Add piecewise reductions. (a8d259ca) · Commits · Cianciosa, Mark / graph_framework

graph_driver/xrays.cpp

+6 −5

Original line number	Diff line number	Diff line
		@@ -83,7 +83,8 @@ int main(int argc, const char * argv[]) {
		}

		omega->set(static_cast<base> (500.0));
		x->set(static_cast<base> (-12.0));
		//x->set(static_cast<base> (-12.0));
		x->set(static_cast<base> (2.5));
		//x->set(static_cast<base> (0.0));
		y->set(static_cast<base> (0.0));
		z->set(static_cast<base> (0.0));
		@@ -92,13 +93,13 @@ int main(int argc, const char * argv[]) {
		ky->set(static_cast<base> (0.0));
		kz->set(static_cast<base> (10.0));

		//auto eq = equilibrium::make_efit<base, use_safe_math> (NC_FILE, sync);
		auto eq = equilibrium::make_efit<base, use_safe_math> (NC_FILE, sync);
		//auto eq = equilibrium::make_slab_density<base, use_safe_math> ();
		auto eq = equilibrium::make_slab_field<base, use_safe_math> ();
		//auto eq = equilibrium::make_slab_field<base, use_safe_math> ();
		//auto eq = equilibrium::make_no_magnetic_field<base, use_safe_math> ();

		const base endtime = static_cast<base> (10.0);
		//const base endtime = static_cast<base> (0.25);
		//const base endtime = static_cast<base> (10.0);
		const base endtime = static_cast<base> (0.25);
		const base dt = endtime/static_cast<base> (num_times);

		//auto dt_var = graph::variable(num_rays, static_cast<base> (dt), "dt");

graph_framework/arithmetic.hpp

+120 −0

Original line number	Diff line number	Diff line
		@@ -80,6 +80,30 @@ namespace graph {
		return this->right + this->left;
		}

		auto pl1 = piecewise_1D_cast(this->left);
		auto pr1 = piecewise_1D_cast(this->right);

		if (pl1.get() && (r.get() \|\| pl1->is_arg_match(this->right))) {
		return piecewise_1D(this->evaluate(), pl1->get_arg());
		} else if (pr1.get() && (l.get() \|\| pr1->is_arg_match(this->left))) {
		return piecewise_1D(this->evaluate(), pr1->get_arg());
		}

		auto pl2 = piecewise_2D_cast(this->left);
		auto pr2 = piecewise_2D_cast(this->right);

		if (pl2.get() && (r.get() \|\| pl2->is_arg_match(this->right))) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right());
		} else if (pr2.get() && (l.get() \|\| pr2->is_arg_match(this->left))) {
		return piecewise_2D(this->evaluate(),
		pr2->get_num_columns(),
		pr2->get_left(),
		pr2->get_right());
		}

		// Idenity reductions.
		if (this->left->is_match(this->right)) {
		return two<T, SAFE_MATH> ()*this->left;
		@@ -462,6 +486,30 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto pl1 = piecewise_1D_cast(this->left);
		auto pr1 = piecewise_1D_cast(this->right);

		if (pl1.get() && (r.get() \|\| pl1->is_arg_match(this->right))) {
		return piecewise_1D(this->evaluate(), pl1->get_arg());
		} else if (pr1.get() && (l.get() \|\| pr1->is_arg_match(this->left))) {
		return piecewise_1D(this->evaluate(), pr1->get_arg());
		}

		auto pl2 = piecewise_2D_cast(this->left);
		auto pr2 = piecewise_2D_cast(this->right);

		if (pl2.get() && (r.get() \|\| pl2->is_arg_match(this->right))) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right());
		} else if (pr2.get() && (l.get() \|\| pr2->is_arg_match(this->left))) {
		return piecewise_2D(this->evaluate(),
		pr2->get_num_columns(),
		pr2->get_left(),
		pr2->get_right());
		}

