示例#1
0
/* Construct a morphism that first does morph2 and then morph1.
 */
__isl_give isl_morph *isl_morph_compose(__isl_take isl_morph *morph1,
	__isl_take isl_morph *morph2)
{
	isl_mat *map, *inv;
	isl_basic_set *dom, *ran;

	if (!morph1 || !morph2)
		goto error;

	map = isl_mat_product(isl_mat_copy(morph1->map), isl_mat_copy(morph2->map));
	inv = isl_mat_product(isl_mat_copy(morph2->inv), isl_mat_copy(morph1->inv));
	dom = isl_morph_basic_set(isl_morph_inverse(isl_morph_copy(morph2)),
				  isl_basic_set_copy(morph1->dom));
	dom = isl_basic_set_intersect(dom, isl_basic_set_copy(morph2->dom));
	ran = isl_morph_basic_set(isl_morph_copy(morph1),
				  isl_basic_set_copy(morph2->ran));
	ran = isl_basic_set_intersect(ran, isl_basic_set_copy(morph1->ran));

	isl_morph_free(morph1);
	isl_morph_free(morph2);

	return isl_morph_alloc(dom, ran, map, inv);
error:
	isl_morph_free(morph1);
	isl_morph_free(morph2);
	return NULL;
}
示例#2
0
/* Given a set of equalities
 *
 *		B(y) + A x = 0						(*)
 *
 * compute and return an affine transformation T,
 *
 *		y = T y'
 *
 * that bijectively maps the integer vectors y' to integer
 * vectors y that satisfy the modulo constraints for some value of x.
 *
 * Let [H 0] be the Hermite Normal Form of A, i.e.,
 *
 *		A = [H 0] Q
 *
 * Then y is a solution of (*) iff
 *
 *		H^-1 B(y) (= - [I 0] Q x)
 *
 * is an integer vector.  Let d be the common denominator of H^-1.
 * We impose
 *
 *		d H^-1 B(y) = 0 mod d
 *
 * and compute the solution using isl_mat_parameter_compression.
 */
__isl_give isl_mat *isl_mat_parameter_compression_ext(__isl_take isl_mat *B,
	__isl_take isl_mat *A)
{
	isl_ctx *ctx;
	isl_vec *d;
	int n_row, n_col;

	if (!A)
		return isl_mat_free(B);

	ctx = isl_mat_get_ctx(A);
	n_row = A->n_row;
	n_col = A->n_col;
	A = isl_mat_left_hermite(A, 0, NULL, NULL);
	A = isl_mat_drop_cols(A, n_row, n_col - n_row);
	A = isl_mat_lin_to_aff(A);
	A = isl_mat_right_inverse(A);
	d = isl_vec_alloc(ctx, n_row);
	if (A)
		d = isl_vec_set(d, A->row[0][0]);
	A = isl_mat_drop_rows(A, 0, 1);
	A = isl_mat_drop_cols(A, 0, 1);
	B = isl_mat_product(A, B);

	return isl_mat_parameter_compression(B, d);
}
示例#3
0
/* Construct a parameter compression for "bset".
 * We basically just call isl_mat_parameter_compression with the right input
 * and then extend the resulting matrix to include the variables.
 *
 * Let the equalities be given as
 *
 *	B(p) + A x = 0
 *
 * and let [H 0] be the Hermite Normal Form of A, then
 *
 *	H^-1 B(p)
 *
 * needs to be integer, so we impose that each row is divisible by
 * the denominator.
 */
__isl_give isl_morph *isl_basic_set_parameter_compression(
	__isl_keep isl_basic_set *bset)
{
	unsigned nparam;
	unsigned nvar;
	int n_eq;
	isl_mat *H, *B;
	isl_vec *d;
	isl_mat *map, *inv;
	isl_basic_set *dom, *ran;

	if (!bset)
		return NULL;

	if (isl_basic_set_plain_is_empty(bset))
		return isl_morph_empty(bset);
	if (bset->n_eq == 0)
		return isl_morph_identity(bset);

