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atomic_reciprocal.cpp.xml @upstream/2015.00.00.7 — raw · history · blame
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 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528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 | <?xml version='1.0'?> <html xmlns='http://www.w3.org/1999/xhtml' xmlns:math='http://www.w3.org/1998/Math/MathML' > <head> <title>Reciprocal as an Atomic Operation: Example and Test</title> <meta http-equiv='Content-Type' content='text/html' charset='utf-8'/> <meta name="description" id="description" content="Reciprocal as an Atomic Operation: Example and Test"/> <meta name="keywords" id="keywords" content=" reciprocal as an atomic operation: example and test operation simple theory start class definition constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end use function recording "/> <style type='text/css'> body { color : black } body { background-color : white } A:link { color : blue } A:visited { color : purple } A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_atomic_reciprocal.cpp_xml.js'> </script> </head> <body> <table><tr> <td> <a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a> </td> <td><a href="atomic_norm_sq.cpp.xml" target="_top">Prev</a> </td><td><a href="atomic_tangent.cpp.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> <option>search</option> <option>external</option> </select> </td> <td> <select onchange='choose_up0(this)'> <option>Up-></option> <option>CppAD</option> <option>AD</option> <option>ADValued</option> <option>atomic</option> <option>atomic_base</option> <option>atomic_reciprocal.cpp</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>ADValued-></option> <option>Arithmetic</option> <option>std_math_ad</option> <option>MathOther</option> <option>CondExp</option> <option>Discrete</option> <option>atomic</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>atomic-></option> <option>checkpoint</option> <option>atomic_base</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>atomic_base-></option> <option>atomic_ctor</option> <option>atomic_option</option> <option>atomic_afun</option> <option>atomic_forward</option> <option>atomic_reverse</option> <option>atomic_for_sparse_jac</option> <option>atomic_rev_sparse_jac</option> <option>atomic_rev_sparse_hes</option> <option>atomic_base_clear</option> <option>atomic_get_started.cpp</option> <option>atomic_norm_sq.cpp</option> <option>atomic_reciprocal.cpp</option> <option>atomic_tangent.cpp</option> <option>atomic_hes_sparse.cpp</option> <option>atomic_mat_mul.cpp</option> </select> </td> <td>atomic_reciprocal.cpp</td> <td> <select onchange='choose_current0(this)'> <option>Headings-></option> <option>Theory</option> <option>Start Class Definition</option> <option>Constructor</option> <option>forward</option> <option>reverse</option> <option>for_sparse_jac</option> <option>rev_sparse_jac</option> <option>rev_sparse_hes</option> <option>End Class Definition</option> <option>Use Atomic Function</option> <option>---..Constructor</option> <option>---..Recording</option> <option>---..forward</option> <option>---..reverse</option> <option>---..for_sparse_jac</option> <option>---..rev_sparse_jac</option> <option>---..rev_sparse_hes</option> </select> </td> </tr></table><br/> <center><b><big><big>Reciprocal as an Atomic Operation: Example and Test</big></big></b></center> <br/> <b><big><a name="Theory" id="Theory">Theory</a></big></b> <br/> This example demonstrates using <a href="atomic_base.xml" target="_top"><span style='white-space: nowrap'>atomic_base</span></a> to define the operation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>f</mi> <mo stretchy="false">:</mo> <msup><mrow><mstyle mathvariant='bold'><mi mathvariant='bold'>R</mi> </mstyle></mrow> <mi mathvariant='italic'>n</mi> </msup> <mo stretchy="false">→</mo> <msup><mrow><mstyle mathvariant='bold'><mi mathvariant='bold'>R</mi> </mstyle></mrow> <mi mathvariant='italic'>m</mi> </msup> </mrow></math> where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>n</mi> <mo stretchy="false">=</mo> <mn>1</mn> </mrow></math> , <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>m</mi> <mo stretchy="false">=</mo> <mn>1</mn> </mrow></math> , and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow> <mi mathvariant='italic'>f</mi> <mo stretchy="false">(</mo> <mi