Skip to content

Commit 8581207

Browse files
committed
toc_md: harmonization
1 parent a84d6b0 commit 8581207

File tree

1 file changed

+12
-0
lines changed

1 file changed

+12
-0
lines changed

src/stdlib_experimental_quadrature.md

+12
Original file line numberDiff line numberDiff line change
@@ -5,21 +5,25 @@
55
<!-- vim-markdown-toc GFM -->
66

77
* [`trapz` - integrate sampled values using trapezoidal rule](#trapz---integrate-sampled-values-using-trapezoidal-rule)
8+
* [Description](#description)
89
* [Syntax](#syntax)
910
* [Arguments](#arguments)
1011
* [Return value](#return-value)
1112
* [Example](#example)
1213
* [`trapz_weights` - trapezoidal rule weights for given abscissas](#trapz_weights---trapezoidal-rule-weights-for-given-abscissas)
14+
* [Description](#description-1)
1315
* [Syntax](#syntax-1)
1416
* [Arguments](#arguments-1)
1517
* [Return value](#return-value-1)
1618
* [Example](#example-1)
1719
* [`simps` - integrate sampled values using Simpson's rule (to be implemented)](#simps---integrate-sampled-values-using-simpsons-rule-to-be-implemented)
20+
* [Description](#description-2)
1821
* [Syntax](#syntax-2)
1922
* [Arguments](#arguments-2)
2023
* [Return value](#return-value-2)
2124
* [Example](#example-2)
2225
* [`simps_weights` - Simpson's rule weights for given abscissas (to be implemented)](#simps_weights---simpsons-rule-weights-for-given-abscissas-to-be-implemented)
26+
* [Description](#description-3)
2327
* [Syntax](#syntax-3)
2428
* [Arguments](#arguments-3)
2529
* [Return value](#return-value-3)
@@ -29,6 +33,8 @@
2933

3034
## `trapz` - integrate sampled values using trapezoidal rule
3135

36+
### Description
37+
3238
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`.
3339

3440
### Syntax
@@ -68,6 +74,8 @@ end program
6874

6975
## `trapz_weights` - trapezoidal rule weights for given abscissas
7076

77+
### Description
78+
7179
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.
7280

7381
### Syntax
@@ -102,6 +110,8 @@ end program
102110

103111
## `simps` - integrate sampled values using Simpson's rule (to be implemented)
104112

113+
### Description
114+
105115
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`.
106116

107117
Simpson's rule is defined for odd-length arrays only. For even-length arrays, an optional argument `even` may be used to specify at which index to replace Simpson's rule with Simpson's 3/8 rule. The 3/8 rule will be used for the array section `y(even:even+4)` and the ordinary Simpon's rule will be used elsewhere.
@@ -136,6 +146,8 @@ TBD
136146

137147
## `simps_weights` - Simpson's rule weights for given abscissas (to be implemented)
138148

149+
### Description
150+
139151
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.
140152

141153
Simpson's rule is defined for odd-length arrays only. For even-length arrays, an optional argument `even` may be used to specify at which index to replace Simpson's rule with Simpson's 3/8 rule. The 3/8 rule will be used for the array section `x(even:even+4)` and the ordinary Simpon's rule will be used elsewhere.

0 commit comments

Comments
 (0)