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1 | 1 | # Numerical integration
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2 | 2 |
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3 |
| -## Implemented |
4 |
| - |
5 |
| -* `trapz` |
6 |
| -* `trapz_weights` |
| 3 | +* [`trapz` - integrate sampled values using trapezoidal rule](#trapz---integrate-sampled-values-using-trapezoidal-rule) |
| 4 | +* [`trapz_weights` - trapezoidal rule weights for given abscissas](#trapz_weights---trapezoidal-rule-weights-for-given-abscissas) |
| 5 | +* [`simps` - integrate sampled values using Simpson's rule (to be implemented)](#simps---integrate-sampled-values-using-simpsons-rule-to-be-implemented) |
| 6 | +* [`simps_weights` - Simpson's rule weights for given abscissas (to be implemented)](#simps_weights---simpsons-rule-weights-for-given-abscissas-to-be-implemented) |
7 | 7 |
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8 | 8 | ## `trapz` - integrate sampled values using trapezoidal rule
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9 | 9 |
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| 10 | +### Description |
| 11 | + |
10 | 12 | Returns the trapezoidal rule integral of an array `y` representing discrete samples of a function. The integral is computed assuming either equidistant abscissas with spacing `dx` or arbitary abscissas `x`.
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11 | 13 |
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12 | 14 | ### Syntax
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@@ -46,6 +48,8 @@ end program
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46 | 48 |
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47 | 49 | ## `trapz_weights` - trapezoidal rule weights for given abscissas
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48 | 50 |
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| 51 | +### Description |
| 52 | + |
49 | 53 | Given an array of abscissas `x`, computes the array of weights `w` such that if `y` represented function values tabulated at `x`, then `sum(w*y)` produces a trapezoidal rule approximation to the integral.
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50 | 54 |
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51 | 55 | ### Syntax
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@@ -78,7 +82,9 @@ end program
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78 | 82 |
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79 | 83 | ```
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80 | 84 |
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81 |
| -# `simps` - integrate sampled values using Simpson's rule |
| 85 | +## `simps` - integrate sampled values using Simpson's rule (to be implemented) |
| 86 | + |
| 87 | +### Description |
82 | 88 |
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83 | 89 | Returns the Simpson's rule integral of an array `y` representing discrete samples of a function. The integral is computed assuming either equidistant abscissas with spacing `dx` or arbitary abscissas `x`.
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84 | 90 |
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@@ -112,7 +118,9 @@ If the size of `y` is two, the result is the same as if `trapz` had been called
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112 | 118 |
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113 | 119 | TBD
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114 | 120 |
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115 |
| -# `simps_weights` - Simpson's rule weights for given abscissas |
| 121 | +## `simps_weights` - Simpson's rule weights for given abscissas (to be implemented) |
| 122 | + |
| 123 | +### Description |
116 | 124 |
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117 | 125 | Given an array of abscissas `x`, computes the array of weights `w` such that if `y` represented function values tabulated at `x`, then `sum(w*y)` produces a Simpson's rule approximation to the integral.
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118 | 126 |
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