x  any A of {int, long, float, double} 
y  A 
(returns)  A 
Description: Add x and y.
Details:
Runtime Errors:
x  any A of {int, long, float, double} 
y  A 
(returns)  A 
Description: Subtract y from x.
Details:
Runtime Errors:
x  any A of {int, long, float, double} 
y  A 
(returns)  A 
Description: Multiply x and y.
Details:
Runtime Errors:
x  double 
y  double 
(returns)  double 
Description: Divide y from x, returning a floatingpoint number (even if x and y are integers).
Details:
x  any A of {int, long} 
y  A 
(returns)  A 
Description: Divide y from x, returning the largest whole number N for which N ≤ x/y (integral floor division).
Runtime Errors:
x  any A of {int, long, float, double} 
(returns)  A 
Description: Return the additive inverse of x.
Runtime Errors:
k  any A of {int, long, float, double} 
n  A 
(returns)  A 
Description: Return k modulo n; the result has the same sign as the modulus n.
Details:
Runtime Errors:
k  any A of {int, long, float, double} 
n  A 
(returns)  A 
Description: Return the remainder of k divided by n; the result has the same sign as the dividend k.
Details:
Runtime Errors:
x  any A of {int, long, float, double} 
y  A 
(returns)  A 
Description: Raise x to the power n.
Details:
Runtime Errors:
x  any A 
y  A 
(returns)  int 
Description: Return 1 if x is greater than y, 1 if x is less than y, and 0 if x and y are equal.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is equal to y, false otherwise.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is greater than or equal to y, false otherwise.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is greater than y, false otherwise.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is not equal to y, false otherwise.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is less than y, false otherwise.
x  any A 
y  A 
(returns)  boolean 
Description: Return true if x is less than or equal to y, false otherwise.
x  any A 
y  A 
(returns)  A 
Description: Return x if x ≥ y, y otherwise.
Details:
x  any A 
y  A 
(returns)  A 
Description: Return x if x < y, y otherwise.
Details:
x  boolean 
y  boolean 
(returns)  boolean 
Description: Return true if x and y are both true, false otherwise.
Details:
x  boolean 
y  boolean 
(returns)  boolean 
Description: Return true if either x or y (or both) are true, false otherwise.
Details:
x  boolean 
y  boolean 
(returns)  boolean 
Description: Return true if x is true and y is false or if x is false and y is true, but return false for any other case.
x  boolean 
(returns)  boolean 
Description: Return true if x is false and false if x is true.
x  union of {boolean, null} 
y  union of {boolean, null} 
(returns)  union of {boolean, null} 
Description: Return false if x or y is false, true if x and y are true, and null otherwise.
Details:
x  union of {boolean, null} 
y  union of {boolean, null} 
(returns)  union of {boolean, null} 
Description: Return true if x or y is true, false if both x and y is false, or null otherwise.
Details:
x  union of {boolean, null} 
(returns)  union of {boolean, null} 
Description: Return true if x is false, false if x is true, or null if x is null.
Details:
x  int 
y  int 
(returns)  int 
x  long 
y  long 
(returns)  long 
Description: Calculate the bitwiseand of x and y.
x  int 
y  int 
(returns)  int 
x  long 
y  long 
(returns)  long 
Description: Calculate the bitwiseor of x and y.
x  int 
y  int 
(returns)  int 
x  long 
y  long 
(returns)  long 
Description: Calculate the bitwiseexclusiveor of x and y.
x  int 
(returns)  int 
x  long 
(returns)  long 
Description: Calculate the bitwisenot of x.
(returns)  double 
Description: The doubleprecision number that is closer than any other to \(\pi\), the ratio of a circumference of a circle to its diameter.
(returns)  double 
Description: The doubleprecision number that is closer than any other to \(e\), the base of natural logarithms.
x  any A of {int, long, float, double} 
(returns)  A 
Description: Return the absolute value of x.
Details:
Runtime Errors:
x  double 
(returns)  double 
Description: Return the arccosine (inverse of the cosine function) of x as an angle in radians between \(0\) and \(\pi\).
Details:
x  double 
(returns)  double 
Description: Return the arcsine (inverse of the sine function) of x as an angle in radians between \(\pi/2\) and \(\pi/2\).
Details:
x  double 
(returns)  double 
Description: Return the arctangent (inverse of the tangent function) of x as an angle in radians between \(\pi/2\) and \(\pi/2\).
Details:
y  double 
x  double 
(returns)  double 
Description: Return the arctangent (inverse of the tangent function) of y/x without loss of precision for small x.
Details:
x  double 
(returns)  double 
Description: Return the smallest (closest to negative infinity, not closest to zero) whole number that is greater than or equal to the input.
Details:
mag  any A of {int, long, float, double} 
sign  A 
(returns)  A 
Description: Return a number with the magnitude of mag and the sign of sign.
Details:
x  double 
(returns)  double 
Description: Return the trigonometric cosine of x, which is assumed to be in radians.
Details:
x  double 
(returns)  double 
Description: Return the hyperbolic cosine of x, which is equal to \(\frac{e^x + e^{x}}{2}\)
Details:
x  double 
(returns)  double 
Description: Return m.e raised to the power of x.
Details:
x  double 
(returns)  double 
Description: Return \(e^x  1\).
Details:
x  double 
(returns)  double 
Description: Return the largest (closest to positive infinity) whole number that is less than or equal to the input.
Details:
x  double 
y  double 
(returns)  double 
Description: Return \(\sqrt{x^2 + y^2}\).
Details:
x  double 
(returns)  double 
Description: Return the natural logarithm of x.
Details:
x  double 
(returns)  double 
Description: Return the logarithm base 10 of x.
Details:
x  double 
base  int 
(returns)  double 
Description: Return the logarithm of x with a given base.
Details:
Runtime Errors:
x  double 
(returns)  double 
Description: Return \(ln(x^2 + 1)\).
Details:
x  float 
(returns)  int 
x  double 
(returns)  long 
Description: Return the closest whole number to x, rounding up if the fractional part is exactly onehalf.
Details:
Runtime Errors:
x  double 
(returns)  double 
Description: Return the closest whole number to x, rounding toward the nearest even number if the fractional part is exactly onehalf.
x  double 
(returns)  int 
Description: Return 0 if x is zero, 1 if x is positive, and 1 if x is negative.
Details:
x  double 
(returns)  double 
Description: Return the trigonometric sine of x, which is assumed to be in radians.
Details:
x  double 
(returns)  double 
Description: Return the hyperbolic sine of x, which is equal to \(\frac{e^x  e^{x}}{2}\).
Details:
x  double 
(returns)  double 
Description: Return the positive square root of x.
Details:
x  double 
(returns)  double 
Description: Return the trigonometric tangent of x, which is assumed to be in radians.
Details:
x  double 
(returns)  double 
Description: Return the hyperbolic tangent of x, which is equal to \(\frac{e^x  e^{x}}{e^x + e^{x}}\).
Details:
n  int 
k  int 
(returns)  int 
Description: The number of ways to choose k elements from a set of n elements.
Parameters:
n  Total number of elements. 
k  Numer of elements chosen. 
Returns:
With \(n\) and \(k\), this function evaluates the binomial coefficient. 
Runtime Errors:
a  double 
b  double 
(returns)  double 
Description: Compute the beta function parameterized by a and b.
Returns:
With \(a\) and \(b\), this function evaluates natural logarithm of the beta function. The beta function is \(\int_{0}^{1} t^{a  1}(1  t)^{b  1} dt \). 
Runtime Errors:
x  double 
(returns)  double 
Description: Return the error function of x.
x  double 
(returns)  double 
Description: Return the complimentary error function of x.
x  double 
(returns)  double 
Description: Return the natural log of the gamma function of x.
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the softmax function.
Returns:
Each element \(x_i\) is mapped to \(\exp(x_i)/\sum_j \exp(x_j)\). 
Runtime Errors:
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the logit function.
Returns:
Each element \(x_i\) is mapped to \(1 / (1 + \exp(x_i))\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the probit function.
Returns:
Each element \(x_i\) is mapped to \((\mbox{erf}(x_i/\sqrt{2}) + 1)/2\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the cloglog function.
Returns:
Each element \(x_i\) is mapped to \(1  \exp(\exp(x_i))\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the loglog function.
Returns:
Each element \(x_i\) is mapped to \(\exp(\exp(x_i))\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the cauchit function.
Returns:
Each element \(x_i\) is mapped to \(0.5 + (1/\pi) \tan^{1}(x_i)\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the softplus function.
Returns:
Each element \(x_i\) is mapped to \(\log(1.0 + \exp(x_i))\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the rectified linear unit (ReLu) function.
Returns:
Each element \(x_i\) is mapped to \(\log(1.0 + \exp(x_i))\). 
x  double 
(returns)  double 
x  array of double 
(returns)  array of double 
x  map of double 
(returns)  map of double 
Description: Normalize a prediction with the hyperbolic tangent function.
Returns:
Each element \(x_i\) is mapped to \(\tanh(x_i)\). 
x  array of double 
y  array of double 
(returns)  double 
Description: Linear kernel function.
Parameters:
x  Length n vector. 
y  Length n vector. 
Returns:
Returns the dot product of x and y, \(\sum_{i=1}^{n} x_{i} y_{j}\). 
Runtime Errors:
x  array of double 
y  array of double 
gamma  double 
(returns)  double 
Description: Radial Basis Function (RBF) kernel function.
Parameters:
x  Length n vector. 
y  Length n vector. 
gamma  Gamma coefficient. 
Returns:
Returns the result of \(\mathrm{exp}(\gamma  x  y ^{2})\). 
Runtime Errors:
x  array of double 
y  array of double 
gamma  double 
intercept  double 
degree  double 
(returns)  double 
Description: Polynomial kernel function.
Parameters:
x  Length n vector. 
y  Length n vector. 
gamma  Gamma coefficient. 
intecept  Intercept constant. 
degree  Degree of the polynomial kernel. 
Returns:
Returns the result of \((\gamma \sum_{i=1}^{n} x_{i} y_{j} + \mathrm{intercept})^{\mathrm{degree}}\). 
Runtime Errors:
x  array of double 
y  array of double 
gamma  double 
intercept  double 
(returns)  double 
Description: Sigmoid kernel function.
Parameters:
x  Length n vector. 
y  Length n vector. 
gamma  Gamma coefficient. 
intecept  Intercept constant. 
Returns:
Returns the result of \(\mathrm{tanh}( \mathrm{gamma} \sum_{i=1}^{n} x_{i} y_{j} + \mathrm{intercept})\). 
Runtime Errors:
x  array of array of double 
fcn  function of (double) → double 
(returns)  array of array of double 
x  map of map of double 
fcn  function of (double) → double 
(returns)  map of map of double 
Description: Apply fcn to each element from x.
Details:
x  array of double 
alpha  double 
(returns)  array of double 
x  array of array of double 
alpha  double 
(returns)  array of array of double 
x  map of double 
alpha  double 
(returns)  map of double 
x  map of map of double 
alpha  double 
(returns)  map of map of double 
Description: Scale vector or matrix x by factor alpha.
Details:
x  array of array of double 
y  array of array of double 
fcn  function of (double, double) → double 
(returns)  array of array of double 
x  map of map of double 
y  map of map of double 
fcn  function of (double, double) → double 
(returns)  map of map of double 
Description: Apply fcn to each pair of elements from x and y.
Details:
Runtime Errors:
x  array of double 
y  array of double 
(returns)  array of double 
x  array of array of double 
y  array of array of double 
(returns)  array of array of double 
x  map of double 
y  map of double 
(returns)  map of double 
x  map of map of double 
y  map of map of double 
(returns)  map of map of double 
Description: Add two vectors or matrices x and y.
Details:
Runtime Errors:
x  array of double 
y  array of double 
(returns)  array of double 
x  array of array of double 
y  array of array of double 
(returns)  array of array of double 
x  map of double 
y  map of double 
(returns)  map of double 
x  map of map of double 
y  map of map of double 
(returns)  map of map of double 
Description: Subtract vector or matrix y from x (returns \(x  y\)).
Details:
Runtime Errors:
x  array of array of double 
y  array of double 
(returns)  array of double 
x  map of map of double 
y  map of double 
(returns)  map of double 
x  array of array of double 
y  array of array of double 
(returns)  array of array of double 
x  map of map of double 
y  map of map of double 
(returns)  map of map of double 
Description: Multiply two matrices or a matrix and a vector, which may be represented as dense arrays or potentially sparse maps.
Details:
Runtime Errors:
x  array of array of double 
(returns)  array of array of double 
x  map of map of double 
(returns)  map of map of double 
Description: Transpose a rectangular matrix.
Runtime Errors:
x  array of array of double 
(returns)  array of array of double 
x  map of map of double 
(returns)  map of map of double 
Description: Compute the inverse (or MoorePenrose pseudoinverse, if not square) of x.
Runtime Errors:
x  array of array of double 
(returns)  double 
x  map of map of double 
(returns)  double 
Description: Compute the trace of a matrix (sum of diagonal elements).
Runtime Errors:
x  array of array of double 
(returns)  double 
x  map of map of double 
(returns)  double 
Description: Compute the determinant of a matrix.
Runtime Errors:
x  array of array of double 
tolerance  double 
(returns)  boolean 
x  map of map of double 
tolerance  double 
(returns)  boolean 
Description: Determine if a matrix is symmetric withing tolerance.
Returns:
Returns true if the absolute value of element \(i\), \(j\) minus element \(j\), \(i\) is less than tolerance. 
Runtime Errors:
x  array of array of double 
(returns)  array of array of double 
x  map of map of double 
(returns)  map of map of double 
Description: Compute the eigenvalues and eigenvectors of a real, symmetric matrix x (which are all real).
Returns:
A matrix in which each row (first level of array or map hierarchy) is a normalized eigenvector of x divided by the square root of the corresponding eigenvalue (The sign is chosen such that the first component is positive.). If provided as an array, the rows are in decreasing order of eigenvalue (increasing order of inverse square root eigenvalue). If provided as a map, the rows are keyed by string representations of integers starting with "0", and increasing row keys are in decreasing order of eigenvalue. 
Details:
Runtime Errors:
x  array of array of double 
keep  int 
(returns)  array of array of double 
x  map of map of double 
keep  array of string 
(returns)  map of map of double 
Description: Remove rows from a matrix so that it becomes a projection operator.
Parameters:
x  The matrix to truncate. 
keep  If x is an array, this is the number of rows to keep, starting with the first row. If x is a map, this is the set of keys to keep. If keep is larger than the number of rows or is not a subset of the keys, the excess is ignored. 
Details:
Runtime Errors:
x  array of double 
y  array of double 
(returns)  double 
Description: Euclidean metric without a special similarity function and without any handling of missing values.
Parameters:
x  First sample vector. 
y  Second sample vector. (Must have the same dimension as x.) 
Returns:
Returns \(\sqrt{\sum_i (x_i  y_i)^2}\). 
Runtime Errors:
x  double 
y  double 
(returns)  double 
Description: Similarity function (1dimensional metric) that returns the absolute Euclidean distance between x and y.
x  double 
y  double 
sigma  double 
(returns)  double 
Description: Similarity function (1dimensional metric) that returns \(\exp(\ln(2) (x  y)^2 / \mbox{sigma}^2)\).
similarity  function of (any A, any B) → double 
x  array of union of {null, A} 
y  array of union of {null, B} 
(returns)  double 
similarity  function of (any A, any B) → double 
x  array of union of {null, A} 
y  array of union of {null, B} 
missingWeight  array of double 
(returns)  double 
Description: Euclidean metric, which is the distance function for ordinary space, given by the Pythagorean formula (also known as the 2norm).
Parameters:
similarity  Similarity function (1dimensional metric) that quantifies the distance between components of x and components of y. 
x  First sample vector, which may have missing values. 
y  Second sample vector, which may have missing values. (Must have the same dimension as x.) 
missingWeight  Optional missingvalue weights: a vector with the same dimension as x and y that determines the normalized contribution of missing values in the sum. If not provided, missingvalue weights of 1.0 are assumed. 
Returns:
With \(I(x_i,y_i)\) = 0 if component \(i\) of x or y is missing, 1 otherwise, this function returns \(\sqrt{(\sum_i I(x_i,y_i) \mbox{similarity}(x_i,y_i)^2)(\sum_i q_i)/(\sum_i I(x_i,y_i) q_i)}\) where \(q_i\) are components of the missingvalue weights. Without missing values, it is \(\sqrt{\sum_i \mbox{similarity}(x_i,y_i)^2}\). 
Details:
Runtime Errors:
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
(returns)  double 
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
missingWeight  array of double 
(returns)  double 
Description: Euclidean metric squared, which has the same ordering as the Euclidean metric, but avoids a square root calculation.
Parameters:
similarity  Similarity function (1dimensional metric) that quantifies the distance between components of x and components of y. 
x  First sample vector, which may have missing values. 
y  Second sample vector, which may have missing values. (Must have the same dimension as x.) 
missingWeight  Optional missingvalue weights: a vector with the same dimension as x and y that determines the normalized contribution of missing values in the sum. If not provided, missingvalue weights of 1.0 are assumed. 
Returns:
With \(I(x_i,y_i)\) = 0 if component \(i\) of x or y is missing, 1 otherwise, this function returns \((\sum_i I(x_i,y_i) \mbox{similarity}(x_i,y_i)^2)(\sum_i q_i)/(\sum_i I(x_i,y_i) q_i)\) where \(q_i\) are components of the missingvalue weights. Without missing values, it is \(\sum_i \mbox{similarity}(x_i,y_i)^2\). 
Details:
Runtime Errors:
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
(returns)  double 
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
missingWeight  array of double 
(returns)  double 
Description: Chebyshev metric, also known as the infinity norm or chessboard distance (since it is the number of moves required for a chess king to travel between two points).
Parameters:
similarity  Similarity function (1dimensional metric) that quantifies the distance between components of x and components of y. 
x  First sample vector, which may have missing values. 
y  Second sample vector, which may have missing values. (Must have the same dimension as x.) 
missingWeight  Optional missingvalue weights: a vector with the same dimension as x and y that determines the normalized contribution of missing values in the sum. If not provided, missingvalue weights of 1.0 are assumed. 
Returns:
With \(I(x_i,y_i)\) = 0 if component \(i\) of x or y is missing, 1 otherwise, this function returns \((\max_i I(x_i,y_i) \mbox{similarity}(x_i,y_i))(\sum_i q_i)/(\sum_i I(x_i,y_i) q_i)\) where \(q_i\) are components of the missingvalue weights. Without missing values, it is \(\max_i \mbox{similarity}(x_i,y_i)\). 
Details:
Runtime Errors:
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
(returns)  double 
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
missingWeight  array of double 
(returns)  double 
Description: Taxicab metric, also known as the 1norm, cityblock or Manhattan distance (since it is the distance when confined to a rectilinear city grid).
Parameters:
similarity  Similarity function (1dimensional metric) that quantifies the distance between components of x and components of y. 
x  First sample vector, which may have missing values. 
y  Second sample vector, which may have missing values. (Must have the same dimension as x.) 
missingWeight  Optional missingvalue weights: a vector with the same dimension as x and y that determines the normalized contribution of missing values in the sum. If not provided, missingvalue weights of 1.0 are assumed. 
Returns:
With \(I(x_i,y_i)\) = 0 if component \(i\) of x or y is missing, 1 otherwise, this function returns \((\sum_i I(x_i,y_i) \mbox{similarity}(x_i,y_i))(\sum_i q_i)/(\sum_i I(x_i,y_i) q_i)\) where \(q_i\) are components of the missingvalue weights. Without missing values, it is \(\sum_i \mbox{similarity}(x_i,y_i)\). 
Details:
Runtime Errors:
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
p  double 
(returns)  double 
similarity  function of (double, double) → double 
x  array of union of {null, double} 
y  array of union of {null, double} 
p  double 
missingWeight  array of double 
(returns)  double 
Description: Minkowski metric, also known as the pnorm, a generalized norm whose limits include Euclidean, Chebyshev, and Taxicab.
Parameters:
similarity  Similarity function (1dimensional metric) that quantifies the distance between components of x and components of y. 
x  First sample vector, which may have missing values. 
y  Second sample vector, which may have missing values. (Must have the same dimension as x.) 
missingWeight  Optional missingvalue weights: a vector with the same dimension as x and y that determines the normalized contribution of missing values in the sum. If not provided, missingvalue weights of 1.0 are assumed. 
Returns:
With \(I(x_i,y_i)\) = 0 if component \(i\) of x or y is missing, 1 otherwise, this function returns \(((\sum_i I(x_i,y_i) \mbox{similarity}(x_i,y_i)^p)(\sum_i q_i)/(\sum_i I(x_i,y_i) q_i))^{1/p}\) where \(q_i\) are components of the missingvalue weights. Without missing values, it is \((\sum_i \mbox{similarity}(x_i,y_i)^p)^{1/p}\). 
Details:
Runtime Errors:
x  array of boolean 
y  array of boolean 
(returns)  double 
Description: Simple metric on binary vectors.
Parameters:
x  First sample vector. 
y  Second sample vector. (Must have the same dimension as x.) 
Returns:
Where \(a_{11}\) is the number of x, y coordinate pairs that are equal to true, true, \(a_{10}\) is the number of true, false, \(a_{01}\) is the number of false, true, and \(a_{00}\) is the number of false, false, this function returns \((a_{11} + a_{00})/(a_{11} + a_{10} + a_{01} + a_{00})\). 
Runtime Errors:
x  array of boolean 
y  array of boolean 
(returns)  double 
Description: Jaccard similarity of binary vectors.
Parameters:
x  First sample vector. 
y  Second sample vector. (Must have the same dimension as x.) 
Returns:
Where \(a_{11}\) is the number of x, y coordinate pairs that are equal to true, true, \(a_{10}\) is the number of true, false, \(a_{01}\) is the number of false, true, and \(a_{00}\) is the number of false, false, this function returns \(a_{11}/(a_{11} + a_{10} + a_{01})\). 
Runtime Errors:
x  array of boolean 
y  array of boolean 
(returns)  double 
Description: Tanimoto similarity of binary vectors.
Parameters:
x  First sample vector. 
y  Second sample vector. (Must have the same dimension as x.) 
Returns:
Where \(a_{11}\) is the number of x, y coordinate pairs that are equal to true, true, \(a_{10}\) is the number of true, false, \(a_{01}\) is the number of false, true, and \(a_{00}\) is the number of false, false, this function returns \((a_{11} + a_{00})/(a_{11} + 2*(a_{10} + a_{01}) + a_{00})\). 
Runtime Errors:
x  array of boolean 
y  array of boolean 
c00  double 
c01  double 
c10  double 
c11  double 
d00  double 
d01  double 
d10  double 
d11  double 
(returns)  double 
Description: Genaralized similarity of binary vectors, using c00, c01, c10, c11, d00, d01, d10, and d11 as parameters to reproduce all other binary similarity metrics.
Parameters:
x  First sample vector. 
y  Second sample vector. (Must have the same dimension as x.) 
Returns:
Where \(a_{11}\) is the number of x, y coordinate pairs that are equal to true, true, \(a_{10}\) is the number of true, false, \(a_{01}\) is the number of false, true, and \(a_{00}\) is the number of false, false, this function returns \((c_{11}a_{11} + c_{10}a_{10} + c_{01}a_{01} + c_{00}a_{00})/(d_{11}a_{11} + d_{10}a_{10} + d_{01}a_{01} + d_{00}a_{00})\). 
Runtime Errors:
(returns)  int 
low  int 
high  int 
(returns)  int 
Description: Return a random integer, either on the entire entire 32bit range or between low (inclusive) and high (exclusive).
Details:
Runtime Errors:
(returns)  long 
low  long 
high  long 
(returns)  long 
Description: Return a random long integer, either on the entire 64bit range or between low (inclusive) and high (exclusive).
Details:
Runtime Errors:
low  float 
high  float 
(returns)  float 
Description: Return a random float between low and high.
Details:
Runtime Errors:
low  double 
high  double 
(returns)  double 
Description: Return a random double between low and high.
Details:
Runtime Errors:
population  array of any A 
(returns)  A 
Description: Return a random item from a bag of items.
Details:
Runtime Errors:
size  int 
population  array of any A 
(returns)  array of A 
Description: Return an array of random items (with replacement) from a bag of items.
Details:
Runtime Errors:
size  int 
population  array of any A 
(returns)  array of A 
Description: Return an array of random items (without replacement) from a bag of items.
Details:
Runtime Errors:
distribution  array of double 
(returns)  int 
distribution  array of any record A with fields {prob: double} 
(returns)  A 
Description: Return a random index of distribution with probability proportional to the value of that index or a random item from distribution with probability proportional to the prob field.
Details:
Runtime Errors:
size  int 
(returns)  string 
size  int 
population  string 
(returns)  string 
size  int 
low  int 
high  int 
(returns)  string 
Description: Return a random string with size characters from a range, if provided.
Parameters:
size  Number of characters in the resulting string. 
population  Bag of characters to choose from. Characters repeated \(N\) times in the population have probability \(N\)/size, but order is irrelevant. 
low  Minimum codepoint to sample (inclusive). 
high  Maximum codepoint to sample (exclusive). 
Details:
Runtime Errors:
size  int 
(returns)  bytes 
size  int 
population  bytes 
(returns)  bytes 
size  int 
low  int 
high  int 
(returns)  bytes 
Description: Return size random bytes from a range, if provided.
Parameters:
size  Number of bytes in the result. 
population  Bag of bytes to choose from. Bytes repeated \(N\) times in the population have probability \(N\)/size, but order is irrelevant. 
low  Minimum byte value to sample (inclusive). 
high  Maximum byte value to sample (exclusive). 
Details:
Runtime Errors:
(returns)  string 
Description: Return a random (type 4) UUID with IETF variant (8).
Returns:
The return value is a string with the form xxxxxxxxxxxx4xxx8xxxxxxxxxxxxxxx where x are random, lowercase hexidecimal digits (09af), 4 is the version, and 8 is the IETF variant. 
Details:
(returns)  string 
Description: Return a random (type 4) UUID with IETF variant (8).
Returns:
The return value is a string with the form xxxxxxxxxxxx4xxx8xxxxxxxxxxxxxxx where x are random, lowercase hexidecimal digits (09af), 4 is the version, and 8 is the IETF variant. 
Details:
mu  double 
sigma  double 
(returns)  double 
Description: Return a random number from a Gaussian (normal) distribution with mean mu and standard deviation sigma.
Details:
s  string 
(returns)  int 
Description: Return the length of string s.
s  string 
start  int 
end  int 
(returns)  string 
Description: Return the substring of s from start (inclusive) until end (exclusive).
Details:
s  string 
start  int 
end  int 
replacement  string 
(returns)  string 
Description: Replace s from start (inclusive) until end (exclusive) with replacement.
Details:
haystack  string 
needle  string 
(returns)  boolean 
Description: Return true if haystack contains needle, false otherwise.
haystack  string 
needle  string 
(returns)  int 
Description: Count the number of times needle appears in haystack.
Details:
haystack  string 
needle  string 
(returns)  int 
Description: Return the lowest index where haystack contains needle or 1 if haystack does not contain needle.
haystack  string 
needle  string 
(returns)  int 
Description: Return the highest index where haystack contains needle or 1 if haystack does not contain needle.
haystack  string 
needle  string 
(returns)  boolean 
Description: Return true if the first (leftmost) subseqence of haystack is equal to needle, false otherwise.
haystack  string 
needle  string 
(returns)  boolean 
Description: Return true if the last (rightmost) subseqence of haystack is equal to needle, false otherwise.
array  array of string 
sep  string 
(returns)  string 
Description: Combine strings from array into a single string, delimited by sep.
s  string 
sep  string 
(returns)  array of string 
Description: Divide a string into an array of substrings, splitting at and removing delimiters sep.
Details:
x  long 
(returns)  string 
x  long 
width  int 
zeroPad  boolean 
(returns)  string 
Description: Format an unsigned number as a hexidecimal string.
Parameters:
x  The number. 
width  Width of the string. If negative, leftjustify. If omitted, the string will be as wide as it needs to be to provide the precision. 
zeroPad  If true, pad the integer with zeros to fill up to width. 
Details:
Runtime Errors:
x  long 
(returns)  string 
x  long 
width  int 
zeroPad  boolean 
(returns)  string 
Description: Format an integer as a decimal string.
Parameters:
x  The integer. 
width  Width of the string. If negative, leftjustify. If omitted, the string will be as wide as it needs to be to provide enough precision. 
zeroPad  If true, pad the integer with zeros to fill up to width. 
Runtime Errors:
x  long 
(returns)  string 
x  long 
width  int 
zeroPad  boolean 
(returns)  string 
x  double 
width  union of {int, null} 
precision  union of {int, null} 
(returns)  string 
x  double 
width  union of {int, null} 
precision  union of {int, null} 
minNoExp  double 
maxNoExp  double 
(returns)  string 
Description: Format a number as a decimal string.
Parameters:
x  The number. Note that different signatures apply to integers and floating point numbers. 
width  Width of the string. If negative, leftjustify. If omitted, the string will be as wide as it needs to be to provide the precision. 
zeroPad  If true, pad the integer with zeros to fill up to width. 
precision  Optional precision with which to represent the number. If omitted, at most six digits after the decimal point will be shown, unless they are zero. 
minNoExp  Minimum absolute value that is not presented in scientific notation; 0.0001 if omitted. 
maxNoExp  Maxiumum absolute value that is not presented in scientific notation; 100000 if omitted. 
Details:
Runtime Errors:
x  string 
y  string 
(returns)  string 
Description: Append y to x to form a single string.
Details:
s  string 
n  int 
(returns)  string 
Description: Create a string by concatenating s with itself n times.
s  string 
(returns)  string 
Description: Convert s to lowercase.
s  string 
(returns)  string 
Description: Convert s to uppercase.
s  string 
chars  string 
(returns)  string 
Description: Remove any characters found in chars from the beginning (left) of s.
Details:
s  string 
chars  string 
(returns)  string 
Description: Remove any characters found in chars from the end (right) of s.
Details:
s  string 
chars  string 
(returns)  string 
Description: Remove any characters found in chars from the beginning or end of s.
Details:
s  string 
original  string 
replacement  string 
(returns)  string 
Description: Replace every instance of the substring original from s with replacement.
s  string 
original  string 
replacement  string 
(returns)  string 
Description: Replace the first (leftmost) instance of the substring original from s with replacement.
s  string 
original  string 
replacement  string 
(returns)  string 
Description: Replace the last (rightmost) instance of the substring original from s with replacement.
s  string 
oldchars  string 
newchars  string 
(returns)  string 
Description: For each character in s that is also in oldchars with some index i, replace it with the character at index i in newchars. Any character in s that is not in oldchars is unchanged. Any index i that is greater than the length of newchars is replaced with nothing.
Details:
haystack  string 
pattern  string 
(returns)  array of int 
haystack  bytes 
pattern  bytes 
(returns)  array of int 
Description: Return the indices in haystack of the begining and end of the first match defined by pattern.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  boolean 
haystack  bytes 
pattern  bytes 
(returns)  boolean 
Description: Return true if pattern matches anywhere within haystack, otherwise return false.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  int 
haystack  bytes 
pattern  bytes 
(returns)  int 
Description: Count the number of times pattern matches in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of int 
haystack  bytes 
pattern  bytes 
(returns)  array of int 
Description: Return the location indices of the last pattern match in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of array of int 
haystack  bytes 
pattern  bytes 
(returns)  array of array of int 
Description: Return the location indices of each pattern submatch (groupmatch) in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of array of int 
haystack  bytes 
pattern  bytes 
(returns)  array of array of int 
Description: Return the location indices of every pattern match in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of string 
haystack  bytes 
pattern  bytes 
(returns)  array of bytes 
Description: Return an array containing each string that pattern matched in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  union of {string, null} 
haystack  bytes 
pattern  bytes 
(returns)  union of {bytes, null} 
Description: Return the first occurance of what pattern matched in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of string 
haystack  bytes 
pattern  bytes 
(returns)  array of bytes 
Description: Return an array of strings or bytes for each pattern submatch (groupmatch) at the first occurance of pattern in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of array of string 
haystack  bytes 
pattern  bytes 
(returns)  array of array of bytes 
Description: Return an array of strings or bytes for each pattern submatch (groupmatch) at every occurance of pattern in haystack.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of array of array of int 
haystack  bytes 
pattern  bytes 
(returns)  array of array of array of int 
Description: Return the location indices of each pattern submatch (groupmatch) for each occurance of pattern in haystack.
Runtime Errors:
haystack  string 
pattern  string 
replacement  string 
(returns)  string 
haystack  bytes 
pattern  bytes 
replacement  bytes 
(returns)  bytes 
Description: Replace the first pattern match in haystack with replacement.
Runtime Errors:
haystack  string 
pattern  string 
replacement  string 
(returns)  string 
haystack  bytes 
pattern  bytes 
replacement  bytes 
(returns)  bytes 
Description: Replace the last pattern match in haystack with replacement.
Runtime Errors:
haystack  string 
pattern  string 
(returns)  array of string 
haystack  bytes 
pattern  bytes 
(returns)  array of bytes 
Description: Break haystack into an array of strings or bytes on the separator defined by pattern.
Runtime Errors:
haystack  string 
pattern  string 
replacement  string 
(returns)  string 
haystack  bytes 
pattern  bytes 
replacement  bytes 
(returns)  bytes 
Description: Replace the all pattern matches in haystack with replacement.
Runtime Errors:
str  string 
base  int 
(returns)  int 
Description: Parse str and return its value as an integer with base base, if possible.
Details:
Runtime Errors:
str  string 
base  int 
(returns)  long 
Description: Parse str and return its value as a long integer with base base, if possible.
Details:
Runtime Errors:
str  string 
(returns)  float 
Description: Parse str and return its value as a singleprecision floating point number.
Details:
Runtime Errors:
str  string 
(returns)  double 
Description: Parse str and return its value as a doubleprecision floating point number.
Details:
Runtime Errors:
x  long 
bits  int 
(returns)  long 
Description: Truncate x as though its signed long two's complement representation were inserted, bitforbit, into a signed two's complement representation that is bits wide, removing the most significant bits.
Details:
Runtime Errors:
x  long 
bits  int 
(returns)  long 
Description: Truncate x as though its signed long two's complement representation were inserted, bitforbit, into an unsigned register that is bits wide, removing the most significant bits.
Details:
Runtime Errors:
x  int 
(returns)  int 
x  long 
(returns)  int 
x  float 
(returns)  int 
x  double 
(returns)  int 
Description: Cast x to an integer, rounding if necessary.
Runtime Errors:
x  int 
(returns)  long 
x  long 
(returns)  long 
x  float 
(returns)  long 
x  double 
(returns)  long 
Description: Cast x to a 64bit integer, rounding if necessary.
Runtime Errors:
x  int 
(returns)  float 
x  long 
(returns)  float 
x  float 
(returns)  float 
x  double 
(returns)  float 
Description: Cast x to a singleprecision floating point number, rounding if necessary.
x  int 
(returns)  double 
x  long 
(returns)  double 
x  float 
(returns)  double 
x  double 
(returns)  double 
Description: Cast x to a doubleprecision floating point number.
x  any enum A 
(returns)  array of boolean 
x  string 
dictionary  array of string 
outOfRange  boolean 
(returns)  array of boolean 
x  int 
minimum  int 
maximum  int 
outOfRange  boolean 
(returns)  array of boolean 
Description: Fanout x to an array of booleans, all false except the matching value.
Parameters:
x  Categorical datum 
dictionary  Possible values of x, which is needed if x is an arbitrary string. 
minimum  Inclusive minimum value of x. 
maximum  Excluded maximum value of x. 
outOfRange  If true, include an extra item in the output to represent values of x that are outside of the specified range. 
Runtime Errors:
x  any enum A 
(returns)  array of int 
x  string 
dictionary  array of string 
outOfRange  boolean 
(returns)  array of int 
x  int 
minimum  int 
maximum  int 
outOfRange  boolean 
(returns)  array of int 
Description: Fanout x to an array of booleans, all false except the matching value.
Parameters:
x  Categorical datum 
dictionary  Possible values of x, which is needed if x is an arbitrary string. 
minimum  Inclusive minimum value of x. 
maximum  Excluded maximum value of x. 
outOfRange  If true, include an extra item in the output to represent values of x that are outside of the specified range. 
Runtime Errors:
x  any enum A 
(returns)  array of long 
x  string 
dictionary  array of string 
outOfRange  boolean 
(returns)  array of long 
x  int 
minimum  int 
maximum  int 
outOfRange  boolean 
(returns)  array of long 
Description: Fanout x to an array of booleans, all false except the matching value.
Parameters:
x  Categorical datum 
dictionary  Possible values of x, which is needed if x is an arbitrary string. 
minimum  Inclusive minimum value of x. 
maximum  Excluded maximum value of x. 
outOfRange  If true, include an extra item in the output to represent values of x that are outside of the specified range. 
Runtime Errors:
x  any enum A 
(returns)  array of float 
x  string 
dictionary  array of string 
outOfRange  boolean 
(returns)  array of float 
x  int 
minimum  int 
maximum  int 
outOfRange  boolean 
(returns)  array of float 
Description: Fanout x to an array of booleans, all false except the matching value.
Parameters:
x  Categorical datum 
dictionary  Possible values of x, which is needed if x is an arbitrary string. 
minimum  Inclusive minimum value of x. 
maximum  Excluded maximum value of x. 
outOfRange  If true, include an extra item in the output to represent values of x that are outside of the specified range. 
Runtime Errors:
x  any enum A 
(returns)  array of double 
x  string 
dictionary  array of string 
outOfRange  boolean 
(returns)  array of double 
x  int 
minimum  int 
maximum  int 
outOfRange  boolean 
(returns)  array of double 
Description: Fanout x to an array of booleans, all false except the matching value.
Parameters:
x  Categorical datum 
dictionary  Possible values of x, which is needed if x is an arbitrary string. 
minimum  Inclusive minimum value of x. 
maximum  Excluded maximum value of x. 
outOfRange  If true, include an extra item in the output to represent values of x that are outside of the specified range. 
Runtime Errors:
x  any A 
(returns)  bytes 
Description: Encode an arbitrary object as Avro bytes.
Details:
x  any A 
(returns)  string 
Description: Encode an arbitrary object as a JSON string.
Details:
a  array of any A 
(returns)  int 
Description: Return the length of array a.
a  array of any A 
start  int 
end  int 
(returns)  array of A 
Description: Return the subsequence of a from start (inclusive) until end (exclusive).
Details:
a  array of any A 
(returns)  A 
Description: Return the first item of the array.
Runtime Errors:
a  array of any A 
(returns)  array of A 
Description: Return all but the first item of the array.
Runtime Errors:
a  array of any A 
(returns)  A 
Description: Return the last item of the array.
Runtime Errors:
a  array of any A 
(returns)  array of A 
Description: Return all but the last item of the array.
Runtime Errors:
a  array of any A 
start  int 
end  int 
replacement  array of A 
(returns)  array of A 
Description: Return a new array by replacing a from start (inclusive) until end (exclusive) with replacement.
Details:
haystack  array of any A 
needle  array of A 
(returns)  boolean 
haystack  array of any A 
needle  A 
(returns)  boolean 
haystack  array of any A 
needle  function of (A) → boolean 
(returns)  boolean 
Description: Return true if haystack contains needle or the needle function evaluates to true, false otherwise.
haystack  array of any A 
needle  array of A 
(returns)  int 
haystack  array of any A 
needle  A 
(returns)  int 
haystack  array of any A 
needle  function of (A) → boolean 
(returns)  int 
Description: Count the number of times needle appears in haystack or the number of times the needle function evaluates to true.
Details:
haystack  array of any A 
needle  array of A 
(returns)  int 
haystack  array of any A 
needle  A 
(returns)  int 
haystack  array of any A 
needle  function of (A) → boolean 
(returns)  int 
Description: Return the lowest index where haystack contains needle or the needle function evaluates to true, \(1\) if there is no such element.
haystack  array of any A 
needle  array of A 
(returns)  int 
haystack  array of any A 
needle  A 
(returns)  int 
haystack  array of any A 
needle  function of (A) → boolean 
(returns)  int 
Description: Return the highest index where haystack contains needle or the needle function evaluates to true, \(1\) if there is no such element.
haystack  array of any A 
needle  array of A 
(returns)  boolean 
haystack  array of any A 
needle  A 
(returns)  boolean 
Description: Return true if the first (leftmost) subseqence of haystack is equal to needle, false otherwise.
haystack  array of any A 
needle  array of A 
(returns)  boolean 
haystack  array of any A 
needle  A 
(returns)  boolean 
Description: Return true if the last (rightmost) subseqence of haystack is equal to needle, false otherwise.
a  array of any A 
b  array of A 
(returns)  array of A 
Description: Concatenate a and b to make a new array of the same type.
Details:
a  array of any A 
item  A 
(returns)  array of A 
Description: Return a new array by adding item at the end of a.
Details:
a  array of any A 
item  A 
maxLength  int 
(returns)  array of A 
Description: Return a new array by adding item at the end of a, but keep the length less than or equal to maxLength by removing items from the beginning.
Details:
Runtime Errors:
a  array of any A 
index  int 
item  A 
(returns)  array of A 
Description: Return a new array by inserting item at index of a.
Details:
Runtime Errors:
a  array of any A 
index  int 
item  A 
(returns)  array of A 
Description: Return a new array by replacing index of a with item.
Details:
Runtime Errors:
a  array of any A 
start  int 
end  int 
(returns)  array of A 
a  array of any A 
index  int 
(returns)  array of A 
Description: Return a new array by removing elements from a from start (inclusive) until end (exclusive) or just a single index.
Details:
Runtime Errors:
a  array of any A 
steps  int 
(returns)  array of A 
Description: Return an array formed by rotating a left steps spaces.
Runtime Errors:
a  array of any A 
(returns)  array of A 
Description: Return an array with the same elements as a but in ascending order (as defined by Avro's sort order).
Details:
a  array of any A 
lessThan  function of (A, A) → boolean 
(returns)  array of A 
Description: Return an array with the same elements as a but in ascending order as defined by the lessThan function.
Details:
a  array of any A 
(returns)  array of A 
Description: Return an array with the same elements as a but in a random order.
Details:
a  array of any A 
(returns)  array of A 
Description: Return the elements of a in reversed order.
a  array of any A 
(returns)  A 
Description: Return the maximum value in a (as defined by Avro's sort order).
Runtime Errors:
a  array of any A 
(returns)  A 
Description: Return the minimum value in a (as defined by Avro's sort order).
Runtime Errors:
a  array of any A 
lessThan  function of (A, A) → boolean 
(returns)  A 
Description: Return the maximum value in a as defined by the lessThan function.
Runtime Errors:
a  array of any A 
lessThan  function of (A, A) → boolean 
(returns)  A 
Description: Return the minimum value in a as defined by the lessThan function.
Runtime Errors:
a  array of any A 
n  int 
(returns)  array of A 
Description: Return the n highest values in a (as defined by Avro's sort order).
Runtime Errors:
a  array of any A 
n  int 
(returns)  array of A 
Description: Return the n lowest values in a (as defined by Avro's sort order).
Runtime Errors:
a  array of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of A 
Description: Return the n highest values in a as defined by the lessThan function.
Runtime Errors:
a  array of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of A 
Description: Return the n lowest values in a as defined by the lessThan function.
Runtime Errors:
a  array of any A 
(returns)  int 
Description: Return the index of the maximum value in a (as defined by Avro's sort order).
Details:
Runtime Errors:
a  array of any A 
(returns)  int 
Description: Return the index of the minimum value in a (as defined by Avro's sort order).
Details:
Runtime Errors:
a  array of any A 
lessThan  function of (A, A) → boolean 
(returns)  int 
Description: Return the index of the maximum value in a as defined by the lessThan function.
Details:
Runtime Errors:
a  array of any A 
lessThan  function of (A, A) → boolean 
(returns)  int 
Description: Return the index of the minimum value in a as defined by the lessThan function.
Details:
Runtime Errors:
a  array of any A 
n  int 
(returns)  array of int 
Description: Return the indexes of the n highest values in a (as defined by Avro's sort order).
Details:
Runtime Errors:
a  array of any A 
n  int 
(returns)  array of int 
Description: Return the indexes of the n lowest values in a (as defined by Avro's sort order).
Details:
Runtime Errors:
a  array of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of int 
Description: Return the indexes of the n highest values in a as defined by the lessThan function.
Details:
Runtime Errors:
a  array of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of int 
Description: Return the indexes of the n lowest values in a as defined by the lessThan function.
Details:
Runtime Errors:
a  array of any A of {int, long, float, double} 
(returns)  A 
Description: Return the sum of numbers in a.