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

	n_eq = bset->n_eq;
	nparam = isl_basic_set_dim(bset, isl_dim_param);
	nvar = isl_basic_set_dim(bset, isl_dim_set);

	isl_assert(bset->ctx, n_eq <= nvar, return NULL);

	d = isl_vec_alloc(bset->ctx, n_eq);
	B = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 0, 1 + nparam);
	H = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, n_eq, 1 + nparam, nvar);
	H = isl_mat_left_hermite(H, 0, NULL, NULL);
	H = isl_mat_drop_cols(H, n_eq, nvar - n_eq);
	H = isl_mat_lin_to_aff(H);
	H = isl_mat_right_inverse(H);
	if (!H || !d)
		goto error;
	isl_seq_set(d->el, H->row[0][0], d->size);
	H = isl_mat_drop_rows(H, 0, 1);
	H = isl_mat_drop_cols(H, 0, 1);
	B = isl_mat_product(H, B);
	inv = isl_mat_parameter_compression(B, d);
	inv = isl_mat_diagonal(inv, isl_mat_identity(bset->ctx, nvar));
	map = isl_mat_right_inverse(isl_mat_copy(inv));

	dom = isl_basic_set_universe(isl_space_copy(bset->dim));
	ran = isl_basic_set_universe(isl_space_copy(bset->dim));

	return isl_morph_alloc(dom, ran, map, inv);
error:
	isl_mat_free(H);
	isl_mat_free(B);
	isl_vec_free(d);
	return NULL;
}
示例#4
0
/* Given a set of modulo constraints
 *
 *		c + A y = 0 mod d
 *
 * this function computes a particular solution y_0
 *
 * The input is given as a matrix B = [ c A ] and a vector d.
 *
 * The output is matrix containing the solution y_0 or
 * a zero-column matrix if the constraints admit no integer solution.
 *
 * The given set of constrains is equivalent to
 *
 *		c + A y = -D x
 *
 * with D = diag d and x a fresh set of variables.
 * Reducing both c and A modulo d does not change the
 * value of y in the solution and may lead to smaller coefficients.
 * Let M = [ D A ] and [ H 0 ] = M U, the Hermite normal form of M.
 * Then
 *		  [ x ]
 *		M [ y ] = - c
 * and so
 *		               [ x ]
 *		[ H 0 ] U^{-1} [ y ] = - c
 * Let
 *		[ A ]          [ x ]
 *		[ B ] = U^{-1} [ y ]
 * then
 *		H A + 0 B = -c
 *
 * so B may be chosen arbitrarily, e.g., B = 0, and then
 *
 *		       [ x ] = [ -c ]
 *		U^{-1} [ y ] = [  0 ]
 * or
 *		[ x ]     [ -c ]
 *		[ y ] = U [  0 ]
 * specifically,
 *
 *		y = U_{2,1} (-c)
 *
 * If any of the coordinates of this y are non-integer
 * then the constraints admit no integer solution and
 * a zero-column matrix is returned.
 */
static struct isl_mat *particular_solution(struct isl_mat *B, struct isl_vec *d)
{
	int i, j;
	struct isl_mat *M = NULL;
	struct isl_mat *C = NULL;
	struct isl_mat *U = NULL;
	struct isl_mat *H = NULL;
	struct isl_mat *cst = NULL;
	struct isl_mat *T = NULL;

