$\newcommand{\B}[1]{{\bf #1}} \newcommand{\R}[1]{{\rm #1}}$
 from pycppad import * # Example using a_float ------------------------------------------------------ def pycppad_test_reverse_2(): # start record a_float operations x = numpy.array( [ 2. , 3. ] ) # value of independent variables a_x = independent(x) # declare a_float independent variables # stop recording and store operations in the function object f a_y = numpy.array( [ 2. * a_x[0] * a_x[1] ] ) # dependent variables f = adfun(a_x, a_y) # f(x0, x1) = 2 * x0 * x1 # evaluate the function at same argument value p = 0 # derivative order x_p = x # zero order Taylor coefficient f_p = f.forward(0, x_p) # function value assert f_p[0] == 2. * x[0] * x[1] # f(x0, x1) = 2 * x0 * x1 # evalute partial derivative with respect to x[0] p = 1 # derivative order x_p = numpy.array( [ 1. , 0 ] ) # first order Taylor coefficient f_p = f.forward(1, x_p) # partial w.r.t. x0 assert f_p[0] == 2. * x[1] # f_x0 (x0, x1) = 2 * x1 # evaluate derivative of partial w.r.t. x[0] p = 2 # derivative order w = numpy.array( [1.] ) # weighting vector dw = f.reverse(p, w) # derivaitive of weighted function assert dw[0] == 0. # f_x0_x1 (x0, x1) = 0 assert dw[1] == 2. # f_x0_x1 (x0, x1) = 2 # Example using a2float ------------------------------------------------------ def pycppad_test_reverse_2_a2(): # start record a_float operations x = numpy.array( [ 2. , 3. ] ) # value of independent variables a_x = ad(x) # value of independent variables a2x = independent(a_x) # declare a2float independent variables # stop recording and store operations in the function object f a2y = numpy.array( [ 2. * a2x[0] * a2x[1] ] ) # dependent variables a_f = adfun(a2x, a2y) # f(x0, x1) = 2 * x0 * x1 # evaluate the function at same argument value p = 0 # derivative order x_p = a_x # zero order Taylor coefficient f_p = a_f.forward(0, x_p) # function value assert f_p[0] == 2. * x[0] * x[1] # f(x0, x1) = 2 * x0 * x1 # evalute partial derivative with respect to x[0] p = 1 # derivative order x_p = ad(numpy.array([1. , 0 ])) # first order Taylor coefficient f_p = a_f.forward(1, x_p) # partial w.r.t. x0 assert f_p[0] == 2. * x[1] # f_x0 (x0, x1) = 2 * x1 # evaluate derivative of partial w.r.t. x[0] p = 2 # derivative order w = ad(numpy.array( [1.] )) # weighting vector dw = a_f.reverse(p, w) # derivaitive of weighted function assert dw[0] == 0. # f_x0_x1 (x0, x1) = 0 assert dw[1] == 2. # f_x0_x1 (x0, x1) = 2