		// Common factor reduction. If the left and right are both muliply nodes check
		// for a common factor. So you can change ab - ac -> a*(b - c).
		auto lm = multiply_cast(this->left);
		@@ -885,6 +933,30 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto pl1 = piecewise_1D_cast(this->left);
		auto pr1 = piecewise_1D_cast(this->right);

		if (pl1.get() && (r.get() \|\| pl1->is_arg_match(this->right))) {
		return piecewise_1D(this->evaluate(), pl1->get_arg());
		} else if (pr1.get() && (l.get() \|\| pr1->is_arg_match(this->left))) {
		return piecewise_1D(this->evaluate(), pr1->get_arg());
		}

		auto pl2 = piecewise_2D_cast(this->left);
		auto pr2 = piecewise_2D_cast(this->right);

		if (pl2.get() && (r.get() \|\| pl2->is_arg_match(this->right))) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right());
		} else if (pr2.get() && (l.get() \|\| pr2->is_arg_match(this->left))) {
		return piecewise_2D(this->evaluate(),
		pr2->get_num_columns(),
		pr2->get_left(),
		pr2->get_right());
		}

		// Move constants to the left.
		if (r.get() && !l.get()) {
		return this->right*this->left;
		@@ -1407,6 +1479,30 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto pl1 = piecewise_1D_cast(this->left);
		auto pr1 = piecewise_1D_cast(this->right);

		if (pl1.get() && (r.get() \|\| pl1->is_arg_match(this->right))) {
		return piecewise_1D(this->evaluate(), pl1->get_arg());
		} else if (pr1.get() && (l.get() \|\| pr1->is_arg_match(this->left))) {
		return piecewise_1D(this->evaluate(), pr1->get_arg());
		}

		auto pl2 = piecewise_2D_cast(this->left);
		auto pr2 = piecewise_2D_cast(this->right);

		if (pl2.get() && (r.get() \|\| pl2->is_arg_match(this->right))) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right());
		} else if (pr2.get() && (l.get() \|\| pr2->is_arg_match(this->left))) {
		return piecewise_2D(this->evaluate(),
		pr2->get_num_columns(),
		pr2->get_left(),
		pr2->get_right());
		}

		if (this->left->is_match(this->right)) {
		if (l.get() && l->is(1)) {
		return this->left;
		@@ -1791,6 +1887,30 @@ namespace graph {
		return this->right - this->left;
		}

		auto pl1 = piecewise_1D_cast(this->left);
		auto pm1 = piecewise_1D_cast(this->middle);

		if (pl1.get() && (m.get() \|\| pl1->is_arg_match(this->middle))) {
		return piecewise_1D(this->evaluate(), pl1->get_arg()) + this->right;
		} else if (pm1.get() && (m.get() \|\| pm1->is_arg_match(this->left))) {
		return piecewise_1D(this->evaluate(), pm1->get_arg()) + this->right;
		}

		auto pl2 = piecewise_2D_cast(this->left);
		auto pm2 = piecewise_2D_cast(this->middle);

		if (pl2.get() && (m.get() \|\| pl2->is_arg_match(this->right))) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right()) + this->right;
		} else if (pm2.get() && (l.get() \|\| pm2->is_arg_match(this->left))) {
		return piecewise_2D(this->evaluate(),
		pm2->get_num_columns(),
		pm2->get_left(),
		pm2->get_right()) + this->right;
		}

		// Common factor reduction. If the left and right are both multiply nodes check
		// for a common factor. So you can change ab + (ac) -> a*(b + c).
		auto lm = multiply_cast(this->left);

graph_framework/equilibrium.hpp

+34 −38

Original line number	Diff line number	Diff line
		@@ -887,8 +887,7 @@ namespace equilibrium {
		get_psi(graph::shared_leaf<T, SAFE_MATH> x,
		graph::shared_leaf<T, SAFE_MATH> y,
		graph::shared_leaf<T, SAFE_MATH> z) {
		auto r = graph::sqrt(xx + yy);
		return get_psi(r, z);
		return get_psi(graph::sqrt(xx + yy), z);
		}