mathvariant='italic'>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">=</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mi mathvariant='italic'>x</mi> </mrow></math> . <br/> <br/> <b><big><a name="Start Class Definition" id="Start Class Definition">Start Class Definition</a></big></b> <code><font color='blue'><pre style='display:inline'> # include <cppad/cppad.hpp> namespace { // isolate items below to this file using CppAD::vector; // abbreviate as vector // // a utility to compute the union of two sets. void my_union( std::set<size_t>& result , const std::set<size_t>& left , const std::set<size_t>& right ) { std::set<size_t> temp; std::set_union( left.begin() , left.end() , right.begin() , right.end() , std::inserter(temp, temp.begin()) ); result.swap(temp); } // class atomic_reciprocal : public CppAD::atomic_base<double> { </pre></font></code> <br/> <br/> <b><big><a name="Constructor" id="Constructor">Constructor</a></big></b> <code><font color='blue'><pre style='display:inline'> public: // constructor (could use const char* for name) atomic_reciprocal(const std::string& name) : CppAD::atomic_base<double>(name) { } private: </pre></font></code> <br/> <br/> <b><big><a name="forward" id="forward">forward</a></big></b> <code><font color='blue'><pre style='display:inline'> // forward mode routine called by CppAD virtual bool forward( size_t p , size_t q , const vector<bool>& vx , vector<bool>& vy , const vector<double>& tx , vector<double>& ty ) { size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); assert( n == 1 ); assert( m == 1 ); assert( p <= q ); // return flag bool ok = q <= 2; // check for defining variable information // This case must always be implemented if( vx.size() > 0 ) vy[0] = vx[0]; // Order zero forward mode. // This case must always be implemented // y^0 = f( x^0 ) = 1 / x^0 double f = 1. / tx[0]; if( p <= 0 ) ty[0] = f; if( q <= 0 ) return ok; assert( vx.size() == 0 ); // Order one forward mode. // This case needed if first order forward mode is used. // y^1 = f'( x^0 ) x^1 double fp = - f / tx[0]; if( p <= 1 ) ty[1] = fp * tx[1]; if( q <= 1 ) return ok; // Order two forward mode. // This case needed if second order forward mode is used. // Y''(t) = X'(t)^\R{T} f''[X(t)] X'(t) + f'[X(t)] X''(t) // 2 y^2 = x^1 * f''( x^0 ) x^1 + 2 f'( x^0 ) x^2 double fpp = - 2.0 * fp / tx[0]; ty[2] = tx[1] * fpp * tx[1] / 2.0 + fp * tx[2]; if( q <= 2 ) return ok; // Assume we are not using forward mode with order > 2 assert( ! ok ); return ok; } </pre></font></code> <br/> <br/> <b><big><a name="reverse" id="reverse">reverse</a></big></b> <code><font color='blue'><pre style='display:inline'> // reverse mode routine called by CppAD virtual bool reverse( size_t q , const vector<double>& tx , const vector<double>& ty , vector<double>& px , const vector<double>& py ) { size_t n = tx.size() / (q + 1); size_t m = ty.size() / (q + 1); assert( px.size() == n * (q + 1) ); assert( py.size() == m * (q + 1) ); assert( n == 1 ); assert( m == 1 ); bool ok = q <= 2; double f, fp, fpp, fppp; switch(q) { case 0: // This case needed if first order reverse mode is used // reverse: F^0 ( tx ) = y^0 = f( x^0 ) f = ty[0]; fp = - f / tx[0]; px[0] = py[0] * fp;; assert(ok); break; case 1: // This case needed if second order reverse mode is used // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; px[1] = py[1] * fp; px[0] = py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; assert(ok); break; case 2: // This needed if third order reverse mode is used // reverse: F^2 ( tx ) = y^2 = // = x^1 * f''( x^0 ) x^1 / 2 + f'( x^0 ) x^2 f = ty[0]; fp = - f / tx[0]; fpp = - 2.0 * fp / tx[0]; fppp = - 3.0 * fpp / tx[0]; px[2] = py[2] * fp; px[1] = py[2] * fpp * tx[1]; px[0] = py[2] * tx[1] * fppp * tx[1] / 2.0 + fpp * tx[2]; // reverse: F^1 ( tx ) = y^1 = f'( x^0 ) x^1 px[1] += py[1] * fp; px[0] += py[1] * fpp * tx[1]; // reverse: F^0 ( tx ) = y^0 = f( x^0 ); px[0] += py[0] * fp; assert(ok); break; default: assert(!ok); } return ok; } </pre></font></code> <br/> <br/> <b><big><a name="for_sparse_jac" id="for_sparse_jac">for_sparse_jac</a></big></b> <code><font color='blue'><pre style='display:inline'> // forward Jacobian bool sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector<bool>& r , vector<bool>& s ) { // This function needed if using f.ForSparseJac // with afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ) size_t n = r.size() / p; size_t m = s.size() / p; assert( n == 1 ); assert( m == 1 ); // sparsity