Details:
Runtime Errors:
a  array of any A of {int, long, float, double} 
(returns)  A 
Description: Return the product of numbers in a.
Details:
Runtime Errors:
a  array of double 
(returns)  double 
Description: Return the sum of the natural logarithm of numbers in a.
Details:
a  array of double 
(returns)  double 
Description: Return the arithmetic mean of numbers in a.
Details:
a  array of double 
(returns)  double 
Description: Return the geometric mean of numbers in a.
Details:
a  array of any A 
(returns)  A 
Description: Return the value that is in the center of a sorted version of a.
Details:
Runtime Errors:
a  array of any A 
p  double 
(returns)  A 
Description: Return the value that is at the "ntile" of a (like a percentile).
Parameters:
a  Array of objects to be take the percentile of. 
p  A double between 0 and 1. 
Details:
Runtime Errors:
a  array of any A 
(returns)  A 
Description: Return the mode (most common) value of a.
Details:
Runtime Errors:
a  array of double 
(returns)  double 
Description: Compute \(z = \\log(\\sum_{n = 1}^{N} e^{x_n})\) in a numerically stable way.
Details:
a  array of any A 
(returns)  array of A 
Description: Return an array with the same contents as a but with duplicates removed.
Details:
a  array of any A 
b  array of A 
(returns)  boolean 
Description: Return true if a and b are equivalent, ignoring order and duplicates, false otherwise.
a  array of any A 
b  array of A 
(returns)  array of A 
Description: Return an array that represents the union of a and b, treated as sets (ignoring order and duplicates).
Details:
a  array of any A 
b  array of A 
(returns)  array of A 
Description: Return an array that represents the intersection of a and b, treated as sets (ignoring order and duplicates).
Details:
a  array of any A 
b  array of A 
(returns)  array of A 
Description: Return an array that represents the difference of a and b, treated as sets (ignoring order and duplicates).
Details:
a  array of any A 
b  array of A 
(returns)  array of A 
Description: Return an array that represents the symmetric difference of a and b, treated as sets (ignoring order and duplicates).
Details:
little  array of any A 
big  array of A 
(returns)  boolean 
Description: Return true if little is a subset of big, false otherwise.
a  array of any A 
b  array of A 
(returns)  boolean 
Description: Return true if a and b are disjoint, false otherwise.
a  array of any A 
fcn  function of (A) → any B 
(returns)  array of B 
Description: Apply fcn to each element of a and return an array of the results.
Details:
a  array of any A 
fcn  function of (int, A) → any B 
(returns)  array of B 
Description: Apply fcn to index, element pairs from a and return an array of the results.
Details:
a  array of any A 
fcn  function of (A) → boolean 
(returns)  array of A 
Description: Apply fcn to each element of a and return an array of the elements for which fcn returns true.
Details:
a  array of any A 
fcn  function of (int, A) → boolean 
(returns)  array of A 
Description: Apply fcn to each index, element pair of a and return an array of the elements for which fcn returns true.
Details:
a  array of any A 
fcn  function of (A) → union of {any B, null} 
(returns)  array of B 
Description: Apply fcn to each element of a and return an array of the results that are not null.
Details:
a  array of any A 
fcn  function of (int, A) → union of {any B, null} 
(returns)  array of B 
Description: Apply fcn to each index, element pair of a and return an array of the results that are not null.
Details:
a  array of any A 
fcn  function of (A) → array of any B 
(returns)  array of B 
Description: Apply fcn to each element of a and flatten the resulting arrays into a single array.
Details:
a  array of any A 
fcn  function of (int, A) → array of any B 
(returns)  array of B 
Description: Apply fcn to each index, element pair of a and flatten the resulting arrays into a single array.
Details:
a  array of any A 
b  array of any B 
fcn  function of (A, B) → any Z 
(returns)  array of Z 
a  array of any A 
b  array of any B 
c  array of any C 
fcn  function of (A, B, C) → any Z 
(returns)  array of Z 
a  array of any A 
b  array of any B 
c  array of any C 
d  array of any D 
fcn  function of (A, B, C, D) → any Z 
(returns)  array of Z 
Description: Apply fcn to the elements of a, b, c, d in lockstep and return a result for row.
Runtime Errors:
a  array of any A 
b  array of any B 
fcn  function of (int, A, B) → any Z 
(returns)  array of Z 
a  array of any A 
b  array of any B 
c  array of any C 
fcn  function of (int, A, B, C) → any Z 
(returns)  array of Z 
a  array of any A 
b  array of any B 
c  array of any C 
d  array of any D 
fcn  function of (int, A, B, C, D) → any Z 
(returns)  array of Z 
Description: Apply fcn to the indexes and elements of a, b, c, d in lockstep and return a result for row.
Runtime Errors:
a  array of any A 
fcn  function of (A, A) → A 
(returns)  A 
Description: Apply fcn to each element of a and accumulate a tally.
Details:
Runtime Errors:
a  array of any A 
fcn  function of (A, A) → A 
(returns)  A 
Description: Apply fcn to each element of a and accumulate a tally.
Details:
Runtime Errors:
a  array of any A 
zero  any B 
fcn  function of (B, A) → B 
(returns)  B 
Description: Apply fcn to each element of a and accumulate a tally, starting with zero.
Details:
a  array of any A 
zero  any B 
fcn  function of (A, B) → B 
(returns)  B 
Description: Apply fcn to each element of a and accumulate a tally, starting with zero.
Details:
a  array of any A 
fcn  function of (A) → boolean 
(returns)  array of A 
Description: Apply fcn to elements of a and create an array of the longest prefix that returns true, stopping with the first false.
Details:
a  array of any A 
fcn  function of (A) → boolean 
(returns)  array of A 
Description: Apply fcn to elements of a and create an array of all elements after the longest prefix that returns true.
Details:
a  array of any A 
fcn  function of (A) → boolean 
(returns)  boolean 
Description: Return true if fcn is true for any element in a (logical or).
Details:
a  array of any A 
fcn  function of (A) → boolean 
(returns)  boolean 
Description: Return true if fcn is true for all elements in a (logical and).
Details:
a  array of any A 
b  array of any B 
fcn  function of (A, B) → boolean 
(returns)  boolean 
Description: Return true if fcn is true when applied to all pairs of elements, one from a and the other from b (logical relation).
Details:
a  array of any A 
b  array of any B 
fcn  function of (int, A, B) → boolean 
(returns)  boolean 
Description: Return true if fcn is true when applied to all triples of index, element from a, element from b (logical relation).
Details:
a  array of any A 
size  int 
step  int 
(returns)  array of array of A 
Description: Return an array of subsequences of a with length size that slide through a in steps of length step from left to right.
Runtime Errors:
a  array of any A 
size  int 
(returns)  array of array of A 
Description: Return all combinations of elements of a with length size.
Runtime Errors:
a  array of any A 
(returns)  array of array of A 
Description: Return all permutations of elements of a.
Details:
a  array of array of any A 
(returns)  array of A 
Description: Concatenate the arrays in a.
a  array of any A 
fcn  function of (A) → string 
(returns)  map of array of A 
Description: Groups elements of a by the string that fcn maps them to.
m  map of any A 
(returns)  int 
Description: Return the length of a map.
m  map of any A 
(returns)  array of string 
Description: Return the keys of a map (in no particular order).
Details:
m  map of any A 
(returns)  array of A 
Description: Return the values of a map (in no particular order).
Details:
m  map of any A 
key  string 
(returns)  boolean 
m  map of any A 
fcn  function of (string) → boolean 
(returns)  boolean 
Description: Return true if the keys of m contains key or fcn evaluates to true for some key of m, false otherwise.
m  map of any A 
value  A 
(returns)  boolean 
m  map of any A 
fcn  function of (A) → boolean 
(returns)  boolean 
Description: Return true if the values of m contains value or fcn evaluates to true for some key of m, false otherwise.
m  map of any A 
key  string 
value  A 
(returns)  map of A 
m  map of any A 
item  A 
(returns)  map of A 
Description: Return a new map by adding the key value pair to m or a new set by adding the item to set m, where a set is represented as a map from serialized objects to objects.
Details:
m  map of any A 
key  string 
(returns)  map of A 
Description: Return a new map by removing key from m.
Details:
m  map of any A 
keys  array of string 
(returns)  map of A 
Description: Return a new map, keeping only keys from m.
Details:
m  map of any A 
keys  array of string 
(returns)  map of A 
Description: Return a new map, keeping all but keys from m.
Details:
base  map of any A 
overlay  map of A 
(returns)  map of A 
Description: Return a new map with keyvalue pairs from overlay in place of or in addition to keyvalue pairs from base.
Details:
m  map of any A 
(returns)  array of map of A 
Description: Split the map into an array of maps, each containing only one keyvalue pair (in no particular order).
Details:
a  array of map of any A 
(returns)  map of A 
Description: Join an array of maps into one map, overlaying from left to right.
m  map of any A 
(returns)  string 
Description: Return the key of the highest value in m (as defined by Avro's sort order).
Details:
Runtime Errors:
m  map of any A 
(returns)  string 
Description: Return the key of the lowest value in m (as defined by Avro's sort order).
Details:
Runtime Errors:
m  map of any A 
lessThan  function of (A, A) → boolean 
(returns)  string 
Description: Return the key of the highest value in m as defined by the lessThan function.
Details:
Runtime Errors:
m  map of any A 
lessThan  function of (A, A) → boolean 
(returns)  string 
Description: Return the key of the lowest value in m as defined by the lessThan function.
Details:
Runtime Errors:
m  map of any A 
n  int 
(returns)  array of string 
Description: Return the keys of the n highest values in m (as defined by Avro's sort order).
Details:
Runtime Errors:
m  map of any A 
n  int 
(returns)  array of string 
Description: Return the keys of the n lowest values in m (as defined by Avro's sort order).
Details:
Runtime Errors:
m  map of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of string 
Description: Return the keys of the n highest values in a as defined by the lessThan function.
Details:
Runtime Errors:
m  map of any A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of string 
Description: Return the keys of the n highest values in a as defined by the lessThan function.
Details:
Runtime Errors:
a  array of any A 
(returns)  map of A 
Description: Convert an array of objects into a set of objects, where a set is represented as a map from serialized objects to objects.
Details:
s  map of any A 
(returns)  array of A 
Description: Convert a set of objects into an array of objects (in no particular order), where a set is represented as a map from serialized objects to objects.
Details:
s  map of any A 
x  A 
(returns)  boolean 
Description: Return true if x is contained in set s, false otherwise, where a set is represented as a map from serialized objects to objects.
Details:
a  map of any A 
b  map of A 
(returns)  map of A 
Description: Return the union of sets a and b, where a set is represented as a map from serialized objects to objects.
Details:
a  map of any A 
b  map of A 
(returns)  map of A 
Description: Return the intersection of sets a and b, where a set is represented as a map from serialized objects to objects.
Details:
a  map of any A 
b  map of A 
(returns)  map of A 
Description: Return the difference of sets a and b, where a set is represented as a map from serialized objects to objects.
Details:
a  map of any A 
b  map of A 
(returns)  map of A 
Description: Return the difference of sets a and b, where a set is represented as a map from serialized objects to objects.
Details:
little  map of any A 
big  map of A 
(returns)  boolean 
Description: Return true if set little is a subset of set big, false otherwise, where a set is represented as a map from serialized objects to objects.
Details:
a  map of any A 
b  map of A 
(returns)  boolean 
Description: Return true if set a and set b are disjoint, false otherwise, where a set is represented as a map from serialized objects to objects.
Details:
m  map of any A 
fcn  function of (A) → any B 
(returns)  map of B 
Description: Apply fcn to each value of m and return a map of transformed values (keys are unchanged).
Details:
m  map of any A 
fcn  function of (string, A) → any B 
(returns)  map of B 
Description: Apply fcn to each key, value pair of m and return a map of transformed values (keys are unchanged).
Details:
m  map of any A 
fcn  function of (A) → boolean 
(returns)  map of A 
Description: Apply fcn to each value of m and return a map of the values for which fcn returns true (keys are unchanged).
Details:
m  map of any A 
fcn  function of (string, A) → boolean 
(returns)  map of A 
Description: Apply fcn to each value of m and return a map of the values for which fcn returns true (keys are unchanged).
Details:
m  map of any A 
fcn  function of (A) → union of {any B, null} 
(returns)  map of B 
Description: Apply fcn to each value of m and return a map of the results that are not null.
Details:
m  map of any A 
fcn  function of (string, A) → union of {any B, null} 
(returns)  map of B 
Description: Apply fcn to each keyvalue pair of m and return a map of the results that are not null.
Details:
m  map of any A 
fcn  function of (A) → map of any B 
(returns)  map of B 
Description: Apply fcn to each value of m and return a map of overlaid results.
Details:
m  map of any A 
fcn  function of (string, A) → map of any B 
(returns)  map of B 
Description: Apply fcn to each keyvalue pair of m and return a map of overlaid results.
Details:
a  map of any A 
b  map of any B 
fcn  function of (A, B) → any Z 
(returns)  map of Z 
a  map of any A 
b  map of any B 
c  map of any C 
fcn  function of (A, B, C) → any Z 
(returns)  map of Z 
a  map of any A 
b  map of any B 
c  map of any C 
d  map of any D 
fcn  function of (A, B, C, D) → any Z 
(returns)  map of Z 
Description: Apply fcn to the elements of a, b, c, d in lockstep and return a result for row.
Runtime Errors:
a  map of any A 
b  map of any B 
fcn  function of (string, A, B) → any Z 
(returns)  map of Z 
a  map of any A 
b  map of any B 
c  map of any C 
fcn  function of (string, A, B, C) → any Z 
(returns)  map of Z 
a  map of any A 
b  map of any B 
c  map of any C 
d  map of any D 
fcn  function of (string, A, B, C, D) → any Z 
(returns)  map of Z 
Description: Apply fcn to the keys and elements of a, b, c, d in lockstep and return a result for row.
Runtime Errors:
a  map of any A 
b  map of any B 
fcn  function of (A, B) → boolean 
(returns)  boolean 
Description: Return true if fcn is true when applied to all pairs of values, one from a and the other from b (logical relation).
Details:
a  map of any A 
b  map of any B 
fcn  function of (string, A, B) → boolean 
(returns)  boolean 
Description: Return true if fcn is true when applied to all triples of key, value from a, value from b (logical relation).
Details:
x  bytes 
(returns)  int 
Description: Return the length of byte array x.
x  bytes 
start  int 
end  int 
(returns)  bytes 
Description: Return the subsequence of x from start (inclusive) until end (exclusive).
Details:
x  bytes 
start  int 
end  int 
replacement  bytes 
(returns)  bytes 
Description: Replace x from start (inclusive) until end (exclusive) with replacement.
Details:
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid ASCII; false otherwise.
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid latin1 (ISO88591); false otherwise.
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid utf8; false otherwise.
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid utf16 (byte order identified by optional byteorder mark); false otherwise.
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid big endian utf16; false otherwise.
x  bytes 
(returns)  boolean 
x  string 
(returns)  boolean 
Description: Returns true if x is valid little endian utf16; false otherwise.
x  bytes 
(returns)  string 
Description: Decode a bytes object as an ASCII string.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Decode a bytes object as a latin1 (ISO88591) string.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Decode a bytes object as a utf8 string.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Decode a bytes object as a utf16 (byte order identified by optional byteorder mark) string.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Decode a bytes object as a big endian utf16 string.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Decode a bytes object as a little endian utf16 string.
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as ASCII bytes.
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as latin1 (ISO88591) bytes.
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as utf8 bytes.
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as utf16 (byte order identified by optional byteorder mark) bytes.
Details:
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as big endian utf16 bytes.
Runtime Errors:
s  string 
(returns)  bytes 
Description: Encode a string as little endian utf16 bytes.
Runtime Errors:
x  bytes 
(returns)  string 
Description: Convert an arbitrary bytes object to a base64encoded string.
s  string 
(returns)  bytes 
Description: Convert a base64encoded string to a bytes object.
Runtime Errors:
x  any fixed A 
(returns)  bytes 
Description: Convert fixedlength, named bytes into arbitrarylength, anonymous bytes.
original  any fixed A 
replacement  bytes 
(returns)  A 
Description: Overlay replacement on top of original.
Details:
x  any enum A 
(returns)  string 
Description: Return the string representation of an enum.
x  any enum A 
(returns)  int 
Description: Return the integer representation of an enum.
x  any enum A 
(returns)  int 
Description: Return the number of symbols associated with this enum (a constant).
ts  double 
zone  string 
(returns)  int 
Description: Get the fourdigit year that the timestamp falls within.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the month that the timestamp falls within, with 1 being January and 12 being December.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the day of the year that the timestamp falls within, from 1 to 365 or 366 inclusive, depending on leap year.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the day of the month that the timestamp falls within, a number from 1 to 28, 29, 30, or 31, inclusive, depending on month.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the day of the week that the timestamp falls within, with 0 being Monday and 6 being Sunday.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the hour of the day that the timestamp falls within, from 0 to 23 inclusive.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the minute of the hour that the timestamp falls within, from 0 to 59 inclusive.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  int 
Description: Get the second of the minute that the timestamp falls within, from 0 to 59 inclusive.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
year  int 
month  int 
day  int 
hour  int 
minute  int 
second  int 
millisecond  int 
zone  string 
(returns)  double 
Description: Given the date and time that this time occurs in, return the timestamp.
Parameters:
year  The fourdigit year, from 1 to 9999 inclusive. 
month  The month of the year, from 1 to 12 inclusive. 
day  The day of the month, from 1 to 28, 29, 30, or 31 inclusive, depending on month. 
hour  The hour of the day, from 0 to 23 inclusive. 
minute  The minute of the hour, from 0 to 59 inclusive. 
second  The second of the minute, from 0 to 59 inclusive. 
millisecond  The millisecond of the second, from 0 to 999 inclusive. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Returns:
The number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified number of seconds in any minute.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum number of seconds (inclusive). 
high  Maximum number of seconds (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified number of minutes in any hour.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum number of minutes (inclusive) 
high  Maximum number of minutes (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified number of hours in any day.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum number of hours (inclusive). 
high  Maximum number of hours (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified day of week range, with 0 being Monday and 6 being Sunday.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum day of the week (inclusive). 
high  Maximum day of the week (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified day of month range, with 1 being the first of the month..
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum day of the month (inclusive). 
high  Maximum day of the month (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified month of year range, with 1 being January and 12 being December.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum month of the year (inclusive). 
high  Maximum month of the year (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
low  double 
high  double 
(returns)  boolean 
Description: Determines if a timestamp falls within a specified day of year range, with 1 being the first of the year.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
low  Minimum day of year (inclusive). 
high  Maximum day of year (exclusive). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  boolean 
Description: Returns true if the timestamp falls on a Saturday or Sunday, false otherwise.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
ts  double 
zone  string 
(returns)  boolean 
Description: Returns true if the timestamp falls between 9 am (inclusive) and 5 pm (exclusive) on Monday through Friday, otherwise false.
Parameters:
ts  Number of seconds since the beginning (just after midnight) of Jan 1, 1970 C.E. in UTC. 
zone  Timezone name from the Olson timezone database, version 2015f (UTC if blank). 
Details:
Runtime Errors:
x  union of {any A, null} 
(returns)  A 
Description: Skip an action by raising a runtime error when x is null.
Runtime Errors:
x  union of {any A, null} 
default  A 
(returns)  A 
Description: Replace null values in x with default.
x  float 
(returns)  boolean 
x  double 
(returns)  boolean 
Description: Return true if x is nan, false otherwise.
x  float 
(returns)  boolean 
x  double 
(returns)  boolean 
Description: Return true if x is positive or negative infinity, false otherwise.
x  float 
(returns)  boolean 
x  double 
(returns)  boolean 
Description: Return true if x is neither nan nor infinite, false otherwise.
x  float 
(returns)  float 
x  double 
(returns)  double 
Description: Pass through x if it is neither nan nor infinite, but raise an error otherwise.
Runtime Errors:
x  float 
default  float 
(returns)  float 
x  double 
default  double 
(returns)  double 
Description: Pass through x if it is neither nan nor infinite, and return default otherwise.
x  double 
numbins  int 
low  double 
high  double 
(returns)  int 
x  double 
origin  double 
width  double 
(returns)  int 
Description: Finds the bin that contains x, declared either as numbins between two endpoints or a bin width starting at some origin.
Details:
Runtime Errors:
x  double 
table  array of any record R with fields {x: double, to: any T} 
(returns)  T 
x  array of double 
table  array of any record R with fields {x: array of double, to: any T} 
(returns)  T 
x  any X1 
table  array of any record R with fields {x: any X2, to: any T} 
metric  function of (X1, X2) → double 
(returns)  T 
Description: Finds the closest x value in the table to the input x and returns the corresponding to value.
Details:
Runtime Errors:
x  double 
