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atomic_tangent.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 | <?xml version='1.0'?> <html xmlns='http://www.w3.org/1999/xhtml' xmlns:math='http://www.w3.org/1998/Math/MathML' > <head> <title>Tan and Tanh as User Atomic Operations: Example and Test</title> <meta http-equiv='Content-Type' content='text/html' charset='utf-8'/> <meta name="description" id="description" content="Tan and Tanh as User Atomic Operations: Example and Test"/> <meta name="keywords" id="keywords" content=" tan and tanh as user atomic operations: example test tangent operation theory start class definition constructor forward reverse for_sparse_jac rev_sparse_jac rev_sparse_hes end use function recording large x values "/> <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_tangent.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_reciprocal.cpp.xml" target="_top">Prev</a> </td><td><a href="atomic_hes_sparse.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_tangent.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_tangent.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> <option>---..Large x Values</option> </select> </td> </tr></table><br/> <center><b><big><big>Tan and Tanh as User Atomic Operations: Example and Test</big></big></b></center> <br/> <b><big><a name="Theory" id="Theory">Theory</a></big></b> <br/> The code below uses the <a href="tan_forward.xml" target="_top"><span style='white-space: nowrap'>tan_forward</span></a> and <a href="tan_reverse.xml" target="_top"><span style='white-space: nowrap'>tan_reverse</span></a> to implement the tangent and hyperbolic tangent functions as user atomic operations. <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 { // Begin empty namespace using CppAD::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_tangent : public CppAD::atomic_base<float> { </pre></font></code> <br/> <br/> <b><big><a name="Constructor" id="Constructor">Constructor</a></big></b> <code><font color='blue'><pre style='display:inline'> private: const bool hyperbolic_; // is this hyperbolic tangent public: // constructor atomic_tangent(const char* name, bool hyperbolic) : CppAD::atomic_base<float>(name), hyperbolic_(hyperbolic) { } 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 bool forward( size_t p , size_t q , const vector<bool>& vx , vector<bool>& vzy , const vector<float>& tx , vector<float>& tzy ) { size_t q1 = q + 1; size_t n = tx.size() / q1; size_t m = tzy.size() / q1; assert( n == 1 ); assert( m == 2 ); assert( p <= q ); size_t j, k; // check if this is during the call to old_tan(id, ax, ay) if( vx.size() > 0 ) { // set variable flag for both y an z vzy[0] = vx[0]; vzy[1] = vx[0]; } if( p == 0 ) { // z^{(0)} = tan( x^{(0)} ) or tanh( x^{(0)} ) if( hyperbolic_ ) tzy[0] = tanh( tx[0] ); else tzy[0] = tan( tx[0] ); // y^{(0)} = z^{(0)} * z^{(0)} tzy[q1 + 0] = tzy[0] * tzy[0]; p++; } for(j = p; j <= q; j++) { float j_inv = 1.f / float(j); if( hyperbolic_ ) j_inv = - j_inv; // z^{(j)} = x^{(j)} +- sum_{k=1}^j k x^{(k)} y^{(j-k)} / j tzy[j] = tx[j]; for(k = 1; k <= j; k++) tzy[j] += tx[k] * tzy[q1 + j-k] * k * j_inv; // y^{(j)} = sum_{k=0}^j z^{(k)} z^{(j-k)} tzy[q1 + j] = 0.; for(k = 0; k <= j; k++) tzy[q1 + j] += tzy[k] * tzy[j-k]; } // All orders are implemented and there are no possible errors return true; } </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<float>& tx , const vector<float>& tzy , vector<float>& px , const vector<float>& pzy ) { size_t q1 = q + 1; size_t n = tx.size() / q1; size_t m = tzy.size() / q1; assert( px.size() == n * q1 ); assert( pzy.size() == m * q1 ); assert( n == 1 ); assert( m == 2 ); size_t j, k; // copy because partials w.r.t. y and z need to change vector<float> qzy = pzy; // initialize accumultion of reverse mode partials for(k = 0; k < q1; k++) px[k] = 0.; // eliminate positive orders for(j = q; j > 0; j--) { float j_inv = 1.f / float(j); if( hyperbolic_ ) j_inv = - j_inv; // H_{x^{(k)}} += delta(j-k) +- H_{z^{(j)} y^{(j-k)} * k / j px[j] += qzy[j]; for(k = 1; k <= j; k++) px[k] += qzy[j] * tzy[q1 + j-k] * k * j_inv; // H_{y^{j-k)} += +- H_{z^{(j)} x^{(k)} * k / j for(k = 1; k <= j; k++) qzy[q1 + j-k] += qzy[j] * tx[k] * k * j_inv; // H_{z^{(k)}} += H_{y^{(j-1)}} * z^{(j-k-1)} * 2. for(k = 0; k < j; k++) qzy[k] += qzy[q1 + j-1] * tzy[j-k-1] * 2.f; } // eliminate order zero if( hyperbolic_ ) px[0] += qzy[0] * (1.f - tzy[q1 + 0]); else px[0] += qzy[0] * (1.f + tzy[q1 + 0]); return true; } </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 sparsity routine called by CppAD virtual bool for_sparse_jac( size_t p , const vector<bool>& r , vector<bool>& s ) { size_t n = r.size() / p; size_t m = s.size() / p; assert( n == 1 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R for(size_t j = 0; j < p; j++) { s[0 * p + j] = r[j]; s[1 * p + j] = r[j]; } return true; } // forward Jacobian 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 ) { size_t n = r.size(); size_t m = s.size(); assert( n == 1 ); assert( m == 2 ); // sparsity for S(x) = f'(x) * R s[0] = r[0]; s[1] = 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 sparsity routine called by CppAD virtual bool rev_sparse_jac( size_t p , const vector<bool>& rt , vector<bool>& st ) { size_t n = st.size() / p; size_t m = rt.size() / p; assert( n == 1 ); assert( m == 2 ); // sparsity for S(x)^T = f'(x)^T * R^T for(size_t j = 0; j < p; j++) st[j] = rt[0 * p + j] | rt[1 * p + j]; return true; } // reverse Jacobian 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 ) { size_t n = st.size(); size_t m = rt.size(); assert( n == 1 ); assert( m == 2 ); // sparsity for S(x)^T = f'(x)^T * R^T my_union(st[0], rt[0], rt[1]); 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 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 ) { 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 == 2 ); // 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) t[0] = s[0] | s[1]; // 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 both components // of f'(x) may be non-zero; size_t j; for(j = 0; j < p; j++) v[j] = u[ 0 * p + j ] | u[ 1 * p + j ]; // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] | s[1] ) { for(j = 0; j < p; j++) v[j] |= r[j]; } return true; } // reverse Hessian 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 ) { size_t m = s.size(); size_t n = t.size(); assert( r.size() == n ); assert( u.size() == m ); assert( v.size() == n ); assert( n == 1 ); assert( m == 2 ); // 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) t[0] = s[0] | s[1]; // 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 both components // of f'(x) may be non-zero; my_union(v[0], u[0], u[1]); // include forward Jacobian sparsity in Hessian sparsity // (note sparsty for f''(x) * R same as for R) if( s[0] | s[1] ) 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_tangent 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 tangent(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; float eps = 10.f * CppAD::numeric_limits<float>::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'> // -------------------------------------------------------------------- // Creater a tan and tanh object atomic_tangent my_tan("my_tan", false), my_tanh("my_tanh", true); </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'> // domain space vector size_t n = 1; float x0 = 0.5; CppAD::vector< <a href="ad.xml" target="_top">AD</a><float> > 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 = 3; CppAD::vector< <a href="ad.xml" target="_top">AD</a><float> > af(m); // temporary vector for computations // (my_tan and my_tanh computes tan or tanh and its square) CppAD::vector< <a href="ad.xml" target="_top">AD</a><float> > az(2); // call atomic tan function and store tan(x) in f[0] (ignore tan(x)^2) my_tan(ax, az); af[0] = az[0]; // call atomic tanh function and store tanh(x) in f[1] (ignore tanh(x)^2) my_tanh(ax, az); af[1] = az[0]; // put a constant in f[2] = tanh(1.) (for sparsity pattern testing) CppAD::vector< <a href="ad.xml" target="_top">AD</a><float> > one(1); one[0] = 1.; my_tanh(one, az); af[2] = az[0]; // create f: x -> f and stop tape recording CppAD::<a href="funconstruct.xml" target="_top">ADFun</a><float> F; F.Dependent(ax, af); </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 float tan = std::tan(x0); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(af[0] , tan, eps, eps); float tanh = std::tanh(x0); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(af[1] , tanh, eps, eps); // check zero order forward CppAD::vector<float> x(n), f(m); x[0] = x0; f = F.