		//------------------------------------------------------------------------------
		@@ -954,8 +953,7 @@ namespace equilibrium {
		get_electron_density(graph::shared_leaf<T, SAFE_MATH> x,
		graph::shared_leaf<T, SAFE_MATH> y,
		graph::shared_leaf<T, SAFE_MATH> z) {
		auto psi = get_psi(x, y, z);
		auto psi_norm = (psi - psimin)/dpsi;
		auto psi_norm = (get_psi(x, y, z) - psimin)/dpsi;

		auto c0_temp = graph::piecewise_1D(ne_c0, psi_norm);
		auto c1_temp = graph::piecewise_1D(ne_c1, psi_norm);
		@@ -997,8 +995,7 @@ namespace equilibrium {
		get_pressure(graph::shared_leaf<T, SAFE_MATH> x,
		graph::shared_leaf<T, SAFE_MATH> y,
		graph::shared_leaf<T, SAFE_MATH> z) {
		auto psi = get_psi(x, y, z);
		auto psi_norm = (psi - psimin)/dpsi;
		auto psi_norm = (get_psi(x, y, z) - psimin)/dpsi;

		auto c0_temp = graph::piecewise_1D(pres_c0, psi_norm);
		auto c1_temp = graph::piecewise_1D(pres_c1, psi_norm);
		@@ -1023,8 +1020,7 @@ namespace equilibrium {
		get_electron_temperature(graph::shared_leaf<T, SAFE_MATH> x,
		graph::shared_leaf<T, SAFE_MATH> y,
		graph::shared_leaf<T, SAFE_MATH> z) {
		auto psi = get_psi(x, y, z);
		auto psi_norm = (psi - psimin)/dpsi;
		auto psi_norm = (get_psi(x, y, z) - psimin)/dpsi;

		auto c0_temp = graph::piecewise_1D(te_c0, psi_norm);
		auto c1_temp = graph::piecewise_1D(te_c1, psi_norm);
		@@ -1093,7 +1089,7 @@ namespace equilibrium {
		auto r = graph::sqrt(xx + yy);
		auto phi = graph::atan(x, y);
		auto none = graph::none<T, SAFE_MATH> ();
		auto psi = get_psi(x, y, z);
		auto psi = get_psi(r, z);

		auto br = psi->df(z)/r;
		auto bp = get_b_phi(r);
		@@ -1304,35 +1300,35 @@ namespace equilibrium {

		const auto c00 = backend::buffer(std::vector<T> (psi_c00_buffer.begin(), psi_c00_buffer.end()));
		const auto c01 = backend::buffer(std::vector<T> (psi_c01_buffer.begin(), psi_c01_buffer.end()));
		auto c02 = backend::buffer(std::vector<T> (psi_c02_buffer.begin(), psi_c02_buffer.end()));
		auto c03 = backend::buffer(std::vector<T> (psi_c03_buffer.begin(), psi_c03_buffer.end()));
		auto c10 = backend::buffer(std::vector<T> (psi_c10_buffer.begin(), psi_c10_buffer.end()));
		auto c11 = backend::buffer(std::vector<T> (psi_c11_buffer.begin(), psi_c11_buffer.end()));
		auto c12 = backend::buffer(std::vector<T> (psi_c12_buffer.begin(), psi_c12_buffer.end()));
		auto c13 = backend::buffer(std::vector<T> (psi_c13_buffer.begin(), psi_c13_buffer.end()));
		auto c20 = backend::buffer(std::vector<T> (psi_c20_buffer.begin(), psi_c20_buffer.end()));
		auto c21 = backend::buffer(std::vector<T> (psi_c21_buffer.begin(), psi_c21_buffer.end()));
		auto c22 = backend::buffer(std::vector<T> (psi_c22_buffer.begin(), psi_c22_buffer.end()));
		auto c23 = backend::buffer(std::vector<T> (psi_c23_buffer.begin(), psi_c23_buffer.end()));
		auto c30 = backend::buffer(std::vector<T> (psi_c30_buffer.begin(), psi_c30_buffer.end()));
		auto c31 = backend::buffer(std::vector<T> (psi_c31_buffer.begin(), psi_c31_buffer.end()));
		auto c32 = backend::buffer(std::vector<T> (psi_c32_buffer.begin(), psi_c32_buffer.end()));
		auto c33 = backend::buffer(std::vector<T> (psi_c33_buffer.begin(), psi_c33_buffer.end()));

		auto pres_c0 = backend::buffer(std::vector<T> (pressure_c0_buffer.begin(), pressure_c0_buffer.end()));
		auto pres_c1 = backend::buffer(std::vector<T> (pressure_c1_buffer.begin(), pressure_c1_buffer.end()));
		auto pres_c2 = backend::buffer(std::vector<T> (pressure_c2_buffer.begin(), pressure_c2_buffer.end()));
		auto pres_c3 = backend::buffer(std::vector<T> (pressure_c3_buffer.begin(), pressure_c3_buffer.end()));

