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
236 lines
6.6 KiB
C++
236 lines
6.6 KiB
C++
# ifndef CPPAD_LOCAL_ATAN_OP_HPP
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# define CPPAD_LOCAL_ATAN_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 atan_op.hpp
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Forward and reverse mode calculations for z = atan(x).
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*/
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/*!
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Forward mode Taylor coefficient for result of op = AtanOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = atan(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = 1 + x * 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_atan_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(AtanOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 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* z = taylor + i_z * cap_order;
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Base* b = z - cap_order; // called y in documentation
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size_t k;
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if( p == 0 )
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{ z[0] = atan( x[0] );
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b[0] = Base(1.0) + x[0] * 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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b[j] = Base(2.0) * x[0] * x[j];
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z[j] = Base(0.0);
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for(k = 1; k < j; k++)
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{ b[j] += x[k] * x[j-k];
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z[j] -= Base(double(k)) * z[k] * b[j-k];
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}
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z[j] /= Base(double(j));
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z[j] += x[j];
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z[j] /= b[0];
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}
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}
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/*!
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Multiple direction Taylor coefficient for op = AtanOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = atan(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = 1 + x * 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_atan_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(AtanOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 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* z = taylor + i_z * num_taylor_per_var;
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Base* b = z - num_taylor_per_var; // called y in documentation
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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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{ b[m+ell] = Base(2.0) * x[m+ell] * x[0];
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z[m+ell] = Base(double(q)) * x[m+ell];
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for(size_t k = 1; k < q; k++)
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{ b[m+ell] += x[(k-1)*r+1+ell] * x[(q-k-1)*r+1+ell];
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z[m+ell] -= Base(double(k)) * z[(k-1)*r+1+ell] * b[(q-k-1)*r+1+ell];
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}
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z[m+ell] /= ( Base(double(q)) * b[0] );
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}
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}
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/*!
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Zero order forward mode Taylor coefficient for result of op = AtanOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = atan(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = 1 + x * 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_atan_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(AtanOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 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* z = taylor + i_z * cap_order;
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Base* b = z - cap_order; // called y in documentation
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z[0] = atan( x[0] );
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b[0] = Base(1.0) + x[0] * x[0];
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}
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/*!
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Reverse mode partial derivatives for result of op = AtanOp.
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The C++ source code corresponding to this operation is
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\verbatim
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z = atan(x)
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\endverbatim
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The auxillary result is
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\verbatim
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y = 1 + x * 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_atan_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(AtanOp) == 1 );
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CPPAD_ASSERT_UNKNOWN( NumRes(AtanOp) == 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* z = taylor + i_z * cap_order;
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Base* pz = partial + i_z * nc_partial;
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// Taylor coefficients and partials corresponding to auxillary result
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const Base* b = z - cap_order; // called y in documentation
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Base* pb = pz - nc_partial;
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Base inv_b0 = Base(1.0) / b[0];
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// number of indices to access
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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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{ // scale partials w.r.t z[j] and b[j]
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pz[j] = azmul(pz[j], inv_b0);
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pb[j] *= Base(2.0);
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pb[0] -= azmul(pz[j], z[j]);
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px[j] += pz[j] + azmul(pb[j], x[0]);
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px[0] += azmul(pb[j], x[j]);
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// more scaling of partials w.r.t z[j]
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pz[j] /= Base(double(j));
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for(k = 1; k < j; k++)
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{ pb[j-k] -= Base(double(k)) * azmul(pz[j], z[k]);
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pz[k] -= Base(double(k)) * azmul(pz[j], b[j-k]);
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px[k] += azmul(pb[j], x[j-k]);
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}
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--j;
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}
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px[0] += azmul(pz[0], inv_b0) + Base(2.0) * azmul(pb[0], x[0]);
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}
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} } // END_CPPAD_LOCAL_NAMESPACE
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# endif
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