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@Ris-Bali
Ris-Bali committed Dec 23, 2023
1 parent ab7c364 commit 3c0580d
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16 changes: 7 additions & 9 deletions docs/userDocs/source/user/UsingClad.rst
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Expand Up @@ -223,16 +223,14 @@ that needs to be differentiated even when we want to differentiate w.r.t entire
.. code-block:: cpp
#include "clad/Differentiator/Differentiator.h"
double fn(double x, double arr[2]) {
return x * arr[0] * arr[1];
}
double fn(double x, double arr[2]) { return x * arr[0] * arr[1]; }
int main() {
auto fn_hessian = clad::hessian(fn, "x, arr[0:1]");
// We have 3 independent variables thus we require space of 9.
double mat_fn[9] = {0};
clad::array_ref<double> mat_fn_ref(mat_fn, 9);
double num[2] = {1, 2};
fn_hessian.execute(3, num, mat_fn_ref);
auto fn_hessian = clad::hessian(fn, "x, arr[0:1]");
// We have 3 independent variables thus we require space of 9.
double mat_fn[9] = {0};
clad::array_ref<double> mat_fn_ref(mat_fn, 9);
double num[2] = {1, 2};
fn_hessian.execute(3, num, mat_fn_ref);
}
Jacobian Computation
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132 changes: 60 additions & 72 deletions docs/userDocs/source/user/tutorials.rst
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Expand Up @@ -12,48 +12,42 @@ API call.

.. code-block:: cpp
#include "clad/Differentiator/Differentiator.h"
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
double func(int x) {
return x * x;
}
double func(int x) { return x * x; }
int main() {
/*Calling clad::differentiate to get the forward mode derivative of
the given mathematical function*/
auto d_func = clad::differentiate(func, "x");
// execute the generated derivative function.
std::cout << d_func.execute(/*x =*/3) <<std::endl;
// Dump the generated derivative code to std output.
d_func.dump();
/*Calling clad::differentiate to get the forward mode derivative of
the given mathematical function*/
auto d_func = clad::differentiate(func, "x");
// execute the generated derivative function.
std::cout << d_func.execute(/*x =*/3) << std::endl;
// Dump the generated derivative code to std output.
d_func.dump();
}
Here we are differentiating a function `func` which takes an input x and
returns a scaler value `x*x`.`.dump()` method is used to get a dump of generated
Here we are differentiating a function `func` which takes an input `x` and
returns a scaler value `x * x`.`.dump()` method is used to get a dump of generated
derivative function to the standard output.

**The Reverse Mode**

Clad also supports reverse mode automatic differentiation, through the `clad::gradient`
API call.


.. code-block:: cpp
#include "clad/Differentiator/Differentiator.h"
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
double f(double x, double y, double z) {
return x * y * z;
}
double f(double x, double y, double z) { return x * y * z; }
int main() {
auto d_f = clad::gradient(f, "x, y");
double dx = 0, dy = 0;
d_f.execute(/*x=*/2,/*y=*/ 3,/*z=*/ 4, &dx, &dy);
std::cout <<"dx : "<< dx << "dy :"<< dy << std::endl;
auto d_f = clad::gradient(f, "x, y");
double dx = 0, dy = 0;
d_f.execute(/*x=*/2, /*y=*/3, /*z=*/4, &dx, &dy);
std::cout << "dx : " << dx << "dy :" << dy << std::endl;
}
In the above example we are differentiating w.r.t `x and y` we can also
Expand All @@ -65,33 +59,32 @@ of the function w.r.t to each input.
**The Hessian Mode**

Clad can also produce an hessian matrix through the `clad::hessian` API call.
This API call is more or less similar to the reverse mode API call and differs
in case of an array type input argument.
It returns the hessian matrix as a flattened vector in row major format.

