          The length of the array WORK.  For best performance, LWORK */
/*          should be at least N*N if RC = 'C' or M*M if RC = 'R', but */
/*          the tests will be done even if LWORK is 0. */

/*  RESULT  (output) DOUBLE PRECISION */
/*          The value computed by the test described above.  RESULT is */
/*          limited to 1/ulp to avoid overflow. */

/*  INFO    (output) INTEGER */
/*          0  indicates a successful exit */
/*          -k indicates the k-th parameter had an illegal value */

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

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

/*     Check inputs */

    /* Parameter adjustments */
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    --work;

    /* Function Body */
    *info = 0;
    if (lsame_(rc, "R")) {
        irc = 0;
    } else if (lsame_(rc, "C")) {
        irc = 1;
    } else {
        irc = -1;
    }
    if (irc == -1) {
        *info = -1;
    } else if (*mu < 0) {
        *info = -2;
    } else if (*mv < 0) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*k < 0 || *k > max(*mu,*mv)) {
        *info = -5;
    } else if (irc == 0 && *ldu < max(1,*mu) || irc == 1 && *ldu < max(1,*n)) 
            {
        *info = -7;
    } else if (irc == 0 && *ldv < max(1,*mv) || irc == 1 && *ldv < max(1,*n)) 
            {
        *info = -9;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DORT03", &i__1);
        return 0;
    }

/*     Initialize result */

    *result = 0.;
    if (*mu == 0 || *mv == 0 || *n == 0) {
        return 0;
    }

/*     Machine constants */

    ulp = dlamch_("Precision");

    if (irc == 0) {

/*        Compare rows */

        res1 = 0.;
        i__1 = *k;
        for (i__ = 1; i__ <= i__1; ++i__) {
            lmx = idamax_(n, &u[i__ + u_dim1], ldu);
            s = d_sign(&c_b7, &u[i__ + lmx * u_dim1]) * d_sign(&c_b7, &v[i__ 
                    + lmx * v_dim1]);
            i__2 = *n;
            for (j = 1; j <= i__2; ++j) {
/* Computing MAX */
                d__2 = res1, d__3 = (d__1 = u[i__ + j * u_dim1] - s * v[i__ + 
                        j * v_dim1], abs(d__1));
                res1 = max(d__2,d__3);
/* L10: */
            }
/* L20: */
        }
        res1 /= (doublereal) (*n) * ulp;

/*        Compute orthogonality of rows of V. */

        dort01_("Rows", mv, n, &v[v_offset], ldv, &work[1], lwork, &res2);

    } else {

/*        Compare columns */

        res1 = 0.;
        i__1 = *k;
        for (i__ = 1; i__ <= i__1; ++i__) {
            lmx = idamax_(n, &u[i__ * u_dim1 + 1], &c__1);
            s = d_sign(&c_b7, &u[lmx + i__ * u_dim1]) * d_sign(&c_b7, &v[lmx 
                    + i__ * v_dim1]);
            i__2 = *n;
            for (j = 1; j <= i__2; ++j) {
/* Computing MAX */
                d__2 = res1, d__3 = (d__1 = u[j + i__ * u_dim1] - s * v[j + 
                        i__ * v_dim1], abs(d__1));
                res1 = max(d__2,d__3);
/* L30: */
            }
/* L40: */
        }
        res1 /= (doublereal) (*n) * ulp;

/*        Compute orthogonality of columns of V. */

        dort01_("Columns", n, mv, &v[v_offset], ldv, &work[1], lwork, &res2);
    }

/* Computing MIN */
    d__1 = max(res1,res2), d__2 = 1. / ulp;
    *result = min(d__1,d__2);
    return 0;

/*     End of DORT03 */

} /* dort03_ */