table  array of any record R with fields {x: double, to: double} 
(returns)  double 
x  double 
table  array of any record R with fields {x: double, to: array of double} 
(returns)  array of double 
Description: Finds the closest x values in the table that are below and above the input x and linearly projects their to values to the input x.
Details:
Runtime Errors:
x  double 
table  array of any record R with fields {x: double, to: double} 
(returns)  double 
x  double 
table  array of any record R with fields {x: double, to: array of double} 
(returns)  array of double 
Description: Like interp.linear, but returns the closest entry's to if the input x is beyond the table.
Details:
Runtime Errors:
x  double 
table  array of any record R with fields {x: double, to: double} 
(returns)  union of {null, double} 
x  double 
table  array of any record R with fields {x: double, to: array of double} 
(returns)  union of {null, array of double} 
Description: Like interp.linear, but returns a missing value (null) if the input x is beyond the table.
Details:
Runtime Errors:
x  double 
mu  double 
sigma  double 
(returns)  double 
x  double 
params  any record A with fields {mean: double, variance: double} 
(returns)  double 
Description: Compute the loglikelihood of a Gaussian (normal) distribution parameterized by mu and sigma or a record params.
Parameters:
x  Value at which to compute the loglikelihood. 
mu  Centroid of the distribution (same as mean). 
sigma  Width of the distribution (same as the square root of variance). 
params  Alternate way of specifying the parameters of the distribution; this record could be created by stat.sample.update. 
Returns:
With \(\mu\) = mu or mean and \(\sigma\) = sigma or the square root of variance, this function returns \((x  \mu)^2/(2 \sigma^2)  \log(\sigma \sqrt{2\pi})\). 
Runtime Errors:
x  double 
mu  double 
sigma  double 
(returns)  double 
x  double 
params  any record A with fields {mean: double, variance: double} 
(returns)  double 
Description: Compute the cumultive distribution function (CDF) for the normal distribution, parameterized by mu and sigma or a record params.
Parameters:
x  Value at which to compute the CDF. 
mu  Centroid of the distribution (same as mean). 
sigma  Width of the distribution (same as the square root of variance). 
params  Alternate way of specifying the parameters of the distribution; this record could be created by stat.sample.update. 
Returns:
With \(\mu\) = mu or mean and \(\sigma\) = sigma or the square root of variance, this function returns \(0.5 * ( 1.0 + \mathrm{Erf}(\frac{x  \mu}{\sigma \sqrt{2}}))\). 
Runtime Errors:
p  double 
mu  double 
sigma  double 
(returns)  double 
p  double 
params  any record A with fields {mean: double, variance: double} 
(returns)  double 
Description: Compute the normal quantile (QF, the inverse of the CDF) parameterized by mu and sigma or a record params.
Parameters:
p  Probability at which to compute the QF. Must be a value between 0 and 1. 
mu  Centroid of the distribution (same as mean). 
sigma  Width of the distribution (same as the square root of variance). 
params  Alternate way of specifying the parameters of the distribution; this record could be created by stat.sample.update. 
Returns:
With \(\mu\) = mu or mean and \(\sigma\) = sigma or the square root of variance, this function returns \(\mu + \sigma \sqrt{2} \mathrm{Erf}^{1} (2p  1)\). 
Runtime Errors:
x  double 
lambda  double 
(returns)  double 
Description: Compute the density (PDF) of the exponential distribution parameterized by lambda.
Parameters:
x  Value at which to compute the PDF. 
lambda  Rate parameter. 
Returns:
With \(lambda\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\lambda \mathrm{e}^{ \lambda x}\). 
Runtime Errors:
x  double 
lambda  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the exponential distribution parameterized by lambda.
Parameters:
x  Value at which to compute the CDF. 
lambda  Rate parameter. 
Returns:
With \(lambda\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
lambda  double 
(returns)  double 
Description: Compute the quantile function (QF) of the exponential distribution parameterized by lambda.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
lambda  Rate parameter. 
Returns:
With \(lambda\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X~\leq~x)~=~p\). 
Runtime Errors:
x  double 
dof  int 
(returns)  double 
Description: Compute the density (PDF) of the Chisquared distribution parameterized by its degrees of freedom dof.
Parameters:
x  Value at which to compute the PDF. 
dof  Degrees of freedom parameter. 
Returns:
With \(dof\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{1}{2^{\frac{\mathrm{df}}{2}} \Gamma(\frac{\mathrm{df}}{2})} x^{\frac{\mathrm{df}}{2}1}\mathrm{e}^{\frac{x}{2}}\). 
Runtime Errors:
x  double 
dof  int 
(returns)  double 
Description: Compute the distribution function (CDF) of the Chisquared distribution parameterized by its degrees of freedom dof.
Parameters:
x  Value at which to compute the CDF. 
dof  Degrees of freedom parameter. 
Returns:
With \(x1\), \(x1\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
dof  int 
(returns)  double 
Description: Compute the quantile function (QF) of the Chisquared distribution parameterized by its degrees of freedom dof.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
dof  Degrees of freedom parameter. 
Returns:
With \(x1\), \(x1\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  int 
lambda  double 
(returns)  double 
Description: Compute the density (PDF) of the poisson distribution parameterized by lambda.
Parameters:
x  Value at which to compute the PDF. 
lambda  Mean and variance parameter. 
Returns:
With \(lambda\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\lambda^{x}}{x!} \mathrm{e}^{\lambda}\). 
Runtime Errors:
x  int 
lambda  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the poisson distribution parameterized by lambda.
Parameters:
x  Value at which to compute the CDF. 
lambda  Mean and variance parameter. 
Returns:
With \(lambda\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
lambda  double 
(returns)  double 
Description: Compute the quantile function (QF) of the poisson distribution parameterized by lambda.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
lambda  Mean and variance parameter. 
Returns:
With \(lambda\), \(lambda\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the density (PDF) of the gamma distribution parameterized by shape and scale.
Parameters:
x  Value at which to compute the PDF. 
shape  Shape parameter (a). 
scale  Scale parameter (s). 
Returns:
With \(shape\), \(scale\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{1}{s^{a} \Gamma(a)} x^{a  1} \mathrm{e}^{\frac{x}{s}} \). 
Runtime Errors:
x  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the gamma distribution parameterized by shape and scale.
Parameters:
x  Value at which to compute the CDF. 
shape  Shape parameter. 
scale  Scale parameter. 
Returns:
With \(shape\), \(scale\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x)~= P(X~\leq~x)\). 
Runtime Errors:
p  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the quantile function (QF) of the gamma distribution parameterized by shape and scale.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
shape  Shape parameter. 
scale  Scale parameter. 
Returns:
With \(shape\), \(scale\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x)~:= P(X~\leq~x)~=~p\). 
Runtime Errors:
x  double 
a  double 
b  double 
(returns)  double 
Description: Compute the density (PDF) of the beta distribution parameterized by shape1 and shape2.
Parameters:
x  Value at which to compute the PDF, defined between zero and one. 
a  First shape parameter. 
b  Second shape parameter. 
Returns:
With \(a\), \(b\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\Gamma(a + n)}{\Gamma(a)\Gamma(b)} x^{a1}(1x)^{b1}\). 
Runtime Errors:
x  double 
a  double 
b  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the beta distribution parameterized by shape1 and shape2.
Parameters:
x  Value at which to compute the CDF. 
a  First shape parameter. 
b  Second shape parameter. 
Returns:
With \(a\), \(b\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
a  double 
b  double 
(returns)  double 
Description: Compute the quantile function (QF) of the beta distribution parameterized by shape1 and shape2.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
a  First shape parameter. 
b  Second shape parameter. 
Returns:
With \(a\), \(b\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  double 
location  double 
scale  double 
(returns)  double 
Description: Compute the density (PDF) of the cauchy distribution parameterized by location and scale.
Parameters:
x  Value at which to compute the PDF. 
location  Location parameter (l). 
scale  Scale parameter (s). 
Returns:
With \(location\), \(scale\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{1}{(\pi s (1 + (\frac{x  l}{s})^{2})) }\). 
Runtime Errors:
x  double 
location  double 
scale  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the cauchy distribution parameterized by location and scale.
Parameters:
x  Value at which to compute the CDF. 
location  Location parameter. 
scale  Scale parameter. 
Returns:
With \(location\), \(scale\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
location  double 
scale  double 
(returns)  double 
Description: Compute the quantile function (QF) of the cauchy distribution parameterized by location and scale.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
location  Location parameter. 
scale  Scale parameter. 
Returns:
With \(location\), \(scale\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  double 
d1  int 
d2  int 
(returns)  double 
Description: Compute the density (PDF) of the F distribution parameterized by d1 and d2.
Parameters:
x  Value at which to compute the PDF. 
d1  Numerator degrees of freedom parameter. 
d2  Denominator degrees of freedom parameter. 
Returns:
With \(d1\), \(d2\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\Gamma(\frac{d1 + d2}{2})}{\Gamma(\frac{d1}{2})\Gamma(\frac{d2}{2})} \frac{d1}{d2}^{\frac{d1}{2}1}(1 + \frac{d1}{d2} x)^{\frac{d1 + d2}{2}}\). 
Runtime Errors:
x  double 
d1  int 
d2  int 
(returns)  double 
Description: Compute the distribution function (CDF) of the F distribution parameterized by d1 and d2.
Parameters:
x  Value at which to compute the CDF. 
d1  Numerator degrees of freedom parameter. 
d2  Denominator degrees of freedom parameter. 
Returns:
With \(d1\), \(d2\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
d1  int 
d2  int 
(returns)  double 
Description: Compute the quantile function (QF) of the F distribution parameterized by d1 and d2.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
d1  Numerator degrees of freedom parameter. 
d2  Denominator degrees of freedom parameter. 
Returns:
With \(d1\), \(d2\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X~\leq~x)~=~p\). 
Runtime Errors:
x  double 
meanlog  double 
sdlog  double 
(returns)  double 
Description: Compute the density (PDF) of the lognormal distribution parameterized by meanlog and sdlog.
Parameters:
x  Value at which to compute the PDF. 
meanlog  Mean of the distribution on the log scale (\(\mu\)). 
sdlog  Standard deviation of the distribution on the log scale (\(\sigma\)). 
Returns:
With \(meanlog\), \(sdlog\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{1}{\sqrt{2 \pi} \sigma x} \mathrm{e}^{\frac{\mathrm{log}(x)  \mu}{2 \sigma^{2}}}\). 
Runtime Errors:
x  double 
meanlog  double 
sdlog  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the lognormal distribution parameterized by meanlog and sdlog.
Parameters:
x  Value at which to compute the CDF. 
meanlog  Mean of the distribution on the log scale. 
sdlog  Standard deviation of the distribution on the log scale. 
Returns:
With \(meanlog\), \(sdlog\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
meanlog  double 
sdlog  double 
(returns)  double 
Description: Compute the quantile function (QF) of the lognormal distribution parameterized by meanlog and sdlog.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
meanlog  Mean of the distribution on the log scale. 
sdlog  Standard deviation of the distribution on the log scale. 
Returns:
With \(meanlog\), \(sdlog\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  double 
dof  int 
(returns)  double 
Description: Compute the density (PDF) of the student's t distribution parameterized by dof and x2.
Parameters:
x  Value at which to compute the PDF. 
dof  Degrees of freedom parameter. 
Returns:
With \(dof\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\Gamma(\frac{\mathrm{df}+1}{2})}{\sqrt{\mathrm{df}\pi} \Gamma{\frac{\mathrm{df}}{2}}}(1 + x^{\frac{2}{n}})^{\frac{\mathrm{df} + 1}{2}}\). 
Runtime Errors:
x  double 
dof  int 
(returns)  double 
Description: Compute the distribution function (CDF) of the student's t distribution parameterized by dof and x2.
Parameters:
x  Value at which to compute the CDF. 
dof  Degrees of freedom parameter. 
Returns:
With \(dof\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
dof  int 
(returns)  double 
Description: Compute the quantile function (QF) of the student's t distribution parameterized by dof and x2.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
dof  Degrees of freedom parameter. 
Returns:
With \(dof\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  int 
size  int 
prob  double 
(returns)  double 
Description: Compute the density (PDF) of the binomial distribution parameterized by size and prob.
Parameters:
x  Value at which to compute the PDF. 
size  The number of trials (n). 
prob  The probability of success in each trial (p). 
Returns:
With \(size\), \(prob\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\mathrm{choose}(n, x) p^{x} (1  p)^{n  x}\). 
Runtime Errors:
x  double 
size  int 
prob  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the binomial distribution parameterized by size and prob.
Parameters:
x  Value at which to compute the CDF. 
size  The number of trials. 
prob  The probability of success in each trial. 
Returns:
With \(size\), \(prob\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
size  int 
prob  double 
(returns)  double 
Description: Compute the quantile function (QF) of the binomial distribution parameterized by size and prob.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
size  The number of trials. 
prob  The probability of success in each trial. 
Returns:
With \(size\), \(prob\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x)~:= P(X~\leq~x)~=~p\). 
Runtime Errors:
x  double 
min  double 
max  double 
(returns)  double 
Description: Compute the density (PDF) of the uniform distribution parameterized by min and max.
Parameters:
x  Value at which to compute the PDF. 
min  Lower bound. 
max  Upper bound. 
Returns:
With \(min\), \(max\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{1}{\mathrm{max}  \mathrm{min}}\). 
Runtime Errors:
x  double 
min  double 
max  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the uniform distribution parameterized by min and max.
Parameters:
x  Value at which to compute the CDF. 
min  Lower bound. 
max  Upper bound. 
Returns:
With \(min\), \(max\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
min  double 
max  double 
(returns)  double 
Description: Compute the quantile function (QF) of the uniform distribution parameterized by min and max.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
min  Lower bound. 
max  Upper bound. 
Returns:
With \(min\), \(max\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X~\leq~x)~=~p\). 
Runtime Errors:
x  int 
prob  double 
(returns)  double 
Description: Compute the density (PDF) of the geometric distribution parameterized by prob.
Parameters:
x  Value at which to compute the PDF. 
prob  Probability of success of each trial (p). 
Returns:
With \(prob\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(p (1  p)^{x}\). 
Runtime Errors:
x  double 
prob  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the geometric distribution parameterized by prob.
Parameters:
x  Value at which to compute the CDF. 
prob  Probability of success of each trial. 
Returns:
With \(prob\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
prob  double 
(returns)  double 
Description: Compute the quantile function (QF) of the geometric distribution parameterized by prob.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
prob  Probability of success of each trial. 
Returns:
With \(prob\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  int 
m  int 
n  int 
k  int 
(returns)  double 
Description: Compute the density (PDF) of the hypergeometric distribution parameterized by m, n and k.
Parameters:
x  The number of white balls drawn without replacement from the urn. 
m  The number of white balls in the urn. 
n  The number of black balls in the urn. 
k  The number of balls drawn from the urn. 
Returns:
With \(m\), \(n\) and \(k\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\mathrm{choose}(m, x) \mathrm{choose}(n, kx)}{\mathrm{choose}(m+n, k)} \). 
Runtime Errors:
x  int 
m  int 
n  int 
k  int 
(returns)  double 
Description: Compute the distribution function (CDF) of the hypergeometric distribution parameterized by m, n and k.
Parameters:
x  The number of white balls drawn without replacement. 
m  The number of white balls in the urn. 
n  The number of black balls in the urn. 
k  The number of balls drawn from the urn. 
Returns:
With \(m\), \(n\) and \(k\) at \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
m  int 
n  int 
k  int 
(returns)  double 
Description: Compute the quantile function (QF) of the hypergeometric distribution parameterized by m, n and k.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
m  The number of white balls in the urn. 
n  The number of black balls in the urn. 
k  The number of balls drawn from the urn. 
Returns:
With \(m\), \(n\) and \(k\) at \(p\), this function returns the value \(x\) such that \(F_{X}(x)~:= P(X~\leq~x)~=~p\). 
Runtime Errors:
x  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the density (PDF) of the weibull distribution parameterized by shape and scale.
Parameters:
x  Value at which to compute the PDF. 
shape  Shape parameter (a). 
scale  Scale parameter (b). 
Returns:
With \(shape\), \(scale\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{a}{b}(\frac{x}{b})^{a  1}\mathrm{e}^{(\frac{x}{b})^{a}}\). 
Runtime Errors:
x  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the weibull distribution parameterized by shape and scale.
Parameters:
x  Value at which to compute the CDF. 
shape  Shape parameter. 
scale  Scale parameter. 
Returns:
With \(shape\), \(scale\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X~\leq~x)\). 
Runtime Errors:
p  double 
shape  double 
scale  double 
(returns)  double 
Description: Compute the quantile function (QF) of the weibull distribution parameterized by shape and scale.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
shape  Shape parameter. 
scale  Scale parameter. 
Returns:
With \(shape\), \(scale\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X~\leq~x)~=~p\). 
Runtime Errors:
x  int 
size  int 
prob  double 
(returns)  double 
Description: Compute the density (PDF) of the negative binomial distribution parameterized by size and prob.
Parameters:
x  Value at which to compute the PDF (integer) . 
size  Size parameter (integer). Target number of successful trials (n). 
prob  Probability of success in each trial (p). 
Returns:
With \(size\), \(prob\) and \(x\), this function evaluates the probability density function at \(x\). The PDF implemented is \(\frac{\Gamma(x+n)}{\Gamma(n) x!} p^{n} (1p)^{x}\). 
Runtime Errors:
x  double 
size  int 
prob  double 
(returns)  double 
Description: Compute the distribution function (CDF) of the negative binomial distribution parameterized by size and prob.
Parameters:
x  Value at which to compute the CDF. 
size  Size parameter (integer). Target number of successful trials. 
prob  Probability of success in each trial. 
Returns:
With \(size\), \(prob\) and \(x\), this function returns the value \(p\) where \(p = F_{X}(x) = P(X \leq x)\). 
Runtime Errors:
p  double 
size  int 
prob  double 
(returns)  double 
Description: Compute the quantile function (QF) of the negative binomial distribution parameterized by size and prob.
Parameters:
p  Value at which to compute the QF. Must be a value between 0 and 1. 
size  Size parameter (integer). Target number of successful trials. 
prob  Probability of success in each trial. 
Returns:
With \(size\), \(prob\) and \(p\), this function returns the value \(x\) such that \(F_{X}(x) := P(X \leq x) = p\). 
Runtime Errors:
x  array of double 
y  array of double 
(returns)  double 
Description: Compare two datasets using the KolmogorovSmirnov test to determine if they might have been drawn from the same parent distribution.
Parameters:
x  A bag of data. 
y  Another bag of data. 
Returns:
Returns a value between 0.0 and 1.0 representing the cumulative probability that x and y were drawn from the same distribution: 1.0 indicates a perfect match. 
Details:
observation  double 
prediciton  double 
(returns)  double 
observation  array of double 
prediciton  array of double 
(returns)  array of double 
observation  map of double 
prediciton  map of double 
(returns)  map of double 
Description: Compare an observation with its prediction by elementwise subtraction.
Parameters:
observation  Scalar or vector of observations. 
prediction  Scalar or vector of predictions. 
Returns:
Scalar or vector of observation minus prediction. 
Runtime Errors:
observation  double 
prediciton  double 
uncertainty  double 
(returns)  double 
observation  array of double 
prediciton  array of double 
uncertainty  array of double 
(returns)  array of double 
observation  map of double 
prediciton  map of double 
uncertainty  map of double 
(returns)  map of double 
Description: Compare an observation with its prediction by elementwise subtraction, weighted by elementwise uncertainties.
Parameters:
observation  Scalar or vector of observations. 
prediction  Scalar or vector of predictions. 
uncertainty  Scalar or vector of predictions. 
Returns:
Scalar or vector of observation minus prediction divided by uncertainty. 
Runtime Errors:
observation  array of double 
prediction  array of double 
covariance  array of array of double 
(returns)  double 
observation  map of double 
prediction  map of double 
covariance  map of map of double 
(returns)  double 
Description: Compare an observation with its prediction by computing the Mahalanobis distance for a given covariance matrix.
Parameters:
observation  Vector of observations \(\vec{o}\). 
prediction  Vector of predictions \(\vec{p}\). 
covariance  Matrix of covariance \(C\). 
Returns:
Scalar result of a similarity transformation: \(\sqrt{(\vec{o}  \vec{p})^T C^{1} (\vec{o}  \vec{p})}\). 
Runtime Errors:
pull  double 
state  any record A with fields {chi2: double, dof: int} 
(returns)  A 
pull  array of double 
state  any record A with fields {chi2: double, dof: int} 
(returns)  A 
pull  map of double 
state  any record A with fields {chi2: double, dof: int} 
(returns)  A 
Description: Update the state of a chisquare calculation.
Parameters:
pull  Observation minus prediction divided by uncertainty. If this is a scalar, it will be squared and added to the chisquare. If a vector, each component will be squared and added to the chisquare. 
state  Record of the previous chi2 and dof. 
state  any record A with fields {chi2: double, dof: int} 
(returns)  double 
Description: Return the reduced chisquare, which is chi2/dof.
Parameters:
state  Record of the chi2 and dof. 
state  any record A with fields {chi2: double, dof: int} 
(returns)  double 
Description: Return the chisquare probability, which is the CDF of the chisquare function.
Parameters:
state  Record of the chi2 and dof. 
Runtime Errors:
x  double 
w  double 
state  any record A with fields {count: double} 
(returns)  A 
Description: Update the state of a counter, a counter and a mean, or a counter, mean, and variance.
Parameters:
x  Sample value.  
w  Sample weight; set to 1 for no weights.  
state  Record of the previous count, mean, and/or variance.  

