| arithmetic {IntervalQuestionStat} | R Documentation |
Interval arithmetic operations
Description
These commands apply basic interval-valued arithmetic operations.
Usage
## S4 method for signature 'numeric,IntervalData'
e1 + e2
## S4 method for signature 'IntervalData,numeric'
e1 + e2
## S4 method for signature 'IntervalData,IntervalData'
e1 + e2
## S4 method for signature 'numeric,IntervalData'
e1 - e2
## S4 method for signature 'IntervalData,numeric'
e1 - e2
## S4 method for signature 'IntervalData,IntervalData'
e1 - e2
## S4 method for signature 'IntervalData,ANY'
e1 - e2 # -e1
## S4 method for signature 'numeric,IntervalData'
e1 * e2
## S4 method for signature 'IntervalData,numeric'
e1 * e2
## S4 method for signature 'numeric,IntervalList'
e1 + e2
## S4 method for signature 'IntervalList,numeric'
e1 + e2
## S4 method for signature 'IntervalData,IntervalList'
e1 + e2
## S4 method for signature 'IntervalList,IntervalData'
e1 + e2
## S4 method for signature 'IntervalList,IntervalList'
e1 + e2
## S4 method for signature 'numeric,IntervalList'
e1 - e2
## S4 method for signature 'IntervalList,numeric'
e1 - e2
## S4 method for signature 'IntervalData,IntervalList'
e1 - e2
## S4 method for signature 'IntervalList,IntervalData'
e1 - e2
## S4 method for signature 'IntervalList,IntervalList'
e1 - e2
## S4 method for signature 'IntervalList,ANY'
e1 - e2 # -e1
## S4 method for signature 'numeric,IntervalList'
e1 * e2
## S4 method for signature 'IntervalList,numeric'
e1 * e2
## S4 method for signature 'numeric,IntervalMatrix'
e1 + e2
## S4 method for signature 'IntervalMatrix,numeric'
e1 + e2
## S4 method for signature 'matrix,IntervalMatrix'
e1 + e2
## S4 method for signature 'IntervalMatrix,matrix'
e1 + e2
## S4 method for signature 'IntervalData,IntervalMatrix'
e1 + e2
## S4 method for signature 'IntervalMatrix,IntervalData'
e1 + e2
## S4 method for signature 'IntervalList,IntervalMatrix'
e1 + e2
## S4 method for signature 'IntervalMatrix,IntervalList'
e1 + e2
## S4 method for signature 'IntervalMatrix,IntervalMatrix'
e1 + e2
## S4 method for signature 'numeric,IntervalMatrix'
e1 - e2
## S4 method for signature 'IntervalMatrix,numeric'
e1 - e2
## S4 method for signature 'matrix,IntervalMatrix'
e1 - e2
## S4 method for signature 'IntervalMatrix,matrix'
e1 - e2
## S4 method for signature 'IntervalData,IntervalMatrix'
e1 - e2
## S4 method for signature 'IntervalMatrix,IntervalData'
e1 - e2
## S4 method for signature 'IntervalList,IntervalMatrix'
e1 - e2
## S4 method for signature 'IntervalMatrix,IntervalList'
e1 - e2
## S4 method for signature 'IntervalMatrix,IntervalMatrix'
e1 - e2
## S4 method for signature 'IntervalMatrix,ANY'
e1 - e2 # -e1
## S4 method for signature 'numeric,IntervalMatrix'
e1 * e2
## S4 method for signature 'IntervalMatrix,numeric'
e1 * e2
## S4 method for signature 'matrix,IntervalMatrix'
e1 * e2
## S4 method for signature 'IntervalMatrix,matrix'
e1 * e2
Arguments
e1 |
A single numeric value, a vector, a matrix, a single interval, or
a list or a matrix of intervals saved as a |
e2 |
A single numeric value, a vector, a matrix, a single interval, or
a list or a matrix of intervals saved as a |
Details
Implementation of basic interval arithmetic calculations (see, for example,
Moore et al., 2009) through Minkowski's sum (see Minkowski, 1903)
and a product by a scalar operation. In particular, +, -,
and * operators allow to carry out these computations.
Using mid/spr-characterization, these operations can be settled
for any two interval-valued data A and B and a real number
\gamma as follows:
A + B = [(\mathrm{mid}~A +\mathrm{mid}~B) \mp (\mathrm{spr}~A
+ \mathrm{spr}~B)]
and
\gamma \cdot A =
\left\{ \begin{array}{ll}
\left[\gamma\cdot \mathrm{mid}~A\mp\gamma\cdot\mathrm{spr}~A\right] &
\hbox{if $\gamma \geq 0$,}\\[1.5ex]
\left[\gamma\cdot \mathrm{mid}~A\pm\gamma\cdot\mathrm{spr}~A\right] &
\hbox{if $\gamma < 0$.}\end{array}\right.
