def _hessian(xs, f_x_expr):
hess = ComponentMap()
df_dx_map = reverse_sd(f_x_expr)
for x in xs:
ddf_ddx_map = reverse_sd(df_dx_map[x])
hess[x] = ddf_ddx_map
return hess
def test_cos(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2.0)
e = pe.cos(m.x)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
def test_cos(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2.0)
e = pe.cos(m.x)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
def test_sum(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2.0)
m.y = pe.Var(initialize=3.0)
e = 2.0*m.x + 3.0*m.y - m.x*m.y
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.y], pe.value(symbolic[m.y]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
self.assertAlmostEqual(derivs[m.y], approx_deriv(e, m.y), tol)
def test_sum(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2.0)
m.y = pe.Var(initialize=3.0)
e = 2.0*m.x + 3.0*m.y - m.x*m.y
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.y], pe.value(symbolic[m.y]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
self.assertAlmostEqual(derivs[m.y], approx_deriv(e, m.y), tol)
def test_nested(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2)
m.y = pe.Var(initialize=3)
m.p = pe.Param(initialize=0.5, mutable=True)
e = pe.exp(m.x**m.p + 3.2*m.y - 12)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.y], pe.value(symbolic[m.y]), tol+3)
self.assertAlmostEqual(derivs[m.p], pe.value(symbolic[m.p]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
self.assertAlmostEqual(derivs[m.y], approx_deriv(e, m.y), tol)
self.assertAlmostEqual(derivs[m.p], approx_deriv(e, m.p), tol)
def test_nested(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2)
m.y = pe.Var(initialize=3)
m.p = pe.Param(initialize=0.5, mutable=True)
e = pe.exp(m.x**m.p + 3.2*m.y - 12)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.y], pe.value(symbolic[m.y]), tol+3)
self.assertAlmostEqual(derivs[m.p], pe.value(symbolic[m.p]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
self.assertAlmostEqual(derivs[m.y], approx_deriv(e, m.y), tol)
self.assertAlmostEqual(derivs[m.p], approx_deriv(e, m.p), tol)
def test_expressiondata(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=3)
m.e = pe.Expression(expr=m.x * 2)
@m.Expression([1, 2])
def e2(m, i):
if i == 1:
return m.x + 4
else:
return m.x ** 2
m.o = pe.Objective(expr=m.e + 1 + m.e2[1] + m.e2[2])
derivs = reverse_ad(m.o.expr)
symbolic = reverse_sd(m.o.expr)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol)
def test_expressiondata(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=3)
m.e = pe.Expression(expr=m.x * 2)
@m.Expression([1, 2])
def e2(m, i):
if i == 1:
return m.x + 4
else:
return m.x**2
m.o = pe.Objective(expr=m.e + 1 + m.e2[1] + m.e2[2])
derivs = reverse_ad(m.o.expr)
symbolic = reverse_sd(m.o.expr)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol)
import pyomo.environ as pe
from pyomo.contrib.derivatives.differentiate import reverse_ad, reverse_sd
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2)
m.y = pe.Var(initialize=3)
m.p = pe.Param(initialize=0.5, mutable=True)
e = pe.exp(m.x**m.p + 0.1*m.y)
derivs = reverse_ad(e)
print('dfdx: ', derivs[m.x])
print('dfdy: ', derivs[m.y])
print('dfdp: ', derivs[m.p])
derivs = reverse_sd(e)
print('dfdx: ', derivs[m.x])
print('dfdy: ', derivs[m.y])
print('dfdp: ', derivs[m.p])
def _build_multivariate_underestimator(xs, f):
df = reverse_sd(f)
result = pyo.value(f)
for x in xs:
result += pyo.value(df[x]) * (x - x.value)
return result
