示例#1
0
/* Given a basic set, exploit the equalties in the a basic set to construct
 * a morphishm that maps the basic set to a lower-dimensional space.
 * Specifically, the morphism reduces the number of dimensions of type "type".
 *
 * This function is a slight generalization of isl_mat_variable_compression
 * in that it allows the input to be parametric and that it allows for the
 * compression of either parameters or set variables.
 *
 * We first select the equalities of interest, that is those that involve
 * variables of type "type" and no later variables.
 * Denote those equalities as
 *
 *		-C(p) + M x = 0
 *
 * where C(p) depends on the parameters if type == isl_dim_set and
 * is a constant if type == isl_dim_param.
 *
 * First compute the (left) Hermite normal form of M,
 *
 *		M [U1 U2] = M U = H = [H1 0]
 * or
 *		              M = H Q = [H1 0] [Q1]
 *                                             [Q2]
 *
 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 * Define the transformed variables as
 *
 *		x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 *		            [ x2' ]           [Q2]
 *
 * The equalities then become
 *
 *		-C(p) + H1 x1' = 0   or   x1' = H1^{-1} C(p) = C'(p)
 *
 * If the denominator of the constant term does not divide the
 * the common denominator of the parametric terms, then every
 * integer point is mapped to a non-integer point and then the original set has no
 * integer solutions (since the x' are a unimodular transformation
 * of the x).  In this case, an empty morphism is returned.
 * Otherwise, the transformation is given by
 *
 *		x = U1 H1^{-1} C(p) + U2 x2'
 *
 * The inverse transformation is simply
 *
 *		x2' = Q2 x
 *
 * Both matrices are extended to map the full original space to the full
 * compressed space.
 */
__isl_give isl_morph *isl_basic_set_variable_compression(
	__isl_keep isl_basic_set *bset, enum isl_dim_type type)
{
	unsigned otype;
	unsigned ntype;
	unsigned orest;
	unsigned nrest;
	int f_eq, n_eq;
	isl_space *dim;
	isl_mat *H, *U, *Q, *C = NULL, *H1, *U1, *U2;
	isl_basic_set *dom, *ran;

	if (!bset)
		return NULL;

	if (isl_basic_set_plain_is_empty(bset))
		return isl_morph_empty(bset);

	isl_assert(bset->ctx, bset->n_div == 0, return NULL);

	otype = 1 + isl_space_offset(bset->dim, type);
	ntype = isl_basic_set_dim(bset, type);
	orest = otype + ntype;
	nrest = isl_basic_set_total_dim(bset) - (orest - 1);

	for (f_eq = 0; f_eq < bset->n_eq; ++f_eq)
		if (isl_seq_first_non_zero(bset->eq[f_eq] + orest, nrest) == -1)
			break;
	for (n_eq = 0; f_eq + n_eq < bset->n_eq; ++n_eq)
		if (isl_seq_first_non_zero(bset->eq[f_eq + n_eq] + otype, ntype) == -1)
			break;
	if (n_eq == 0)
		return isl_morph_identity(bset);

	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, f_eq, n_eq, otype, ntype);
	H = isl_mat_left_hermite(H, 0, &U, &Q);
	if (!H || !U || !Q)
		goto error;
	Q = isl_mat_drop_rows(Q, 0, n_eq);
	Q = isl_mat_diagonal(isl_mat_identity(bset->ctx, otype), Q);
	Q = isl_mat_diagonal(Q, isl_mat_identity(bset->ctx, nrest));
	C = isl_mat_alloc(bset->ctx, 1 + n_eq, otype);
	if (!C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	isl_seq_clr(C->row[0] + 1, otype - 1);
	isl_mat_sub_neg(C->ctx, C->row + 1, bset->eq + f_eq, n_eq, 0, 0, otype);
	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
	H1 = isl_mat_lin_to_aff(H1);
	C = isl_mat_inverse_product(H1, C);
	if (!C)
		goto error;
	isl_mat_free(H);

	if (!isl_int_is_one(C->row[0][0])) {
		int i;
		isl_int g;

		isl_int_init(g);
		for (i = 0; i < n_eq; ++i) {
			isl_seq_gcd(C->row[1 + i] + 1, otype - 1, &g);
			isl_int_gcd(g, g, C->row[0][0]);
			if (!isl_int_is_divisible_by(C->row[1 + i][0], g))
				break;
		}
		isl_int_clear(g);

		if (i < n_eq) {
			isl_mat_free(C);
			isl_mat_free(U);
			isl_mat_free(Q);
			return isl_morph_empty(bset);
		}

		C = isl_mat_normalize(C);
	}

	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, n_eq);
	U1 = isl_mat_lin_to_aff(U1);
	U2 = isl_mat_sub_alloc(U, 0, U->n_row, n_eq, U->n_row - n_eq);
	U2 = isl_mat_lin_to_aff(U2);
	isl_mat_free(U);

