Integral
The Integral object provides implementations for five basic integration methods:
∫f(x)dx on interval [a, b]
trap - trapezoidal method - linear
simpson - Simpson method - quadratic
simpson38 - 3/8 Simpson method - cubic
boole - Boole Method - quartic
romberg - Romberg method - recursive, uses trap
The first four are Composite Newton-Coates type integrators.
Attributes
- See also
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en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas
- Graph
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- Supertypes
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class Objecttrait Matchableclass Any
- Self type
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Integral.type
Members list
Value members
Concrete methods
Integrate '∫f(x)dx' on interval '[a, b]' using the Boole method.
Integrate '∫f(x)dx' on interval '[a, b]' using the Boole method.
Value parameters
- a
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the start of the integration interval
- b
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the end of the integration interval
- f
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the function to be integrated
- sd
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the number of subdivision (intervals) of [a, b]
Attributes
Integrate '∫f(x)dx' on interval 'on' using the default method.
Integrate '∫f(x)dx' on interval 'on' using the default method.
Value parameters
- f
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the function to be integrated
- on
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the interval of integration, e.g., (0.0, 2.0)
Attributes
Integrate '∫f(x)dx' on interval '[a, b]' using the Romberg method. Translation of Java code from the site below to Scala.
Integrate '∫f(x)dx' on interval '[a, b]' using the Romberg method. Translation of Java code from the site below to Scala.
Value parameters
- a
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the start of the integration interval
- b
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the end of the integration interval
- f
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the function to be integrated
- iter
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the number of iterative steps
Attributes
- See also
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cs.roanoke.edu/Spring2012/CPSC402A/Integrate.java FIX: shouldn't need a 2D array/matrix.
Integrate '∫f(x)dx' on interval '[a, b]' using the Simpson method.
Integrate '∫f(x)dx' on interval '[a, b]' using the Simpson method.
Value parameters
- a
-
the start of the integration interval
- b
-
the end of the integration interval
- f
-
the function to be integrated
- sd
-
the number of subdivision (intervals) of [a, b]
Attributes
Integrate '∫f(x)dx' on interval '[a, b]' using the 3/8 Simpson method.
Integrate '∫f(x)dx' on interval '[a, b]' using the 3/8 Simpson method.
Value parameters
- a
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the start of the integration interval
- b
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the end of the integration interval
- f
-
the function to be integrated
- sd
-
the number of subdivision (intervals) of [a, b]
Attributes
Test each of the numerical integrators: '∫f(x)dx' on interval '[a, b]'.
Test each of the numerical integrators: '∫f(x)dx' on interval '[a, b]'.
Value parameters
- a
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the start of the integration interval
- ans
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the answer to the integration problem, if known (for % error)
- b
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the end of the integration interval
- f
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the function to be integrated
- sd
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the number of subdivision (intervals) of [a, b]
Attributes
Integrate '∫f(x)dx' on interval '[a, b]' using the trapezoidal method.
Integrate '∫f(x)dx' on interval '[a, b]' using the trapezoidal method.
Value parameters
- a
-
the start of the integration interval
- b
-
the end of the integration interval
- f
-
the function to be integrated
- sd
-
the number of subdivision (intervals) of [a, b]