Returns:
Returns an updated version of state with count incremented by w, mean updated to the current mean of all x, and variance updated to the current variance of all x. If the state has fields other than count, mean, and variance, they are copied unaltered to the output state. 
x  array of double 
w  double 
state  any record A with fields {count: double, mean: array of double, covariance: array of array of double} 
(returns)  A 
x  map of double 
w  double 
state  any record A with fields {count: map of map of double, mean: map of double, covariance: map of map of double} 
(returns)  A 
Description: Update the state of a covariance calculation.
Parameters:
x  Sample vector, expressed as an array or map; must have at least two components.  
w  Sample weight; set to 1 for no weights.  
state  Record of the previous count, mean, and covariance.  

Returns:
Returns an updated version of state with count incremented by w, mean updated to the current componentwise mean of all x, and covariance updated to the current covariance matrix of all x. If the state has fields other than count, mean, and covariance, they are copied unaltered to the output state. 
Details:
Runtime Errors:
x  double 
w  double 
state  array of any record A with fields {x: double, w: double, count: double} 
windowSize  int 
(returns)  array of A 
Description: Update the state of a counter, a counter and a mean, or a counter, mean, and variance, within a window of windowSize recent samples.
Parameters:
x  Sample value.  
w  Sample weight; set to 1 for no weights.  
state  Array of previous count, mean, and/or variance and samples in the window.  
 