Value
This function returns a single interval or a list or matrix of intervals,
that is, an IntervalData object or an IntervalList or
IntervalMatrix instance, containing the result of the involved
operation. When these binary operators are used with IntervalList and
IntervalMatrix objects, they return the result of the element by
element operations recycling the elements of the object with the shortest
dimensions if necessary, showing a warning when they are recycled only
fractionally.
Author(s)
José García-García garciagarjose@uniovi.es
References
Minkowski, H. (1903). Volumen und oberfläche. Mathematische Annalen, 57:447-495.
Moore, R.E.; Kearfott, R.B.; Cloud, M.J. (2009). Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, USA. doi:10.1137/1.9780898717716.
Examples
## Some basic arithmetic interval operations
## IntervalData
i1 <- IntervalData(0, 1)
i2 <- IntervalData(2, 3)
i1 + i2 ## Sum of two intervals
i1 + 1 ## Sum of an interval and a real number
1 + i1 ## Sum of a real number and an interval
i1 - i2 ## Subtraction of two intervals
i1 - i1 ## Note that i1 - i1 is not {0}
i1 - 1 ## Subtraction of an interval and a real number
1 - i1 ## Subtraction of a real number and an interval
- i1
2 * i1 ## Product between a scalar and an interval
-2 * i1 ## Product between a scalar and an interval
i1 * 2 ## Product between an interval and a scalar
i1 * (-2) ## Product between an interval and a scalar
## IntervalList
list1 <- IntervalList(c(0, 3, 2, 5), c(4, 5, 4, 8))
list2 <- IntervalList(c(3, 0, 3, 1), c(7, 4, 6, 2))
list1 + list2 ## Sum of two list of intervals
list1 + 1 ## Sum of a list of intervals and a real number
1 + list1 ## Sum of a real number and a list of intervals
1:4 + list1 ## Sum of a vector and a list of intervals
list1 + 1:4 ## Sum of a list of intervals and a vector
list1 - list2 ## Subtraction of two lists of intervals
list1 - 1 ## Subtraction of a list of intervals and a real number
1 - list1 ## Subtraction of a real number and a list of intervals
1:4 - list1 ## Subtraction of a vector and a list of intervals
list1 - 1:4 ## Subtraction of a list of intervals and a vector
- list1
2 * list1 ## Product between a scalar and a list of intervals
-2 * list1 ## Product between a scalar and a list of intervals
list1 * 2 ## Product between a list of intervals and a scalar
list1 * (-2) ## Product between a list of intervals and a scalar
1:4 * list1 ## Product between a vector and a list of intervals
list1 * 1:4 ## Product between a list of intervals and vector
## IntervalMatrix
matrix1 <- IntervalMatrix(matrix(c(0, 1, 1, 2, 2, 3, 3, 4), 2, 4))
matrix2 <- IntervalMatrix(matrix(c(4, 5, 5, 6, 6, 7, 7, 8), 2, 4))
m <- matrix(1:4, 2, 2)
matrix1 + matrix2 ## Sum of two matrices of intervals
matrix1 + 1 ## Sum of a matrix of intervals and a scalar
1 + matrix1 ## sum of a scalar and a matrix of intervals
matrix1 + m ## Sum of a matrix of intervals and a matrix
m + matrix1 ## Sum of a matrix and a matrix of intervals
matrix1 + i1 ## Sum of a matrix of intervals and an interval
i1 + matrix1 ## Sum of an interval and a matrix of intervals
matrix1 + list1 ## Sum of a matrix and a list of intervals
list1 + matrix1 ## Sum of a list and a matrix of intervals
matrix1 - matrix2 ## Subtraction of two matrices of intervals
matrix1 - 1 ## Subtraction of a matrix of intervals and a scalar
1 - matrix1 ## Subtraction of a scalar and a matrix of intervals
matrix1 - m ## Subtraction of a matrix of intervals and a matrix
m - matrix1 ## Subtraction of a matrix and a matrix of intervals
matrix1 - i1 ## Subtraction of a matrix of intervals and an interval
i1 - matrix1 ## Subtraction of an interval and a matrix of intervals
matrix1 - list1 ## Subtraction of a matrix and a list of intervals
list1 - matrix1 ## Subtraction of a list and a matrix of intervals
- matrix1
matrix1 * 2 ## Product between a matrix of intervals and a scalar
2 * matrix1 ## Product between a scalar and a matrix of intervals
matrix1 * m ## Product between a matrix of intervals and a matrix
m * matrix1 ## Product between a matrix and a matrix of intervals