Calculator Functions

The Calculator component supports a comprehensive set of functions. You can apply functions to scalar or array values, unless otherwise noted. For array values, the result is an array of the same size as the argument(s). Isight applies the function to each array element individually.

This page discusses:

Arithmetic Functions
Array Functions
Constants Functions
Logical Functions
Hyperbolic Functions
Statistical Functions
Trigonometry Functions
Vector and Matrix Functions

Arithmetic Functions

The Calculator component supports the following arithmetic functions:


`abs(x)`	absolute value
`angle(x, y)`	converts rectangular coordinates (y, x) to polar
`ceil(x)`	smallest integer greater than or equal to x
`exp(x)`	E to the power
`fact(i)`	factorial
`floor(x)`	largest integer less than or equal to x
`int(x)`	truncate to integer
`ln(x)`	natural logarithm
`log10(x)`	log base 10
`mod(x, y)`	remainder of x / y
`power(x, y)`	power
`rand()`	random number 0..1
`round(x)`	round to integer
`sqrt(x)`	square root

Array Functions

The array functions take an array as the argument and returns the scalar result of applying the operation to all elements of the array. The Calculator component supports the following array functions:


`absMax(arr)`	maximum absolute value
`absMin(arr)`	minimum absolute value
`absMaxIdx(arr)`	index of the largest absolute value
`absMinIdx(arr)`	index of the smallest absolute value
`absSum(arr)`	sum of absolute values
`dim(arr, dim)`	size of one dimension of an array
`max(arr)`	maximum
`maxIdx(arr)`	index of the largest value
`mean(arr)`	arithmetic mean
`min(arr)`	minimum
`minIdx(arr)`	index of the smallest value
`size(arr)`	number of elements in an array
`stdDev(arr)`	standard deviation
`sum(arr)`	sum

Note: The Idx functions return the index of the array element that meets the rest of the function name. For example, a{maxIdx(a)} == max(a). If there are multiple array elements with the same value, Isight chooses the first function.

Constants Functions

The Calculator component supports the following constants functions:


`e()`	Base of natural logarithms
`inf()`	IEEE floating point extended value infinity
`nan()`	IEEE floating point extended value (not a number)
`pi()`	Ratio of diameter of a circle to circumference

Logical Functions

The Calculator component supports the following logical functions:


`if(b, x, y)`	conditional (if b then x else y)
`true()`	logical true
`false()`	logical false

Hyperbolic Functions

The Calculator component supports the following hyperbolic functions:


`acosh(x)`	hyperbolic arc cosine
`acoth(x)`	hyperbolic arc cotangent
`acsch(x)`	hyperbolic arc cosecant
`asech(x)`	hyperbolic arc secant
`asinh(x)`	hyperbolic arc sine
`atanh(x)`	hyperbolic arc tangent
`cosh(x)`	hyperbolic cosine
`coth(x)`	hyperbolic cotangent
`csch(x)`	hyperbolic cosecant
`sech(x)`	hyperbolic secant
`sinh(x)`	hyperbolic sine
`tanh(x)`	hyperbolic tangent

Statistical Functions

The statistical functions take an arbitrary number of scalar arguments and return a single scalar value. If there is only one array argument, the function behaves as the array function. If there are multiple arguments and at least one argument is an array, the operation is performed separately on each element of the array and returns an array. The Calculator component supports the following statistical functions:


`sum(x, y,...)`	sum
`max(x, y,...)`	maximum
`min(x, y,...)`	minimum
`absSum(x, y,...)`	sum of absolute values
`absMax(x, y,...)`	maximum absolute value
`absMin(x, y,...)`	minimum absolute value
`mean(x, y,...)`	mean
`stdDev(x, y,...)`	standard deviation

Trigonometry Functions

Trigonometry functions are in radians. Use the expression degrees / 180 * pi() to convert degrees to radians. The Calculator component supports the following trigonometry functions:


`acos(x)`	arc cosine
`acot(x)`	arc cotangent
`acsc(x)`	arc cosecant
`asec(x)`	arc secant
`asin(x)`	arc sine
`atan(x)`	arc tangent
`atan2(x, y)`	arc tangent of x/y
`cos(x)`	cosine
`cot(x)`	cotangent
`csc(x)`	cosecant
`sec(x)`	secant
`sin(x)`	sine
`tan(x)`	tangent

Vector and Matrix Functions

The Calculator component supports the following vector and matrix functions:


`dot(a,b)`	Takes two vectors and computes the dot product. The `a` and `b` vectors must be the same size. Takes two 1D arrays as arguments and returns a scalar real value.
`cross(a,b)`	Takes two vectors with three elements each and computes the cross product (also a vector with three elements). Takes two 1D arrays as arguments and returns a 1D array. Cross product is available only for 1D arrays with exactly three elements.
`prod(A,B)`	Takes two matrices and returns the product (also a matrix). Takes two 2D arrays as arguments and returns a 2D array.
`transpose(A)`	Computes the transpose of a matrix/vector. Takes a 2D array as an argument and returns a 2D array.
`inv(A)`	Computes the inverse of the square matrix `A`. Takes a square 2D array as an argument and returns a 2D array.
`powerm(A,n)`	Computes the power of a matrix `A` using eigen value decomposition. Takes a 2D array and a scalar as arguments and returns a 2D array.
`det(A)`	Computes the determinant of a matrix. Takes a square 2D array as an argument and returns a scalar real value.
`rank(A)`	Computes the rank of a matrix A (i.e., the number of linearly independent rows).
`norminf(A)`	Calculates the L-infinity norm (or maximum row sum norm) of a matrix `A`. Takes a 1D or 2D array as an argument and returns a scalar real value. ${‖ A ‖}_{\infty} = \max_{i} \sum_{j} \| a_{i j} \|$
`norm1(A)`	Calculates the L1 norm (or maximum column sum norm) of the matrix or vector `A`. Takes a 1D or 2D array as an argument and returns a scalar real value. ${‖ A ‖}_{1} = \max_{j} \sum_{i} \| a_{i j} \|$
`norm2(A)`	Calculates the L2 norm (or spectral norm) of the matrix or vector `A`. Takes a 1D or 2D array as an argument and returns a scalar real value ${‖ A ‖}_{2} = \sqrt{\max λ}, (A^{T} A) x = λ I x$ (i.e., $λ$ is an eigen value of A^TA).
`trace(A)`	Computes the trace (i.e., the sum of values along the main diagonal). Takes a 2D array as an argument and returns a scalar real value.
`eig(A)`	Computes the set of real eigen values of a square matrix. Takes a square 2D array as an argument and returns a 1D array.
Decompositions
`chol(A)`	Computes the Cholesky decomposition (i.e., LLT = A) of a positive definite matrix. Takes a square 2D array as an argument and returns a 2D array.
`lu(A)`	Computes the LU decomposition of `A`. Takes a 2D array as an argument and returns an aggregate containing two 2D arrays (L&U) and an integer array (pivot).
`singularValues(A)`	Computes the singular value and returns the S matrix. Takes a 2D array as an argument and returns a 2D array.
Matrix Assignments
`A=ones(m,n)`	Creates a matrix with 1 at all locations. Takes two integers as arguments and returns a 2D array.
`A=zeros(m,n)`	Creates an `m` by `n` zero matrix. Takes two integers as arguments and returns a 2D array.
`A=identity(n)`	Creates an `n` by `n` identity matrix. Takes an integer as an argument and returns a 2D array.