Trapezoid
Log-trapezoidal integrator.
Functions¶
log_trapezoidal_integrand_dx(log_y: Array, x: Array) -> Array
Compute the log integrand dx of the following integral using the trapezoidal rule.
\[
\log z = \log \int \exp(\log y(x)) \mathrm{d}x
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
log_y
|
Array
|
Log of y(x). |
required |
x
|
Array
|
Argument of the function y. |
required |
Return
Log of the integrand dx.
log_trapezoidal_integrate(log_y: Array, x: Array) -> Array
Compute the following integral using the trapezoidal rule.
\[
\log z = \log \int \exp(\log y(x)) \mathrm{d}x
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
log_y
|
Array
|
Log of y(x). |
required |
x
|
Array
|
Argument of the function y. |
required |
Return
Log of the integral.
log_trapezoidal_cumsum(log_y: Array, x: Array) -> Array
Compute the log of the cumulative sum of the following integral using the trapezoidal rule.
\[
\log z(x) = \log \int^{x} \exp(\log y(x')) \mathrm{d}x'
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
log_y
|
Array
|
Log of y(x). |
required |
x
|
Array
|
Argument of the function y. |
required |
Return
Log of the cumulative sum.