windowSize  Size of the window. When the length of state is less than windowSize, this function is equivalent to stat.sample.update. 
Returns:
If the length of state is zero, this function returns a singleton array with count = w, mean = x, and/or variance = 0. If the length of state is less than windowSize, then it returns a copy of state with the next record added. Otherwise, it is trunctated to windowSize, removing the old values from the running count/mean/variance. In all cases, the a.last item is the latest result. 
Runtime Errors:
x  double 
alpha  double 
state  any record A with fields {mean: double} 
(returns)  A 
Description: Update the state of an exponentially weighted moving average (EWMA).
Parameters:
x  Sample value.  
alpha  Weighting factor (usually a constant) between 0 and 1, inclusive. If alpha is close to 1, recent data are heavily weighted at the expense of old data; if alpha is close to 0, the EWMA approaches a simple mean.  
state  Record of the previous mean and variance.  

Returns:
Returns a new record with updated mean and variance. If the input state has fields other than mean and variance, they are copied unaltered to the output state. 
Runtime Errors:
x  double 
alpha  double 
beta  double 
state  any record A with fields {level: double, trend: double} 
(returns)  A 
Description: Update the state of a time series analysis with an exponentially weighted linear fit.
Parameters:
x  Sample value.  
alpha  Weighting factor (usually a constant) between 0 and 1, inclusive, that governs the responsiveness of the level. If alpha is close to 1, recent data are heavily weighted at the expense of old data.  
beta  Weighting factor (usually a constant) between 0 and 1, inclusive, that governs the responsiveness of the trend. If beta is close to 1, recent data are heavily weighted at the expense of old data.  
state  Record of the previous level and trend.  