		auto te_c0 = backend::buffer(std::vector<T> (te_c0_buffer.begin(), te_c0_buffer.end()));
		auto te_c1 = backend::buffer(std::vector<T> (te_c1_buffer.begin(), te_c1_buffer.end()));
		auto te_c2 = backend::buffer(std::vector<T> (te_c2_buffer.begin(), te_c2_buffer.end()));
		auto te_c3 = backend::buffer(std::vector<T> (te_c3_buffer.begin(), te_c3_buffer.end()));

		auto ne_c0 = backend::buffer(std::vector<T> (ne_c0_buffer.begin(), ne_c0_buffer.end()));
		auto ne_c1 = backend::buffer(std::vector<T> (ne_c1_buffer.begin(), ne_c1_buffer.end()));
		auto ne_c2 = backend::buffer(std::vector<T> (ne_c2_buffer.begin(), ne_c2_buffer.end()));
		auto ne_c3 = backend::buffer(std::vector<T> (ne_c3_buffer.begin(), ne_c3_buffer.end()));
		const auto c02 = backend::buffer(std::vector<T> (psi_c02_buffer.begin(), psi_c02_buffer.end()));
		const auto c03 = backend::buffer(std::vector<T> (psi_c03_buffer.begin(), psi_c03_buffer.end()));
		const auto c10 = backend::buffer(std::vector<T> (psi_c10_buffer.begin(), psi_c10_buffer.end()));
		const auto c11 = backend::buffer(std::vector<T> (psi_c11_buffer.begin(), psi_c11_buffer.end()));
		const auto c12 = backend::buffer(std::vector<T> (psi_c12_buffer.begin(), psi_c12_buffer.end()));
		const auto c13 = backend::buffer(std::vector<T> (psi_c13_buffer.begin(), psi_c13_buffer.end()));
		const auto c20 = backend::buffer(std::vector<T> (psi_c20_buffer.begin(), psi_c20_buffer.end()));
		const auto c21 = backend::buffer(std::vector<T> (psi_c21_buffer.begin(), psi_c21_buffer.end()));
		const auto c22 = backend::buffer(std::vector<T> (psi_c22_buffer.begin(), psi_c22_buffer.end()));
		const auto c23 = backend::buffer(std::vector<T> (psi_c23_buffer.begin(), psi_c23_buffer.end()));
		const auto c30 = backend::buffer(std::vector<T> (psi_c30_buffer.begin(), psi_c30_buffer.end()));
		const auto c31 = backend::buffer(std::vector<T> (psi_c31_buffer.begin(), psi_c31_buffer.end()));
		const auto c32 = backend::buffer(std::vector<T> (psi_c32_buffer.begin(), psi_c32_buffer.end()));
		const auto c33 = backend::buffer(std::vector<T> (psi_c33_buffer.begin(), psi_c33_buffer.end()));

		const auto pres_c0 = backend::buffer(std::vector<T> (pressure_c0_buffer.begin(), pressure_c0_buffer.end()));
		const auto pres_c1 = backend::buffer(std::vector<T> (pressure_c1_buffer.begin(), pressure_c1_buffer.end()));
		const auto pres_c2 = backend::buffer(std::vector<T> (pressure_c2_buffer.begin(), pressure_c2_buffer.end()));
		const auto pres_c3 = backend::buffer(std::vector<T> (pressure_c3_buffer.begin(), pressure_c3_buffer.end()));

		const auto te_c0 = backend::buffer(std::vector<T> (te_c0_buffer.begin(), te_c0_buffer.end()));
		const auto te_c1 = backend::buffer(std::vector<T> (te_c1_buffer.begin(), te_c1_buffer.end()));
		const auto te_c2 = backend::buffer(std::vector<T> (te_c2_buffer.begin(), te_c2_buffer.end()));
		const auto te_c3 = backend::buffer(std::vector<T> (te_c3_buffer.begin(), te_c3_buffer.end()));