for S(x) = f'(x) * R is same as sparsity for R for(size_t j = 0; j < p; j++) s[j] = r[j]; return true; } // forward Jacobian set sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector< std::set<size_t> >& r , vector< std::set<size_t> >& s ) { // This function needed if using f.ForSparseJac // with afun.option( CppAD::atomic_base<double>::set_sparsity_enum ) size_t n = r.size(); size_t m = s.size(); assert( n == 1 ); assert( m == 1 ); // sparsity for S(x) = f'(x) * R is same as sparsity for R s[0] = r[0]; return true; } </pre></font></code> <br/> <br/> <b><big><a name="rev_sparse_jac" id="rev_sparse_jac">rev_sparse_jac</a></big></b> <code><font color='blue'><pre style='display:inline'> // reverse Jacobian bool sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector<bool>& rt , vector<bool>& st ) { // This function needed if using RevSparseJac or optimize // with afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ) size_t n = st.size() / p; size_t m = rt.size() / p; assert( n == 1 ); assert( m == 1 ); // sparsity for S(x)^T = f'(x)^T * R^T is same as sparsity for R^T for(size_t i = 0; i < p; i++) st[i] = rt[i]; return true; } // reverse Jacobian set sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector< std::set<size_t> >& rt , vector< std::set<size_t> >& st ) { // This function needed if using RevSparseJac or optimize // with afun.option( CppAD::atomic_base<double>::set_sparsity_enum ) size_t n = st.size(); size_t m = rt.size(); assert( n == 1 ); assert( m == 1 ); // sparsity for S(x)^T = f'(x)^T * R^T is same as sparsity for R^T st[0] = rt[0]; return true; } </pre></font></code> <br/> <br/> <b><big><a name="rev_sparse_hes" id="rev_sparse_hes">rev_sparse_hes</a></big></b> <code><font color='blue'><pre style='display:inline'> // reverse Hessian bool sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector<bool>& vx, const vector<bool>& s , vector<bool>& t , size_t p , const vector<bool>& r , const vector<bool>& u , vector<bool>& v ) { // This function needed if using RevSparseHes // with afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ) size_t m = s.size(); size_t n = t.size(); assert( r.size() == n * p ); assert( u.size() == m * p ); assert( v.size() == n * p ); assert( n == 1 ); assert( m == 1 ); // There are no cross term second derivatives for this case, // so it is not necessary to vx. // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S t[0] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U, note f'(x) may be non-zero; size_t j; for(j = 0; j < p; j++) v[j] = u[j]; // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] ) { for(j = 0; j < p; j++) v[j] |= r[j]; } return true; } // reverse Hessian set sparsity routine called by CppAD virtual bool rev_sparse_hes( const vector<bool>& vx, const vector<bool>& s , vector<bool>& t , size_t p , const vector< std::set<size_t> >& r , const vector< std::set<size_t> >& u , vector< std::set<size_t> >& v ) { // This function needed if using RevSparseHes // with afun.option( CppAD::atomic_base<double>::set_sparsity_enum ) size_t n = vx.size(); size_t m = s.size(); assert( t.size() == n ); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 1 ); assert( m == 1 ); // There are no cross term second derivatives for this case, // so it is not necessary to vx. // sparsity for T(x) = S(x) * f'(x) is same as sparsity for S t[0] = s[0]; // V(x) = f'(x)^T * g''(y) * f'(x) * R + g'(y) * f''(x) * R // U(x) = g''(y) * f'(x) * R // S(x) = g'(y) // back propagate the sparsity for U, note f'(x) may be non-zero; v[0] = u[0]; // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] ) my_union(v[0], v[0], r[0] ); return true; } </pre></font></code> <br/> <br/> <b><big><a name="End Class Definition" id="End Class Definition">End Class Definition</a></big></b> <code><font color='blue'><pre style='display:inline'> }; // End of atomic_reciprocal class } // End empty namespace </pre></font></code> <br/> <br/> <b><big><a name="Use Atomic Function" id="Use Atomic Function">Use Atomic Function</a></big></b> <code><font color='blue'><pre style='display:inline'> bool reciprocal(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * CppAD::numeric_limits<double>::epsilon(); </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.Constructor" id="Use Atomic Function.Constructor">Constructor</a></b> <code><font color='blue'><pre style='display:inline'> // -------------------------------------------------------------------- // Create