Emily Boudreaux
2bca6e447c
we need an autodiff library at some point (or we need to roll our own but I do not think that makes sense). CppAD is well tested and header only and easy to include. It is also Liscene compatible with GPL v3.0. Here we bring it in as a dependency
239 lines
6.9 KiB
C++
239 lines
6.9 KiB
C++
# ifndef CPPAD_LOCAL_COS_OP_HPP
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# define CPPAD_LOCAL_COS_OP_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell
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CppAD is distributed under the terms of the
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Eclipse Public License Version 2.0.
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This Source Code may also be made available under the following
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Secondary License when the conditions for such availability set forth
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in the Eclipse Public License, Version 2.0 are satisfied:
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GNU General Public License, Version 2.0 or later.
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---------------------------------------------------------------------------- */
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namespace CppAD { namespace local { // BEGIN_CPPAD_LOCAL_NAMESPACE
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/*!
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\file cos_op.hpp
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Forward and reverse mode calculations for z = cos(x).
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*/
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/*!
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Compute forward mode Taylor coefficient for result of op = CosOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = cos(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = sin(x)
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\endverbatim
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The value of y, and its derivatives, are computed along with the value
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and derivatives of z.
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\copydetails CppAD::local::forward_unary2_op
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*/
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template <class Base>
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void forward_cos_op(
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size_t p ,
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size_t q ,
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size_t i_z ,
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size_t i_x ,
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size_t cap_order ,
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Base* taylor )
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{
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// check assumptions
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CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 );
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CPPAD_ASSERT_UNKNOWN( q < cap_order );
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CPPAD_ASSERT_UNKNOWN( p <= q );
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// Taylor coefficients corresponding to argument and result
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Base* x = taylor + i_x * cap_order;
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Base* c = taylor + i_z * cap_order;
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Base* s = c - cap_order;
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// rest of this routine is identical for the following cases:
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// forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op.
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// (except that there is a sign difference for the hyperbolic case).
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size_t k;
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if( p == 0 )
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{ s[0] = sin( x[0] );
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c[0] = cos( x[0] );
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p++;
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}
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for(size_t j = p; j <= q; j++)
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{
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s[j] = Base(0.0);
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c[j] = Base(0.0);
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for(k = 1; k <= j; k++)
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{ s[j] += Base(double(k)) * x[k] * c[j-k];
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c[j] -= Base(double(k)) * x[k] * s[j-k];
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}
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s[j] /= Base(double(j));
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c[j] /= Base(double(j));
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}
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}
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/*!
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Compute forward mode Taylor coefficient for result of op = CosOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = cos(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = sin(x)
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\endverbatim
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The value of y, and its derivatives, are computed along with the value
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and derivatives of z.
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\copydetails CppAD::local::forward_unary2_op_dir
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*/
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template <class Base>
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void forward_cos_op_dir(
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size_t q ,
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size_t r ,
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size_t i_z ,
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size_t i_x ,
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size_t cap_order ,
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Base* taylor )
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{
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// check assumptions
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CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 );
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CPPAD_ASSERT_UNKNOWN( 0 < q );
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CPPAD_ASSERT_UNKNOWN( q < cap_order );
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// Taylor coefficients corresponding to argument and result
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size_t num_taylor_per_var = (cap_order-1) * r + 1;
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Base* x = taylor + i_x * num_taylor_per_var;
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Base* c = taylor + i_z * num_taylor_per_var;
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Base* s = c - num_taylor_per_var;
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// rest of this routine is identical for the following cases:
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// forward_sin_op, forward_cos_op, forward_sinh_op, forward_cosh_op
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// (except that there is a sign difference for the hyperbolic case).
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size_t m = (q-1) * r + 1;
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for(size_t ell = 0; ell < r; ell++)
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{ s[m+ell] = Base(double(q)) * x[m + ell] * c[0];
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c[m+ell] = - Base(double(q)) * x[m + ell] * s[0];
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for(size_t k = 1; k < q; k++)
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{ s[m+ell] += Base(double(k)) * x[(k-1)*r+1+ell] * c[(q-k-1)*r+1+ell];
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c[m+ell] -= Base(double(k)) * x[(k-1)*r+1+ell] * s[(q-k-1)*r+1+ell];
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}
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s[m+ell] /= Base(double(q));
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c[m+ell] /= Base(double(q));
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}
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}
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/*!
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Compute zero order forward mode Taylor coefficient for result of op = CosOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = cos(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = sin(x)
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\endverbatim
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The value of y is computed along with the value of z.
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\copydetails CppAD::local::forward_unary2_op_0
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*/
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template <class Base>
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void forward_cos_op_0(
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size_t i_z ,
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size_t i_x ,
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size_t cap_order ,
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Base* taylor )
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{
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// check assumptions
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CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 );
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CPPAD_ASSERT_UNKNOWN( 0 < cap_order );
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// Taylor coefficients corresponding to argument and result
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Base* x = taylor + i_x * cap_order;
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Base* c = taylor + i_z * cap_order; // called z in documentation
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Base* s = c - cap_order; // called y in documentation
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c[0] = cos( x[0] );
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s[0] = sin( x[0] );
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}
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/*!
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Compute reverse mode partial derivatives for result of op = CosOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = cos(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = sin(x)
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\endverbatim
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The value of y is computed along with the value of z.
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\copydetails CppAD::local::reverse_unary2_op
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*/
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template <class Base>
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void reverse_cos_op(
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size_t d ,
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size_t i_z ,
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size_t i_x ,
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size_t cap_order ,
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const Base* taylor ,
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size_t nc_partial ,
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Base* partial )
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{
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// check assumptions
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CPPAD_ASSERT_UNKNOWN( NumArg(CosOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(CosOp) == 2 );
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CPPAD_ASSERT_UNKNOWN( d < cap_order );
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CPPAD_ASSERT_UNKNOWN( d < nc_partial );
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// Taylor coefficients and partials corresponding to argument
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const Base* x = taylor + i_x * cap_order;
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Base* px = partial + i_x * nc_partial;
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// Taylor coefficients and partials corresponding to first result
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const Base* c = taylor + i_z * cap_order; // called z in doc
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Base* pc = partial + i_z * nc_partial;
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// Taylor coefficients and partials corresponding to auxillary result
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const Base* s = c - cap_order; // called y in documentation
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Base* ps = pc - nc_partial;
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// rest of this routine is identical for the following cases:
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// reverse_sin_op, reverse_cos_op, reverse_sinh_op, reverse_cosh_op.
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size_t j = d;
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size_t k;
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while(j)
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{
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ps[j] /= Base(double(j));
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pc[j] /= Base(double(j));
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for(k = 1; k <= j; k++)
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{
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px[k] += Base(double(k)) * azmul(ps[j], c[j-k]);
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px[k] -= Base(double(k)) * azmul(pc[j], s[j-k]);
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ps[j-k] -= Base(double(k)) * azmul(pc[j], x[k]);
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pc[j-k] += Base(double(k)) * azmul(ps[j], x[k]);
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}
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--j;
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}
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px[0] += azmul(ps[0], c[0]);
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px[0] -= azmul(pc[0], s[0]);
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}
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} } // END_CPPAD_LOCAL_NAMESPACE
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# endif
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