		const auto ne_c0 = backend::buffer(std::vector<T> (ne_c0_buffer.begin(), ne_c0_buffer.end()));
		const auto ne_c1 = backend::buffer(std::vector<T> (ne_c1_buffer.begin(), ne_c1_buffer.end()));
		const auto ne_c2 = backend::buffer(std::vector<T> (ne_c2_buffer.begin(), ne_c2_buffer.end()));
		const auto ne_c3 = backend::buffer(std::vector<T> (ne_c3_buffer.begin(), ne_c3_buffer.end()));

		return std::make_shared<efit<T, SAFE_MATH>> (psimin, dpsi,
		te_c0, te_c1, te_c2, te_c3, te_scale,

graph_framework/math.hpp

+105 −18

Original line number	Diff line number	Diff line
		@@ -60,6 +60,7 @@ namespace graph {
		//------------------------------------------------------------------------------
		virtual shared_leaf<T, SAFE_MATH> reduce() {
		auto ac = constant_cast(this->arg);

		if (ac.get()) {
		if (ac->is(0) \|\| ac->is(1)) {
		return this->arg;
		@@ -67,6 +68,20 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto ap1 = piecewise_1D_cast(this->arg);
		if (ap1.get()) {
		return piecewise_1D(this->evaluate(),
		ap1->get_arg());
		}

		auto ap2 = piecewise_2D_cast(this->arg);
		if (ap2.get()) {
		return piecewise_2D(this->evaluate(),
		ap2->get_num_columns(),
		ap2->get_left(),
		ap2->get_right());
		}

		// Handle casses like sqrt(a^b).
		auto ap = pow_cast(this->arg);
		if (ap.get()) {
		@@ -85,8 +100,12 @@ namespace graph {
		if (am.get()) {
		if (pow_cast(am->get_left()).get() \|\|
		constant_cast(am->get_left()).get() \|\|
		piecewise_1D_cast(am->get_left()).get() \|\|
		piecewise_2D_cast(am->get_left()).get() \|\|
		pow_cast(am->get_right()).get() \|\|
		constant_cast(am->get_right()).get()) {
		constant_cast(am->get_right()).get() \|\|
		piecewise_1D_cast(am->get_right()).get() \|\|
		piecewise_2D_cast(am->get_right()).get()) {
		return sqrt(am->get_left()) *
		sqrt(am->get_right());
		}
		@@ -98,8 +117,12 @@ namespace graph {
		if (ad.get()) {
		if (pow_cast(ad->get_left()).get() \|\|
		constant_cast(ad->get_left()).get() \|\|
		piecewise_1D_cast(ad->get_left()).get() \|\|
		piecewise_2D_cast(ad->get_left()).get() \|\|
		pow_cast(ad->get_right()).get() \|\|
		constant_cast(ad->get_right()).get()) {
		constant_cast(ad->get_right()).get() \|\|
		piecewise_1D_cast(ad->get_right()).get() \|\|
		piecewise_2D_cast(ad->get_right()).get()) {
		return sqrt(ad->get_left()) /
		sqrt(ad->get_right());
		}
		@@ -306,6 +329,20 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto ap1 = piecewise_1D_cast(this->arg);
		if (ap1.get()) {
		return piecewise_1D(this->evaluate(),
		ap1->get_arg());
		}

		auto ap2 = piecewise_2D_cast(this->arg);
		if (ap2.get()) {
		return piecewise_2D(this->evaluate(),
		ap2->get_num_columns(),
		ap2->get_left(),
		ap2->get_right());
		}

		// Reduce exp(log(x)) -> x
		auto a = log_cast(this->arg);
		if (a.get()) {
		@@ -484,6 +521,20 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto ap1 = piecewise_1D_cast(this->arg);
		if (ap1.get()) {
		return piecewise_1D(this->evaluate(),
		ap1->get_arg());
		}

		auto ap2 = piecewise_2D_cast(this->arg);
		if (ap2.get()) {
		return piecewise_2D(this->evaluate(),
		ap2->get_num_columns(),
		ap2->get_left(),
		ap2->get_right());
		}

