Integral with change of variables (substitution). More...
#include <integral.hpp>
Public Types | |
| using | value_type = typename OriginalIntegral::value_type |
Public Member Functions | |
| constexpr | TransformedIntegral (OriginalIntegral orig, Phi p, Jacobian j, value_type new_lo, value_type new_hi, value_type tol=value_type(1e-10)) noexcept |
| algorithms::integration_result< value_type > | eval (std::span< value_type const > args) const |
| Evaluate the transformed integral numerically. | |
| algorithms::integration_result< value_type > | eval () const |
| algorithms::integration_result< value_type > | evaluate (std::span< value_type const > args) const |
| algorithms::integration_result< value_type > | evaluate () const |
| std::string | to_string () const |
Public Attributes | |
| OriginalIntegral | original |
| Phi | phi |
| Jacobian | jacobian |
| value_type | new_lower |
| value_type | new_upper |
| value_type | tolerance |
Static Public Attributes | |
| static constexpr std::size_t | arity_v = OriginalIntegral::arity_v |
Detailed Description
struct limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >
Integral with change of variables (substitution).
Applies the transformation rule:
![\[
\int_a^b f(x) \, dx = \int_c^d f(\phi(t)) \cdot |\phi'(t)| \, dt
\]](form_1.png)
This is useful for removing singularities or improving convergence.
- Template Parameters
-
OriginalIntegral The original integral type Phi The substitution function type (t → x) Jacobian The Jacobian |dφ/dt| function type
- Example: Removing √x singularity
- // ∫₀¹ 1/√x dx has singularity at x=0// Substitute x = t² to get ∫₀¹ 1/t · 2t dt = ∫₀¹ 2 dtauto T = I.transform([](double t) { return t*t; }, // φ: t → t²[](double t) { return 2*t; }, // |φ'|: 2t0.0, 1.0 // new bounds);constexpr auto integral(E expr)Create an IntegralBuilder for fluent integral construction.Definition integral.hpp:505
- See also
- Integral::transform() Factory method
- transforms::quadratic Predefined quadratic transform
Definition at line 544 of file integral.hpp.
Member Typedef Documentation
◆ value_type
| using limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::value_type = typename OriginalIntegral::value_type |
Definition at line 545 of file integral.hpp.
Constructor & Destructor Documentation
◆ TransformedIntegral()
|
inlineconstexprnoexcept |
Definition at line 556 of file integral.hpp.
Member Function Documentation
◆ eval() [1/2]
|
inline |
Definition at line 588 of file integral.hpp.
References limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval(), limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::evaluate(), and limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::evaluate().
◆ eval() [2/2]
|
inline |
Evaluate the transformed integral numerically.
Definition at line 574 of file integral.hpp.
References limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::jacobian, limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::new_lower, limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::new_upper, limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::original, limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::phi, limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::tolerance, and limes::expr::x.
◆ evaluate() [1/2]
|
inline |
Definition at line 600 of file integral.hpp.
References limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
◆ evaluate() [2/2]
|
inline |
Definition at line 594 of file integral.hpp.
References limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
◆ to_string()
|
inline |
Member Data Documentation
◆ arity_v
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staticconstexpr |
Definition at line 547 of file integral.hpp.
◆ jacobian
| Jacobian limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::jacobian |
Definition at line 551 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
◆ new_lower
| value_type limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::new_lower |
Definition at line 552 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval(), and limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::to_string().
◆ new_upper
| value_type limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::new_upper |
Definition at line 553 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval(), and limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::to_string().
◆ original
| OriginalIntegral limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::original |
Definition at line 549 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval(), and limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::to_string().
◆ phi
| Phi limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::phi |
Definition at line 550 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
◆ tolerance
| value_type limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::tolerance |
Definition at line 554 of file integral.hpp.
Referenced by limes::expr::TransformedIntegral< OriginalIntegral, Phi, Jacobian >::eval().
The documentation for this struct was generated from the following file:
- include/limes/expr/integral.hpp
