Funcs

Return constant for pi: 3.141592653589793

Return the remainder or modulo of division: a % b. Result has same unit as a.

Return the smallest whole number greater than or equal to val. Result has same unit as val.

Return the largest whole number less than or equal to val. Result has same unit as val.

Returns the nearest whole number to val. Result has same unit as val.

Return e raised to val.

Return natural logarithm to the base e of val.

Return base 10 logarithm of val.

Return val raised to the specified power.

Return square root of val.

Return random integer within given inclusive range. If range is null, then full range of representative integers is assumed.

Examples:

 random()       // random num with no range
 random(0..100) // random num between 0 and 100

Bitwise not: ~a

Bitwise and: a & b

Bitwise or: a | b

Bitwise xor: a ^ b

Bitwise right shift: a >> b

Bitwise left shift: a << b

Return the arc cosine.

Return the arc sine.

Return the arc tangent.

Converts rectangular coordinates (x, y) to polar (r, theta).

Return the cosine of angle in radians.

Return the hyperbolic cosine.

Return sine of angle in radians.

Return hyperbolic sine.

Return tangent of angle in radians.

Return hyperbolic tangent.

Convert angle in radians to an angle in degrees.

Convert angle in degrees to an angle in radians.

Fold a sample of numbers into their standard average or arithmetic mean. This function is the same as core::avg. Nulls values are ignored. Return null if no values.

Example:

[2, 4, 5, 3].fold(mean)

Fold a sample of numbers into their median value which is the middle value of the sorted samples. If there are an even number of sample, then the median is the mean of the middle two. Null values are ignored. Return null if no values.

Example:

[2, 4, 5, 3, 1].fold(median)

Fold a sample of numbers into their RMSE (root mean square error). The RMSE function determines the RMSE between a sample set and its mean using the n-degrees of freedom RMSE:

RMBE = sqrt( Σ(xᵢ - median)² ) / (n - nDegrees)

Examples:

samples.fold(rootMeanSquareErr)         // unbiased zero degrees of freedom
samples.fold(rootMeanSquareErr(_,_,1))  // 1 degree of freedom

Fold a sample of numbers into their MBE (mean bias error). The MBE function determines the MBE between a sample set and its mean:

MBE = Σ(xᵢ - median) / (n - nDegrees)

Examples:

samples.fold(meanBiasErr)         // unbiased zero degrees of freedom
samples.fold(meanBiasErr(_,_,1))  // 1 degree of freedom

Fold a series of numbers into the standard deviation of a sample:

s = sqrt(Σ (xᵢ - mean)² / (n-1))

Example:

[4, 2, 5, 8, 6].fold(standardDeviation)

Computes the pth quantile of a list of numbers, according to the specified interpolation method. The value p must be a number between 0.0 to 1.0.

• linear (default): Interpolates proportionally between the two closest values
• nearest: Rounds to the nearest data point
• lower: Rounds to the nearest lower data point
• higher: Rounds to the nearest higher data point
• midpoint: Averages two nearest values

Usage:

[1,2,3].fold(quantile(p, method))

Examples:

[10,10,10,25,100].fold(quantile(0.7 )) => 22 //default to linear
[10,10,10,25,100].fold(quantile(0.7, "nearest")) => 25
[10,10,10,25,100].fold(quantile(0.7, "lower")) => 10
[10,10,10,25,100].fold(quantile(0.7, "higher")) => 25
[10,10,10,25,100].fold(quantile(0.7, "linear")) => 22 //same as no arg
[10,10,10,25,100].fold(quantile(0.7, "midpoint")) => 17.5

Detailed Logic:

 p: percentile (decimal 0-1)
 n: list size
 rank: p * (n-1) // this is the index of the percentile in your list
 // if rank is an integer, return list[rank]
 // if rank is not an integer, interpolate via one of the above methods (illustrated below in examples)

 [1,2,3,4,5].percentile(0.5) => 3 // rank=2 is an int so we can index[2] directly

 [10,10,10, 25, 100].percentile(0.7, method)
   rank = (0.7 * 4) => 2.8

   //adjust rank based on method
   nearest =  index[3]                // => 25
   lower =    index[2]                // => 10
   higher =   index[3]                // => 25

   //or interpolate for these methods

   //takes the 2 closest indices and calculates midpoint
   midpoint = (25-10)/2 + 10          // => 17.5

   //takes the 2 closest indices and calculates weighted average
   linear =   (0.2 * 10) + (0.8 * 25) // => 22

Convert a general grid to an optimized matrix grid. Matrixs are two dimensional grids of Numbers. Columns are named "v0", "v1", "v2", etc. Grid meta is preserved, but not column meta. Numbers in the resulting matrix are unitless; any units passed in are stripped.

The following options are supported:

• nullVal (Number): replace null values in the grid with this value
• naVal (Number): replace NA values in the grid with this value

  toMatrix(grid, {nullVal: 0, naVal: 0})

To create a sparse or initialized matrix you can pass a Dict with the the following tags (all required)

toMatrix({rows:10, cols: 1000, init: 0})

Transpose the given matrix which is any value accepted by toMatrix.

Return the determinant as a unitless Number for the given matrix which is any value accepted by toMatrix. The matrix must be square.

Return the inverse of the given matrix which is any value accepted by toMatrix.

Add two matrices together and return new matrix. The parameters may be any value supported toMatrix. Matrices must have the same dimensions.

Subtract two matrices and return new matrix. The parameters may be any value supported toMatrix. Matrices must have the same dimensions.

Multiply two matrices and return new matrix. The parameters may be any value supported toMatrix. Matrix a column count must match matrix b row count.

Given a matrix of y coordinates and a matrix of multiple x coordinates compute the best fit multiple linear regression equation using the ordinary least squares method. Both y and x may be any value accepted by toMatrix.

The resulting linear equation for r X coordinates is:

yᵢ = bias + b₁xᵢ₁ + b₂xᵢ₂ +...+ bᵣxᵢᵣ

The equation is returned as a grid. The grid meta:

• bias: bias or zero coefficient which is independent of any of the x factors
• r2: R² coefficient of determination as a number between 1.0 (perfect correlation) and 0.0 (no correlation)
• r: the square root of R², referred to as the correlation coefficient
• rowCount: the number of rows of data used in the correlation For each X factor there is a row with the following tags:
• b: the correlation coefficient for the given X factor

Given a grid of x, y coordinates compute the best fit linear regression equation using the ordinary least squares method. The first column of the grid is used for x and the second column is y. Any rows without a Number for both x and y are skipped. Any special Numbers (infinity/NaN) are skipped.

Options:

• x: column name to use for x if not first column
• y: column name to use for y if not second column

The resulting linear equation is:

yᵢ = mxᵢ + b

The equation is returned as a dictionary with these keys:

• m: slope of the best fit regression line
• b: intercept of the best fit regression line
• r2: R² coefficient of determination as a number between 1.0 (perfect correlation) and 0.0 (no correlation)
• xmin: minimum value of x variable in sample data
• xmax: maximum value of x variable in sample data
• ymin: minimum value of y variable in sample data
• ymax: maximum value of y variable in sample data

Also see matrixFitLinearRegression to compute a multiple linear regression.

Example:

data: [{x:1, y:2},
       {x:2, y:4},
       {x:4, y:4},
       {x:6, y:5}].toGrid
 fitLinearRegression(data)

 >>> {m:0.4915, b: 2.1525, r2: 0.7502}