		// Reduce log(exp(x)) -> x
		auto a = exp_cast(this->arg);
		if (a.get()) {
		@@ -678,6 +729,20 @@ namespace graph {
		if (constant_cast(this->left).get()) {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto pl1 = piecewise_1D_cast(this->left);
		if (pl1.get()) {
		return piecewise_1D(this->evaluate(),
		pl1->get_arg());
		}

		auto pl2 = piecewise_2D_cast(this->left);
		if (pl2.get()) {
		return piecewise_2D(this->evaluate(),
		pl2->get_num_columns(),
		pl2->get_left(),
		pl2->get_right());
		}
		}

		auto lp = pow_cast(this->left);
		@@ -690,6 +755,10 @@ namespace graph {
		if (lm.get()) {
		if (constant_cast(lm->get_left()).get() \|\|
		constant_cast(lm->get_right()).get() \|\|
		piecewise_1D_cast(lm->get_left()).get() \|\|
		piecewise_1D_cast(lm->get_right()).get() \|\|
		piecewise_2D_cast(lm->get_left()).get() \|\|
		piecewise_2D_cast(lm->get_right()).get() \|\|
		sqrt_cast(lm->get_left()).get() \|\|
		sqrt_cast(lm->get_right()).get() \|\|
		pow_cast(lm->get_left()).get() \|\|
		@@ -704,6 +773,10 @@ namespace graph {
		if (ld.get()) {
		if (constant_cast(ld->get_left()).get() \|\|
		constant_cast(ld->get_right()).get() \|\|
		piecewise_1D_cast(ld->get_left()).get() \|\|
		piecewise_1D_cast(ld->get_right()).get() \|\|
		piecewise_2D_cast(ld->get_left()).get() \|\|
		piecewise_2D_cast(ld->get_right()).get() \|\|
		sqrt_cast(ld->get_left()).get() \|\|
		sqrt_cast(ld->get_right()).get() \|\|
		pow_cast(ld->get_left()).get() \|\|
		@@ -962,6 +1035,20 @@ namespace graph {
		return constant<T, SAFE_MATH> (this->evaluate());
		}

		auto ap1 = piecewise_1D_cast(this->arg);
		if (ap1.get()) {
		return piecewise_1D(this->evaluate(),
		ap1->get_arg());
		}

		auto ap2 = piecewise_2D_cast(this->arg);
		if (ap2.get()) {
		return piecewise_2D(this->evaluate(),
		ap2->get_num_columns(),
		ap2->get_left(),
		ap2->get_right());
		}

		return this->shared_from_this();
		}

graph_framework/piecewise.hpp

+27 −1

Original line number	Diff line number	Diff line
		@@ -303,6 +303,17 @@ namespace graph {
		virtual shared_leaf<T, SAFE_MATH> get_power_exponent() const {
		return one<T, SAFE_MATH> ();
		}

		//------------------------------------------------------------------------------
		/// @brief Check if the args match.
		///
		/// @param[in] x Node to match.
		/// @returns True if the arguments match.
		//------------------------------------------------------------------------------
		bool is_arg_match(shared_leaf<T, SAFE_MATH> x) {
		auto temp = piecewise_1D_cast(x);
		return temp.get() && this->arg->is_match(temp->get_arg());
		}
		};

		//------------------------------------------------------------------------------
		@@ -469,7 +480,7 @@ namespace graph {
		///
		/// @returns The number of columns in the constant.
		//------------------------------------------------------------------------------
		size_t get_num_columns() {
		size_t get_num_columns() const {
		return num_columns;
		}

		@@ -498,6 +509,7 @@ namespace graph {
		if (evaluate().is_same()) {
		return constant<T, SAFE_MATH> (evaluate().at(0));
		}

		return this->shared_from_this();
		}

		@@ -687,6 +699,20 @@ namespace graph {
		virtual shared_leaf<T, SAFE_MATH> get_power_exponent() const {
		return one<T, SAFE_MATH> ();
		}

		//------------------------------------------------------------------------------
		/// @brief Check if the args match.
		///
		/// @param[in] x Node to match.
		/// @returns True if the arguments match.
		//------------------------------------------------------------------------------
		bool is_arg_match(shared_leaf<T, SAFE_MATH> x) {
		auto temp = piecewise_2D_cast(x);
		return temp.get() &&
		this->left->is_match(temp->get_left()) &&
		this->right->is_match(temp->get_right()) &&
		(num_columns == this->get_num_columns());
		}
		};

		//------------------------------------------------------------------------------