<a href="forward.xml" target="_top">Forward</a>(0, x); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(f[0] , tan, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(f[1] , tanh, eps, eps); // compute first partial of f w.r.t. x[0] using forward mode CppAD::vector<float> dx(n), df(m); dx[0] = 1.; df = F.<a href="forward.xml" target="_top">Forward</a>(1, dx); </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'> // compute derivative of tan - tanh using reverse mode CppAD::vector<float> w(m), dw(n); w[0] = 1.; w[1] = 1.; w[2] = 0.; dw = F.<a href="reverse.xml" target="_top">Reverse</a>(1, w); // tan'(x) = 1 + tan(x) * tan(x) // tanh'(x) = 1 - tanh(x) * tanh(x) float tanp = 1.f + tan * tan; float tanhp = 1.f - tanh * tanh; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(df[0], tanp, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(df[1], tanhp, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(dw[0], w[0]*tanp + w[1]*tanhp, eps, eps); // compute second partial of f w.r.t. x[0] using forward mode CppAD::vector<float> ddx(n), ddf(m); ddx[0] = 0.; ddf = F.<a href="forward.xml" target="_top">Forward</a>(2, ddx); // compute second derivative of tan - tanh using reverse mode CppAD::vector<float> ddw(2); ddw = F.<a href="reverse.xml" target="_top">Reverse</a>(2, w); // tan''(x) = 2 * tan(x) * tan'(x) // tanh''(x) = - 2 * tanh(x) * tanh'(x) // Note that second order Taylor coefficient for u half the // corresponding second derivative. float two = 2; float tanpp = two * tan * tanp; float tanhpp = - two * tanh * tanhp; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(two * ddf[0], tanpp, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(two * ddf[1], tanhpp, eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(ddw[0], w[0]*tanp + w[1]*tanhp , eps, eps); ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(ddw[1], w[0]*tanpp + w[1]*tanhpp, 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 computation of sparsity pattern for F. size_t p = n; // user vectorBool because m and n are small CppAD::vectorBool r1(p), s1(m * p); r1[0] = true; // propagate sparsity for x[0] s1 = F.ForSparseJac(p, r1); ok &= (s1[0] == true); // f[0] depends on x[0] ok &= (s1[1] == true); // f[1] depends on x[0] ok &= (s1[2] == false); // f[2] does not depend 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 computation of sparsity pattern for F. size_t q = m; CppAD::vectorBool s2(q * m), r2(q * n); // Sparsity pattern for identity matrix size_t i, j; for(i = 0; i < q; i++) { for(j = 0; j < m; j++) s2[i * q + j] = (i == j); } r2 = F.RevSparseJac(q, s2); ok &= (r2[0] == true); // f[0] depends on x[0] ok &= (r2[1] == true); // f[1] depends on x[0] ok &= (r2[2] == false); // f[2] does not depend 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 for f[0] CppAD::vectorBool s3(m), h(p * n); s3[0] = true; s3[1] = false; s3[2] = false; h = F.RevSparseHes(p, s3); ok &= (h[0] == true); // Hessian is non-zero // Hessian sparsity for f[2] s3[0] = false; s3[2] = true; h = F.RevSparseHes(p, s3); ok &= (h[0] == false); // Hessian is zero </pre></font></code> <br/> <br/> <b><a name="Use Atomic Function.Large x Values" id="Use Atomic Function.Large x Values">Large x Values</a></b> <code><font color='blue'><pre style='display:inline'> // check tanh results for a large value of x x[0] = std::numeric_limits<float>::max() / two; f = F.<a href="forward.xml" target="_top">Forward</a>(0, x); tanh = 1.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(f[1], tanh, eps, eps); df = F.<a href="forward.xml" target="_top">Forward</a>(1, dx); tanhp = 0.; ok &= <a href="nearequal.xml" target="_top">NearEqual</a>(df[1], tanhp, eps, eps); return ok; } </pre></font></code> <hr/>Input File: example/atomic/tangent.cpp </body> </html> |