	M = isl_mat_alloc(B->ctx, B->n_row, B->n_row + B->n_col - 1);
	C = isl_mat_alloc(B->ctx, 1 + B->n_row, 1);
	if (!M || !C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	for (i = 0; i < B->n_row; ++i) {
		isl_seq_clr(M->row[i], B->n_row);
		isl_int_set(M->row[i][i], d->block.data[i]);
		isl_int_neg(C->row[1 + i][0], B->row[i][0]);
		isl_int_fdiv_r(C->row[1+i][0], C->row[1+i][0], M->row[i][i]);
		for (j = 0; j < B->n_col - 1; ++j)
			isl_int_fdiv_r(M->row[i][B->n_row + j],
					B->row[i][1 + j], M->row[i][i]);
	}
	M = isl_mat_left_hermite(M, 0, &U, NULL);
	if (!M || !U)
		goto error;
	H = isl_mat_sub_alloc(M, 0, B->n_row, 0, B->n_row);
	H = isl_mat_lin_to_aff(H);
	C = isl_mat_inverse_product(H, C);
	if (!C)
		goto error;
	for (i = 0; i < B->n_row; ++i) {
		if (!isl_int_is_divisible_by(C->row[1+i][0], C->row[0][0]))
			break;
		isl_int_divexact(C->row[1+i][0], C->row[1+i][0], C->row[0][0]);
	}
	if (i < B->n_row)
		cst = isl_mat_alloc(B->ctx, B->n_row, 0);
	else
		cst = isl_mat_sub_alloc(C, 1, B->n_row, 0, 1);
	T = isl_mat_sub_alloc(U, B->n_row, B->n_col - 1, 0, B->n_row);
	cst = isl_mat_product(T, cst);
	isl_mat_free(M);
	isl_mat_free(C);
	isl_mat_free(U);
	return cst;
error:
	isl_mat_free(M);
	isl_mat_free(C);
	isl_mat_free(U);
	return NULL;
}
示例#5
0
static struct isl_mat *isl_basic_set_samples(struct isl_basic_set *bset)
{
	struct isl_mat *T;
	struct isl_mat *samples;

	if (!bset)
		return NULL;

	if (bset->n_eq == 0)
		return isl_basic_set_scan_samples(bset);

	bset = isl_basic_set_remove_equalities(bset, &T, NULL);
	samples = isl_basic_set_scan_samples(bset);
	return isl_mat_product(samples, isl_mat_transpose(T));
}
示例#6
0
/* Apply the morphism to the basic set.
 * We basically just compute the preimage of "bset" under the inverse mapping
 * in morph, add in stride constraints and intersect with the range
 * of the morphism.
 */
__isl_give isl_basic_set *isl_morph_basic_set(__isl_take isl_morph *morph,
	__isl_take isl_basic_set *bset)
{
	isl_basic_set *res = NULL;
	isl_mat *mat = NULL;
	int i, k;
	int max_stride;

	if (!morph || !bset)
		goto error;

	isl_assert(bset->ctx, isl_space_is_equal(bset->dim, morph->dom->dim),
		    goto error);

	max_stride = morph->inv->n_row - 1;
	if (isl_int_is_one(morph->inv->row[0][0]))
		max_stride = 0;
	res = isl_basic_set_alloc_space(isl_space_copy(morph->ran->dim),
		bset->n_div + max_stride, bset->n_eq + max_stride, bset->n_ineq);

	for (i = 0; i < bset->n_div; ++i)
		if (isl_basic_set_alloc_div(res) < 0)
			goto error;

	mat = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
					0, morph->inv->n_row);
	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
	if (!mat)
		goto error;
	for (i = 0; i < bset->n_eq; ++i) {
		k = isl_basic_set_alloc_equality(res);
		if (k < 0)
			goto error;
		isl_seq_cpy(res->eq[k], mat->row[i], mat->n_col);
		isl_seq_scale(res->eq[k] + mat->n_col, bset->eq[i] + mat->n_col,
				morph->inv->row[0][0], bset->n_div);
	}
	isl_mat_free(mat);

	mat = isl_mat_sub_alloc6(bset->ctx, bset->ineq, 0, bset->n_ineq,
					0, morph->inv->n_row);
	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
	if (!mat)
		goto error;
	for (i = 0; i < bset->n_ineq; ++i) {
		k = isl_basic_set_alloc_inequality(res);
		if (k < 0)
			goto error;
		isl_seq_cpy(res->ineq[k], mat->row[i], mat->n_col);
		isl_seq_scale(res->ineq[k] + mat->n_col,
				bset->ineq[i] + mat->n_col,
				morph->inv->row[0][0], bset->n_div);
	}
	isl_mat_free(mat);