the atomic reciprocal object atomic_reciprocal afun("atomic_reciprocal"); </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.Recording" id="Use Atomic Function.Recording">Recording</a></b> <code><font color='blue'><pre style='display:inline'> // Create the function f(x) // // domain space vector size_t n = 1; double x0 = 0.5; vector< <a href="ad.xml" target="_top">AD</a><double> > ax(n); ax[0] = x0; // declare independent variables and start tape recording CppAD::<a href="independent.xml" target="_top">Independent</a>(ax); // range space vector size_t m = 1; vector< <a href="ad.xml" target="_top">AD</a><double> > ay(m); // call user function and store reciprocal(x) in au[0] vector< <a href="ad.xml" target="_top">AD</a><double> > au(m); afun(ax, au); // u = 1 / x // now use AD division to invert to invert the operation ay[0] = 1.0 / au[0]; // y = 1 / u = x // create f: x -> y and stop tape recording CppAD::<a href="funconstruct.xml" target="_top">ADFun</a><double> f; f.Dependent (ax, ay); // f(x) = x </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.forward" id="Use Atomic Function.forward">forward</a></b> <code><font color='blue'><pre style='display:inline'> // check function value double check = x0; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>( Value(ay[0]) , check, eps, eps); // check zero order forward mode size_t q; vector<double> x_q(n), y_q(m); q = 0; x_q[0] = x0; y_q = f.<a href="forward.xml" target="_top">Forward</a>(q, x_q); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(y_q[0] , check, eps, eps); // check first order forward mode q = 1; x_q[0] = 1; y_q = f.<a href="forward.xml" target="_top">Forward</a>(q, x_q); check = 1.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(y_q[0] , check, eps, eps); // check second order forward mode q = 2; x_q[0] = 0; y_q = f.<a href="forward.xml" target="_top">Forward</a>(q, x_q); check = 0.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(y_q[0] , check, eps, eps); </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.reverse" id="Use Atomic Function.reverse">reverse</a></b> <code><font color='blue'><pre style='display:inline'> // third order reverse mode q = 3; vector<double> w(m), dw(n * q); w[0] = 1.; dw = f.<a href="reverse.xml" target="_top">Reverse</a>(q, w); check = 1.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0] , check, eps, eps); check = 0.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[1] , check, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[2] , check, eps, eps); </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.for_sparse_jac" id="Use Atomic Function.for_sparse_jac">for_sparse_jac</a></b> <code><font color='blue'><pre style='display:inline'> // forward mode sparstiy pattern size_t p = n; CppAD::vectorBool r1(n * p), s1(m * p); r1[0] = true; // compute sparsity pattern for x[0] // afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ); s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] // afun.option( CppAD::atomic_base<double>::set_sparsity_enum ); s1 = f.ForSparseJac(p, r1); ok &= s1[0] == true; // f[0] depends on x[0] </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.rev_sparse_jac" id="Use Atomic Function.rev_sparse_jac">rev_sparse_jac</a></b> <code><font color='blue'><pre style='display:inline'> // reverse mode sparstiy pattern q = m; CppAD::vectorBool s2(q * m), r2(q * n); s2[0] = true; // compute sparsity pattern for f[0] // afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ); r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] // afun.option( CppAD::atomic_base<double>::set_sparsity_enum ); r2 = f.RevSparseJac(q, s2); ok &= r2[0] == true; // f[0] depends on x[0] </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.rev_sparse_hes" id="Use Atomic Function.rev_sparse_hes">rev_sparse_hes</a></b> <code><font color='blue'><pre style='display:inline'> // Hessian sparsity (using previous ForSparseJac call) CppAD::vectorBool s3(m), h(p * n); s3[0] = true; // compute sparsity pattern for f[0] // afun.option( CppAD::atomic_base<double>::bool_sparsity_enum ); h = f.RevSparseHes(p, s3); ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero // afun.option( CppAD::atomic_base<double>::set_sparsity_enum ); h = f.RevSparseHes(p, s3); ok &= h[0] == true; // second partial of f[0] w.r.t. x[0] may be non-zero return ok; } </pre></font></code> <hr/>Input File: example/atomic/reciprocal.cpp </body> </html> |