.. code-block:: cpp
#include "clad/Differentiator/Differentiator.h"
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
double f(double x, double y, double z) {
return x * y * z;
}
double f(double x, double y, double z) { return x * y * z; }
// Function with array input
// Function with array input
double f_arr(double x, double y, double z[2]) {
return x * y * z[0] * z[1];
}
double f_arr(double x, double y, double z[2]) { return x * y * z[0] * z[1]; }
int main() {
// Workflow similar to clad::gradient for non-array input arguments.
auto f_hess = clad::hessian(f, "x, y");
double matrix_f[9] = {0};
clad::array_ref<double> matrix_f_ref(matrix_f, 9);
f_hess.execute(3, 4, 5, matrix_f_ref);
std::cout << "[" << matrix_f_ref[0] << ", " << matrix_f_ref[1] << matrix_f_ref[2] << "\n"
<< matrix_f_ref[3] << ", " << matrix_f_ref[4] << matrix_f_ref[5] << "\n"
<< matrix_f_ref[6] << ", " << matrix_f_ref[7] << matrix_f_ref[8] << "]" << "\n";
// Workflow similar to clad::gradient for non-array input arguments.
auto f_hess = clad::hessian(f, "x, y");
double matrix_f[9] = {0};
clad::array_ref<double> matrix_f_ref(matrix_f, 9);
f_hess.execute(3, 4, 5, matrix_f_ref);
std::cout << "[" << matrix_f_ref[0] << ", " << matrix_f_ref[1]
<< matrix_f_ref[2] << "\n"
<< matrix_f_ref[3] << ", " << matrix_f_ref[4] << matrix_f_ref[5]
<< "\n"
<< matrix_f_ref[6] << ", " << matrix_f_ref[7] << matrix_f_ref[8]
<< "]"
<< "\n";
}
When arrays are involved we need to specify the array index that needs to be
Expand All @@ -108,26 +101,26 @@ jacobian matrix as a flattened vector with elements arranged in row-major format

.. code-block:: cpp
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
#include<iostream>
void f(doubl x, double y, double z, double *output) {
output[0] = x*y;
output[1] = y * y * x;
output[2] = 6 * x * y * z;
void f(double x, double y, double z, double* output) {
output[0] = x * y;
output[1] = y * y * x;
output[2] = 6 * x * y * z;
}
int main() {
auto f_jac = clad::jacobian(f);
double jac[9] = {0};
double output[3] = {0};
f_jac.execute(3, 4, 5, output, jac);
std::cout << jac[0] << " " << jac[1] << std::endl
<< jac[2] << " " << jac[3] << std::endl
<< jac[4] << " " << jac[5] << std::endl
<< jac[6] << " " << jac[7] << std::endl
<< jac[8]<< std::endl;
auto f_jac = clad::jacobian(f);
double jac[9] = {0};
double output[3] = {0};
f_jac.execute(3, 4, 5, output, jac);
std::cout << jac[0] << " " << jac[1] << std::endl
<< jac[2] << " " << jac[3] << std::endl
<< jac[4] << " " << jac[5] << std::endl
<< jac[6] << " " << jac[7] << std::endl
<< jac[8] << std::endl;
}
The jacobian matrix size should be equal to `no. of independent variables times
Expand All @@ -139,30 +132,25 @@ an array of size 3x3 = 9.
Clad is capable of annotating a given function with floating point error estimation
code using reverse mode AD.


.. code-block:: cpp
#include "clad/Differentiator/Differentiator.h"
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
void func(double x, double y) {
return x * y;
}
double func(double x, double y) { return x * y; }
int main() {
auto dfunc_error = clad::estimate_error(func);
// Used to print generated code to standard output.
dfunc_error.dump();
double x, y, d_x, d_y, final_error = 0;
// Call execute
df.execute(x, y, &d_x, &d_y, final_error);
std::cout << final_error;
auto dfunc_error = clad::estimate_error(func);
// Used to print generated code to standard output.
dfunc_error.dump();
double x, y, d_x, d_y, final_error = 0;
// Call execute
dfunc_error.execute(x, y, &d_x, &d_y, final_error);
std::cout << final_error;
}
The function signature is similar to `clad::gradient` except we need to add an
extra argument of type `double&` which is used to store the total floating point
error.


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