	C = isl_mat_product(U1, C);
	C = isl_mat_aff_direct_sum(C, U2);
	C = insert_parameter_rows(C, otype - 1);
	C = isl_mat_diagonal(C, isl_mat_identity(bset->ctx, nrest));

	dim = isl_space_copy(bset->dim);
	dim = isl_space_drop_dims(dim, type, 0, ntype);
	dim = isl_space_add_dims(dim, type, ntype - n_eq);
	ran = isl_basic_set_universe(dim);
	dom = copy_equalities(bset, f_eq, n_eq);

	return isl_morph_alloc(dom, ran, Q, C);
error:
	isl_mat_free(C);
	isl_mat_free(H);
	isl_mat_free(U);
	isl_mat_free(Q);
	return NULL;
}
示例#2
0
/* Given a set of equalities
 *
 *		M x - c = 0
 *
 * this function computes a unimodular transformation from a lower-dimensional
 * space to the original space that bijectively maps the integer points x'
 * in the lower-dimensional space to the integer points x in the original
 * space that satisfy the equalities.
 *
 * The input is given as a matrix B = [ -c M ] and the output is a
 * matrix that maps [1 x'] to [1 x].
 * If T2 is not NULL, then *T2 is set to a matrix mapping [1 x] to [1 x'].
 *
 * First compute the (left) Hermite normal form of M,
 *
 *		M [U1 U2] = M U = H = [H1 0]
 * or
 *		              M = H Q = [H1 0] [Q1]
 *                                             [Q2]
 *
 * with U, Q unimodular, Q = U^{-1} (and H lower triangular).
 * Define the transformed variables as
 *
 *		x = [U1 U2] [ x1' ] = [U1 U2] [Q1] x
 *		            [ x2' ]           [Q2]
 *
 * The equalities then become
 *
 *		H1 x1' - c = 0   or   x1' = H1^{-1} c = c'
 *
 * If any of the c' is non-integer, then the original set has no
 * integer solutions (since the x' are a unimodular transformation
 * of the x) and a zero-column matrix is returned.
 * Otherwise, the transformation is given by
 *
 *		x = U1 H1^{-1} c + U2 x2'
 *
 * The inverse transformation is simply
 *
 *		x2' = Q2 x
 */
__isl_give isl_mat *isl_mat_variable_compression(__isl_take isl_mat *B,
	__isl_give isl_mat **T2)
{
	int i;
	struct isl_mat *H = NULL, *C = NULL, *H1, *U = NULL, *U1, *U2, *TC;
	unsigned dim;

	if (T2)
		*T2 = NULL;
	if (!B)
		goto error;

	dim = B->n_col - 1;
	H = isl_mat_sub_alloc(B, 0, B->n_row, 1, dim);
	H = isl_mat_left_hermite(H, 0, &U, T2);
	if (!H || !U || (T2 && !*T2))
		goto error;
	if (T2) {
		*T2 = isl_mat_drop_rows(*T2, 0, B->n_row);
		*T2 = isl_mat_lin_to_aff(*T2);
		if (!*T2)
			goto error;
	}
	C = isl_mat_alloc(B->ctx, 1+B->n_row, 1);
	if (!C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	isl_mat_sub_neg(C->ctx, C->row+1, B->row, B->n_row, 0, 0, 1);
	H1 = isl_mat_sub_alloc(H, 0, H->n_row, 0, H->n_row);
	H1 = isl_mat_lin_to_aff(H1);
	TC = isl_mat_inverse_product(H1, C);
	if (!TC)
		goto error;
	isl_mat_free(H);
	if (!isl_int_is_one(TC->row[0][0])) {
		for (i = 0; i < B->n_row; ++i) {
			if (!isl_int_is_divisible_by(TC->row[1+i][0], TC->row[0][0])) {
				struct isl_ctx *ctx = B->ctx;
				isl_mat_free(B);
				isl_mat_free(TC);
				isl_mat_free(U);
				if (T2) {
					isl_mat_free(*T2);
					*T2 = NULL;
				}
				return isl_mat_alloc(ctx, 1 + dim, 0);
			}
			isl_seq_scale_down(TC->row[1+i], TC->row[1+i], TC->row[0][0], 1);
		}
		isl_int_set_si(TC->row[0][0], 1);
	}
	U1 = isl_mat_sub_alloc(U, 0, U->n_row, 0, B->n_row);
	U1 = isl_mat_lin_to_aff(U1);
	U2 = isl_mat_sub_alloc(U, 0, U->n_row, B->n_row, U->n_row - B->n_row);
	U2 = isl_mat_lin_to_aff(U2);
	isl_mat_free(U);
	TC = isl_mat_product(U1, TC);
	TC = isl_mat_aff_direct_sum(TC, U2);

	isl_mat_free(B);

	return TC;
error:
	isl_mat_free(B);
	isl_mat_free(H);
	isl_mat_free(U);
	if (T2) {
		isl_mat_free(*T2);
		*T2 = NULL;
	}
	return NULL;
}