Returns:
Returns an updated version of the state. 
Details:
Runtime Errors:
x  double 
alpha  double 
beta  double 
gamma  double 
state  any record A with fields {level: double, trend: double, cycle: array of double, multiplicative: boolean} 
(returns)  A 
Description: Update the state of a time series analysis with an exponentially weighted periodicpluslinear fit.
Parameters:
x  Sample value.  
alpha  Weighting factor (usually a constant) between 0 and 1, inclusive, that governs the responsiveness of the level. If alpha is close to 1, recent data are heavily weighted at the expense of old data.  
beta  Weighting factor (usually a constant) between 0 and 1, inclusive, that governs the responsiveness of the trend. If beta is close to 1, recent data are heavily weighted at the expense of old data.  
gamma  Weighting factor (usually a constant) between 0 and 1, inclusive, that governs the responsiveness of the cycle. If gamma is close to 1, recent data are heavily weighted at the expense of old data.  
state  Record of the previous level, trend, and cycle.  

Returns:
Returns an updated version of the state. 
Details:
Runtime Errors:
state  any record A with fields {level: double, trend: double} 
(returns)  double 
Description: Forecast one timestep from a state record prepared by stat.state.updateHoltWinters or stat.state.updateHoltWintersPeriodic.
Parameters:
state  Record of level, trend, and possibly cycle and multiplicative.  

Returns:
Returns a prediction of the next timestep. 
Details:
Runtime Errors:
n  int 
state  any record A with fields {level: double, trend: double} 
(returns)  array of double 
Description: Forecast n timesteps from a state record prepared by stat.state.updateHoltWinters or stat.state.updateHoltWintersPeriodic.
Parameters:
state  Record of level, trend, and possibly cycle and multiplicative.  

Returns:
Returns a series of predictions for the next n timesteps. 
Details:
Runtime Errors:
x  double 
w  double 
histogram  any record A with fields {numbins: int, low: double, high: double, values: array of double} 
(returns)  A 
x  double 
w  double 
histogram  any record A with fields {low: double, binsize: double, values: array of double} 
(returns)  A 
x  double 
w  double 
histogram  any record A with fields {ranges: array of array of double, values: array of double} 
(returns)  A 
Description: Update a histogram by filling it with one value.
Parameters:
x  Sample value.  
w  Sample weight; set to 1 for no weights.  
histogram  The histogram prior to filling. It must have numbins, low, high, and values (fixed bins) xor it must have low, binsize, and values (number of equalsized bins grows), xor it must have ranges and values (arbitrary interval bins). Only one set of required fields is allowed (semantic error otherwise), and the rest of the fields are optional.  

Returns:
Returns an updated version of histogram: all fields are unchanged except for values, underflow, overflow, nanflow, and infflow. 
Details:
Runtime Errors:
x  double 
y  double 
w  double 
histogram  any record A with fields {xnumbins: int, xlow: double, xhigh: double, ynumbins: int, ylow: double, yhigh: double, values: array of array of double} 
(returns)  A 
Description: Update a twodimensional histogram by filling it with one value.
Parameters:
x  Sample x value.  
y  Sample y value.  
w  Sample weight; set to 1 for no weights.  
histogram  The histogram prior to filling.  

Returns:
Returns an updated version of histogram: all fields are unchanged except for values and the under/mid/over/nan/infflow counters. 
Details:
Runtime Errors:
x  string 
w  double 
counter  any record A with fields {values: map of double} 
(returns)  A 
Description: Update a counter (sparse histogram) by filling it with one value.
Parameters:
x  Sample category.  
w  Sample weight; set to 1 for no weights.  
histogram  The counter prior to filling.  

Returns:
Returns the updated counter. 
Details:
x  any A 
top  array of A 
n  int 
lessThan  function of (A, A) → boolean 
(returns)  array of A 
Description: Update an array of the top n sorted items by potentially adding x to that array, using lessThan as a comparison function.
Parameters:
x  Sample value. 
top  Array of items to which x might be added. This array is assumed to be sorted according to lessThan. 
n  Maximum number of items to keep. 
lessThan  Comparison function; should return true if its first argument is less than its second argument, false otherwise. 
Returns:
Returns an updated version of top. If x is among the top n values seen, then it is included in the output. Otherwise, the output is top. 
Details:
predicate  boolean 
history  any record A with fields {numEvents: int, numRuns: int, currentRun: int, longestRun: int} 
(returns)  A 
Description: Update the state of a trigger that counts the number of times predicate is satisfied (true), as well as the number and lengths of runs of true.
Parameters:
predicate  Expression that evaluates to true or false.  
history  Summary of previous results of the predicate.  

Returns:
Returns a new record with updated fields: numEvents is always incremented; numRuns is incremented if predicate is true and currentRun is zero; currentRun is incremented if predicate is true and set to zero if predicate is false; longestRun is set to currentRun if predicate is true and currentRun is longer than longestRun. If the input history has fields other than numEvents, numRuns, currentRun, or longestRun, they are copied unaltered to the output. 
Runtime Errors:
x  double 
meanVariance  any record A with fields {mean: double, variance: double} 
(returns)  double 
x  double 
meanVariance  any record A with fields {count: double, mean: double, variance: double} 
unbiased  boolean 
(returns)  double 
Description: Calculate the zvalue between x and a normal distribution with a given mean and variance.
Parameters:
x  Value to test. 
meanVariance  A record with mean, variance, and possibly count, such as the output of stat.sample.Update. 
unbiased  If true, use count to correct for the bias due to the fact that a variance centered on the mean has one fewer degrees of freedom than the dataset that it was sampled from (Bessel's correction). 
Returns:
If unbiased is false, \((x  mean)/\sqrt{variance}\); otherwise \((x  mean)(1/\sqrt{variance})\sqrt{count/(count  1)}\). 
logLikelihoodRatio  double 
last  double 
reset  double 
(returns)  double 
Description: Update a cumulative sum (CUSUM) to detect the transition of a dataset from one distribution to another.
Parameters:
logLikelihoodRatio  The logarithm of the ratio of the likelihood of a value for the alterate and baseline distributions: \(\ln(\mbox{alt}_{L}/\mbox{base}_{L})\), which is \(\mbox{alt}_{LL}  \mbox{base}_{LL}\) where \(L\) is likelihood and \(LL\) is loglikelihood. Consider using something like {"": [{"prob.dist.gaussianLL": [...]}, {"prob.dist.gaussianLL": [...]}]}. 
last  The previous return value from this function. 
reset  A low value (usually consistent with the baseline hypothesis, such as 0) at which the cumulative sum resets, rather than accumulate very low values and become insensitive to future changes. 
Returns:
An incremented cumulative sum. The output is \(\max\{logLikelihoodRatio + last, reset\}\). 
datum  array of double 
model  any record M with fields {coeff: array of double, const: double} 
(returns)  double 
datum  array of double 
model  any record M with fields {coeff: array of array of double, const: array of double} 
(returns)  array of double 
datum  map of double 
model  any record M with fields {coeff: map of double, const: double} 
(returns)  double 
datum  map of double 
model  any record M with fields {coeff: map of map of double, const: map of double} 
(returns)  map of double 
Description: Apply matrix model to independent variables datum to predict the dependent, predicted variables.
Parameters:
datum  Vector of independent variables with \(d\) dimensions.  
model  Parameters of the linear model.  

Returns:
Returns a \(p\) dimensional vector of dependent, predicted variables. 
Details:
Runtime Errors:
datum  array of double 
model  any record M with fields {covar: array of array of double} 
(returns)  double 
datum  array of double 
model  any record M with fields {covar: array of array of array of double} 
(returns)  array of double 
datum  map of double 
model  any record M with fields {covar: map of map of double} 
(returns)  double 
datum  map of double 
model  any record M with fields {covar: map of map of map of double} 
(returns)  map of double 
Description: Propagate variances from model covar (covariance matrix) to the dependent, predicted variable(s).
Parameters:
datum  Vector of independent variables \(\vec{o}\) with \(d\) dimensions.  
model  Parameters of the linear model.  