	mat = isl_mat_sub_alloc6(bset->ctx, bset->div, 0, bset->n_div,
					1, morph->inv->n_row);
	mat = isl_mat_product(mat, isl_mat_copy(morph->inv));
	if (!mat)
		goto error;
	for (i = 0; i < bset->n_div; ++i) {
		isl_int_mul(res->div[i][0],
				morph->inv->row[0][0], bset->div[i][0]);
		isl_seq_cpy(res->div[i] + 1, mat->row[i], mat->n_col);
		isl_seq_scale(res->div[i] + 1 + mat->n_col,
				bset->div[i] + 1 + mat->n_col,
				morph->inv->row[0][0], bset->n_div);
	}
	isl_mat_free(mat);

	res = add_strides(res, morph);

	if (isl_basic_set_is_rational(bset))
		res = isl_basic_set_set_rational(res);

	res = isl_basic_set_simplify(res);
	res = isl_basic_set_finalize(res);

	res = isl_basic_set_intersect(res, isl_basic_set_copy(morph->ran));

	isl_morph_free(morph);
	isl_basic_set_free(bset);
	return res;
error:
	isl_mat_free(mat);
	isl_morph_free(morph);
	isl_basic_set_free(bset);
	isl_basic_set_free(res);
	return NULL;
}
示例#7
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#8
0
/* Check if dimension dim belongs to a residue class
 *		i_dim \equiv r mod m
 * with m != 1 and if so return m in *modulo and r in *residue.
 * As a special case, when i_dim has a fixed value v, then
 * *modulo is set to 0 and *residue to v.
 *
 * If i_dim does not belong to such a residue class, then *modulo
 * is set to 1 and *residue is set to 0.
 */
int isl_basic_set_dim_residue_class(struct isl_basic_set *bset,
	int pos, isl_int *modulo, isl_int *residue)
{
	struct isl_ctx *ctx;
	struct isl_mat *H = NULL, *U = NULL, *C, *H1, *U1;
	unsigned total;
	unsigned nparam;

	if (!bset || !modulo || !residue)
		return -1;

	if (isl_basic_set_plain_dim_is_fixed(bset, pos, residue)) {
		isl_int_set_si(*modulo, 0);
		return 0;
	}

	ctx = isl_basic_set_get_ctx(bset);
	total = isl_basic_set_total_dim(bset);
	nparam = isl_basic_set_n_param(bset);
	H = isl_mat_sub_alloc6(ctx, bset->eq, 0, bset->n_eq, 1, total);
	H = isl_mat_left_hermite(H, 0, &U, NULL);
	if (!H)
		return -1;

	isl_seq_gcd(U->row[nparam + pos]+bset->n_eq,
			total-bset->n_eq, modulo);
	if (isl_int_is_zero(*modulo))
		isl_int_set_si(*modulo, 1);
	if (isl_int_is_one(*modulo)) {
		isl_int_set_si(*residue, 0);
		isl_mat_free(H);
		isl_mat_free(U);
		return 0;
	}

	C = isl_mat_alloc(ctx, 1 + bset->n_eq, 1);
	if (!C)
		goto error;
	isl_int_set_si(C->row[0][0], 1);
	isl_mat_sub_neg(ctx, C->row + 1, bset->eq, bset->n_eq, 0, 0, 1);
	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);
	isl_mat_free(H);
	U1 = isl_mat_sub_alloc(U, nparam+pos, 1, 0, bset->n_eq);
	U1 = isl_mat_lin_to_aff(U1);
	isl_mat_free(U);
	C = isl_mat_product(U1, C);
	if (!C)
		return -1;
	if (!isl_int_is_divisible_by(C->row[1][0], C->row[0][0])) {
		bset = isl_basic_set_copy(bset);
		bset = isl_basic_set_set_to_empty(bset);
		isl_basic_set_free(bset);
		isl_int_set_si(*modulo, 1);
		isl_int_set_si(*residue, 0);
		return 0;
	}
	isl_int_divexact(*residue, C->row[1][0], C->row[0][0]);
	isl_int_fdiv_r(*residue, *residue, *modulo);
	isl_mat_free(C);
	return 0;
error:
	isl_mat_free(H);
	isl_mat_free(U);
	return -1;
}
示例#9
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;
}