Returns:
Propagated variance(s) \(\vec{o}^T C \vec{o}\) for each dependent, predicted variable. 
Details:
Runtime Errors:
x  double 
table  array of any record R with fields {x: double, to: double} 
krigingWeight  union of {null, double} 
kernel  function of (array of double, array of double) → double 
(returns)  double 
x  double 
table  array of any record R with fields {x: double, to: array of double} 
krigingWeight  union of {null, double} 
kernel  function of (array of double, array of double) → double 
(returns)  array of double 
x  array of double 
table  array of any record R with fields {x: array of double, to: double} 
krigingWeight  union of {null, double} 
kernel  function of (array of double, array of double) → double 
(returns)  double 
x  array of double 
table  array of any record R with fields {x: array of double, to: array of double} 
krigingWeight  union of {null, double} 
kernel  function of (array of double, array of double) → double 
(returns)  array of double 
Description: Fit the training data in table with a Gaussian Process model and predict the value of model at x.
Parameters:
x  Position (scalar or vector) at which to predict the value of the model.  
table  Training data for the Gaussian Process.  
 
krigingWeight  If a number, the Gaussian Process is performed with the specified Kriging weight. If null, universal Kriging is performed.  
kernel  A function to use as a kernel. For instance, m.kernel.rbf (radial basis function) with partially applied gamma is a squared exponential kernel. 
Returns:
Returns a scalar or vector prediction with the same type as to. 
Details:
Runtime Errors:
observation  double 
prediciton  double 
(returns)  double 
observation  array of double 
prediciton  array of double 
(returns)  array of double 
observation  map of double 
prediciton  map of double 
(returns)  map of double 
Description: Compare an observation with its prediction by elementwise subtraction.
Parameters:
observation  Scalar or vector of observations. 
prediction  Scalar or vector of predictions. 
Returns:
Scalar or vector of observation minus prediction. 
Runtime Errors:
observation  double 
prediciton  double 
uncertainty  double 
(returns)  double 
observation  array of double 
prediciton  array of double 
uncertainty  array of double 
(returns)  array of double 
observation  map of double 
prediciton  map of double 
uncertainty  map of double 
(returns)  map of double 
Description: Compare an observation with its prediction by elementwise subtraction, weighted by elementwise uncertainties.
Parameters:
observation  Scalar or vector of observations. 
prediction  Scalar or vector of predictions. 
uncertainty  Scalar or vector of predictions. 
Returns:
Scalar or vector of observation minus prediction divided by uncertainty. 
Runtime Errors:
observation  array of double 
prediction  array of double 
covariance  array of array of double 
(returns)  double 
observation  map of double 
prediction  map of double 
covariance  map of map of double 
(returns)  double 
Description: Compare an observation with its prediction by computing the Mahalanobis distance for a given covariance matrix.
Parameters:
observation  Vector of observations \(\vec{o}\). 
prediction  Vector of predictions \(\vec{p}\). 
covariance  Matrix of covariance \(C\). 
Returns:
Scalar result of a similarity transformation: \(\sqrt{(\vec{o}  \vec{p})^T C^{1} (\vec{o}  \vec{p})}\). 
Runtime Errors:
pull  double 
state  any record A with fields {chi2: double, DOF: int} 
(returns)  A 
pull  array of double 
state  any record A with fields {chi2: double, DOF: int} 
(returns)  A 
pull  map of double 
state  any record A with fields {chi2: double, DOF: int} 
(returns)  A 
Description: Update the state of a chisquare calculation.
Parameters:
pull  Observation minus prediction divided by uncertainty. If this is a scalar, it will be squared and added to the chisquare. If a vector, each component will be squared and added to the chisquare. 
state  Record of the previous chi2 and DOF. 
state  any record A with fields {chi2: double, DOF: int} 
(returns)  double 
Description: Return the reduced chisquare, which is chi2/DOF.
Parameters:
state  Record of the chi2 and DOF. 
state  any record A with fields {chi2: double, DOF: int} 
(returns)  double 
Description: Return the chisquare probability, which is the CDF of the chisquare function.
Parameters:
state  Record of the chi2 and DOF. 
Runtime Errors:
datum  any record D 
comparison  any record T with fields {field: enum F of fields of D, operator: string, value: any V} 
(returns)  boolean 
Description: Determine if datum passes a test defined by comparison.
Parameters:
datum  Sample value to test.  
comparison  Record that describes a test.  

Returns:
Returns true if the field of datum <op> value is true, false otherwise, where <op> is the operator. 
Runtime Errors:
datum  any record D 
comparison  any record T with fields {field: enum F of fields of D, operator: string, value: any V} 
(returns)  union of {null, boolean} 
Description: Determine if datum passes a test defined by comparison, allowing for missing values.
Parameters:
datum  Sample value to test.  
comparison  Record that describes a test.  

Returns:
If the field of datum is null, this function returns null (unknown test result). Otherwise, it returns datum field <op> value, where <op> is the operator 
Runtime Errors:
datum  any record D 
operator  string 
comparisons  array of any record T 
test  function of (D, T) → boolean 
(returns)  boolean 
Description: Apply test to an array of comparisons, returning their logical and, or, or xor, depending on operator.
Parameters:
datum  Simple value to test. 
operator  If "and", return true if no false is encountered, if "or", return true if any true is encountered, and if "xor", return true if an odd number of true is encountered among the comparisons. 
comparisons  Array of records that describe the tests. 
test  Test function applied to each item of comparisons until the result is certain. 
Returns:
Logical combination of comparisons. 
Details:
Runtime Errors:
datum  any record D 
comparisons  array of any record T 
missingTest  function of (D, T) → union of {null, boolean} 
(returns)  boolean 
Description: Apply missingTest to an array of comparisons until one yields a nonnull result.
Parameters:
datum  Sample value to test. 
comparisons  Array of records that describe the tests. 
missingTest  Test function applied to each item of comparisons until one returns a nonnull result. 
Returns:
Returns the value of the first test that returns true or false. 
Runtime Errors:
datum  any record D 
treeNode  any record T with fields {pass: union of {T, any S}, fail: union of {T, S}} 
test  function of (D, T) → boolean 
(returns)  S 
Description: Descend through a tree, testing the fields of datum with the test function using treeNode to define the comparison, continuing to pass or fail until reaching a leaf node of type S (score).
Parameters:
datum  Sample value to test.  
treeNode  Node of the tree, which contains a predicate to be interpreted by test.  
 
test  Test function that converts datum and treeNode into true or false. 
Returns:
Leaf node of type S, which must be different from the tree nodes. For a classification tree, S could be a string or an enumeration set. For a regression tree, S would be a numerical type. For a multivariate regression tree, S would be an array of numbers, etc. 
datum  any record D 
treeNode  any record T with fields {pass: union of {T, any S}, fail: union of {T, S}, missing: union of {T, S}} 
test  function of (D, T) → union of {null, boolean} 
(returns)  S 
Description: Descend through a tree, testing the fields of datum with the test function using treeNode to define the comparison, continuing to pass, fail, or missing until reaching a leaf node of type S (score).
Parameters:
datum  Sample value to test.  
treeNode  Node of the tree, which contains a predicate to be interpreted by test.  
 
test  Test function that converts datum and treeNode into true, false, or null. 
Returns:
Leaf node of type S, which must be different from the tree nodes. For a classification tree, S could be a string or an enumeration set. For a regression tree, S would be a numerical type. For a multivariate regression tree, S would be an array of numbers, etc. 
datum  any record D 
treeNode  any record T with fields {field: enum F of fields of D, operator: string, value: any V, pass: union of {T, any S}, fail: union of {T, S}} 
(returns)  S 
Description: Descend through a tree, testing datum with field, operator, value, following pass or fail until reaching a leaf node of type S (score).
Parameters:
datum  Sample value to test.  
treeNode  Record that describes a tree node (predicate test with branches).  

Returns:
Leaf node of type S, which must be different from the tree nodes. For a classification tree, S could be a string or an enumeration set. For a regression tree, S would be a numerical type. For a multivariate regression tree, S would be an array of numbers, etc. 
Details:
Runtime Errors:
datum  array of double 
clusters  array of any record C with fields {center: array of double} 
(returns)  C 
datum  any A 
clusters  array of any record C with fields {center: any B} 
metric  function of (A, B) → double 
(returns)  C 
Description: Find the cluster C whose center is closest to the datum, according to the metric.
Parameters:
datum  Sample datum. 
clusters  Set of clusters; the record type C may contain additional identifying information for postprocessing. 
metric  Function used to compare each datum with the center of the clusters. (See, for example, metric.euclidean.) 
Returns:
Returns the closest cluster record. 
Details:
Runtime Errors:
n  int 
datum  array of double 
clusters  array of any record C with fields {center: array of double} 
(returns)  array of C 
n  int 
datum  any A 
clusters  array of any record C with fields {center: any B} 
metric  function of (A, B) → double 
(returns)  array of C 
Description: Find the n clusters C whose centers are closest to the datum, according to the metric.
Parameters:
n  Number of clusters to search for. 
datum  Sample datum. 
clusters  Set of clusters; the record type C may contain additional identifying information for postprocessing. 
metric  Function used to compare each datum with the center of the clusters. (See, for example, metric.euclidean.) 
Returns:
An array of the closest cluster records in order from the closest to the farthest. The length of the array is minimum of n and the length of clusters. 
Details:
Runtime Errors:
data  array of array of any A 
k  int 
newCluster  function of (int, array of A) → any record C with fields {center: array of any B} 
(returns)  array of C 
Description: Call newCluster to create k cluster records with random, unique cluster centers drawn from data.
Parameters:
data  Sample data. 
k  Number of times to call newCluster. 
newCluster  Function that creates a cluster record, given an index (ranges from zero up to but not including k) and a random vector from data. 
Returns:
The cluster records created by newCluster. 
Details:
Runtime Errors:
data  array of array of any A 
clusters  array of any record C with fields {center: array of any B} 
metric  function of (array of A, array of B) → double 
update  function of (array of array of A, C) → C 
(returns)  array of C 
Description: Update a cluster set by applying one iteration of kmeans (Lloyd's algorithm).
Parameters:
data  Sample data. 
clusters  Set of clusters; the record type C may contain additional identifying information for postprocessing. 
metric  Function used to compare each datum with the center of the clusters. (See, for example, metric.euclidean.) 
update  Function of matched data and old cluster records that yields new cluster records. (See, for example, model.cluster.updateMean with weight = 0.) 
Returns:
Returns a new cluster set with each of the centers located at the average of all points that match the corresponding cluster in the old cluster set. 
Details:
Runtime Errors:
data  array of array of double 
cluster  any record C with fields {center: array of double} 
weight  double 
(returns)  C 
Description: Update a cluster record by computing the mean of the data vectors and weight times the old cluster center.
Details:
Runtime Errors:
points  array of array of double 
(returns)  array of double 
points  array of array of double 
weight  function of (array of double) → double 
(returns)  array of double 
Description: Return the vectorwise mean of points, possibly weighted by weight.
Parameters:
points  Points from a codebook, for instance from model.neighbor.nearestK. 
weight  Optional weighting function from each element of points to a value. If these values do not add up to 1.0, they will be internally normalized. 
Returns:
The vectorwise mean, which is by construction within the convex hull of the points. 
Runtime Errors:
k  int 
datum  array of double 
codebook  array of array of double 
(returns)  array of array of double 
k  int 
datum  any A 
codebook  array of any B 
metric  function of (A, B) → double 
(returns)  array of B 
Description: Find the k items in the codebook that are closest to the datum, according to the metric.
Parameters:
k  Number of codebook points to attempt to return. 
datum  Sample datum. 
codebook  Set of training data that is compared to the datum. 
metric  Function used to compare each datum to each element of the codebook. (See, for example, metric.euclidean.) 
Returns:
An array of the closest codebook elements in any order. The length of the array is minimum of k and the length of codebook. 
Runtime Errors:
r  double 
datum  array of double 
codebook  array of array of double 
(returns)  array of array of double 
r  double 
datum  any A 
codebook  array of any B 
metric  function of (A, B) → double 
(returns)  array of B 
Description: Find the items in codebook that are within r of the datum, according to the metric.
Parameters:
r  Maximum distance (exclusive) of points to return. 
datum  Sample datum. 
codebook  Set of training data that is compared to the datum. 
metric  Function used to compare each datum to each element of the codebook. (See, for example, metric.euclidean.) 
Returns:
An array of the codebook elements within a distance r in any order. The length of the array could be as low as zero or as high as the length of codebook. 
datum  array of double 
classModel  array of any record A with fields {mean: double, variance: double} 
(returns)  double 
datum  map of double 
classModel  map of any record A with fields {mean: double, variance: double} 
(returns)  double 
Description: Score datum using a Gaussian Naive Bayes model.
Parameters:
datum  Vector of independent variables with \(d\) dimensions. 
classModel  Array or map of \(d\) records, each containing the mean and variance of each of independent variable, for one class. 
Returns:
Returns the unscaled loglikelihood that datum is a member of the class specified by classModel. 
Details:
Runtime Errors:
datum  array of double 
classModel  array of double 
(returns)  double 
datum  map of double 
classModel  map of double 
(returns)  double 
datum  array of double 
classModel  any record C with fields {values: array of double} 
(returns)  double 
datum  map of double 
classModel  any record C with fields {values: map of double} 
(returns)  double 
Description: Score datum using a Multinomial Naive Bayes model.
Parameters:
datum  Vector of independent variables with \(d\) dimensions. 
classModel  Array or map of multinomial (\(d\) different) likelihoods of each independent variable for this class. The record form is for histograms built by stat.sample.fillHistogram or stat.sample.fillCounter. 
Returns:
Returns the unscaled loglikelihood of datum for this class. 
Details:
Runtime Errors:
datum  array of string 
classModel  map of double 
(returns)  double 
datum  array of string 
classModel  any record C with fields {values: map of double} 
(returns)  double 
Description: Score datum using a Bernoulli Naive Bayes model.
Parameters:
datum  Vector of independent variables with \(d\) dimensions. The record form is for histograms built by stat.sample.fillCounter. 
classModel  Array or map of \(d\) likelihoods of the presence of each independent variable for this class. 
Returns:
Returns the unscaled loglikelihood of datum for this class. 
Runtime Errors:
datum  array of double 
model  array of any record M with fields {weights: array of array of double, bias: array of double} 
activation  function of (double) → double 
(returns)  array of double 
Description: Apply a feedforward artificial neural network model to an input datum.
Parameters:
datum  Length d vector of independent variables. 
model  Array containing the parameters of each layer of the feedforward neural network model. 
activation  Function applied at the output of each node, except the last. Usually an "S"shaped sigmoid or hyperbolic tangent. 
Returns:
Returns an array of network outputs. For a neural network with a single neuron in the last layer (single output), this is an array of length one. 
Runtime Errors:
datum  array of double 
model  any record L with fields {const: double, posClass: array of any record M with fields {supVec: array of double, coeff: double}, negClass: array of any record N with fields {supVec: array of double, coeff: double}} 
kernel  function of (array of double, array of double) → double 
(returns)  double 
Description: Score an input datum with a twoclass support vector machine classifier given a model and a kernel function kernel.
Parameters:
datum  Length d vector of independent variables. 
model  Record containing the support vectors, dual space coefficients and constant needed to score new data. 
kernel  Kernel function used to map data and support vectors into the dual space. 
Returns:
Returns the score. If positive, datum classified as same group as posClass support vectors. If negative, datum classified as same group as negClass support vectors. 
Runtime Errors: