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 floating-point 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 bitwise-and of x and y.
x | int |
y | int |
(returns) | int |
x | long |
y | long |
(returns) | long |
Description: Calculate the bitwise-or of x and y.
x | int |
y | int |
(returns) | int |
x | long |
y | long |
(returns) | long |
Description: Calculate the bitwise-exclusive-or of x and y.
x | int |
(returns) | int |
x | long |
(returns) | long |
Description: Calculate the bitwise-not of x.
(returns) | double |
Description: The double-precision number that is closer than any other to \(\pi\), the ratio of a circumference of a circle to its diameter.
(returns) | double |
Description: The double-precision 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 arc-cosine (inverse of the cosine function) of x as an angle in radians between \(0\) and \(\pi\).
Details:
x | double |
(returns) | double |
Description: Return the arc-sine (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 arc-tangent (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 arc-tangent (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 one-half.
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 one-half.
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 Moore-Penrose 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 (1-dimensional metric) that returns the absolute Euclidean distance between x and y.
x | double |
y | double |
sigma | double |
(returns) | double |
Description: Similarity function (1-dimensional 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 2-norm).
Parameters:
similarity | Similarity function (1-dimensional 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 missing-value 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, missing-value 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 missing-value 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 (1-dimensional 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 missing-value 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, missing-value 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 missing-value 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 (1-dimensional 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 missing-value 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, missing-value 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 missing-value 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 1-norm, city-block or Manhattan distance (since it is the distance when confined to a rectilinear city grid).
Parameters:
similarity | Similarity function (1-dimensional 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 missing-value 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, missing-value 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 missing-value 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 p-norm, a generalized norm whose limits include Euclidean, Chebyshev, and Taxicab.
Parameters:
similarity | Similarity function (1-dimensional 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 missing-value 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, missing-value 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 missing-value 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 32-bit 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 64-bit 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 code-point to sample (inclusive). |
high | Maximum code-point 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 xxxxxxxx-xxxx-4xxx-8xxx-xxxxxxxxxxxx where x are random, lowercase hexidecimal digits (0-9a-f), 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 xxxxxxxx-xxxx-4xxx-8xxx-xxxxxxxxxxxx where x are random, lowercase hexidecimal digits (0-9a-f), 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, left-justify. 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, left-justify. 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, left-justify. 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 lower-case.
s | string |
(returns) | string |
Description: Convert s to upper-case.
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 sub-match (group-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 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 sub-match (group-match) 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 sub-match (group-match) 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 sub-match (group-match) 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 single-precision floating point number.
Details:
Runtime Errors:
str | string |
(returns) | double |
Description: Parse str and return its value as a double-precision 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, bit-for-bit, 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, bit-for-bit, 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 64-bit 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 single-precision 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 double-precision 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 "n-tile" 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 lock-step 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 lock-step 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 key-value pairs from overlay in place of or in addition to key-value 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 key-value 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 key-value 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 key-value 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 lock-step 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 lock-step 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 latin-1 (ISO-8859-1); false otherwise.
x | bytes |
(returns) | boolean |
x | string |
(returns) | boolean |
Description: Returns true if x is valid utf-8; false otherwise.
x | bytes |
(returns) | boolean |
x | string |
(returns) | boolean |
Description: Returns true if x is valid utf-16 (byte order identified by optional byte-order mark); false otherwise.
x | bytes |
(returns) | boolean |
x | string |
(returns) | boolean |
Description: Returns true if x is valid big endian utf-16; false otherwise.
x | bytes |
(returns) | boolean |
x | string |
(returns) | boolean |
Description: Returns true if x is valid little endian utf-16; 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 latin-1 (ISO-8859-1) string.
Runtime Errors:
x | bytes |
(returns) | string |
Description: Decode a bytes object as a utf-8 string.
Runtime Errors:
x | bytes |
(returns) | string |
Description: Decode a bytes object as a utf-16 (byte order identified by optional byte-order mark) string.
Runtime Errors:
x | bytes |
(returns) | string |
Description: Decode a bytes object as a big endian utf-16 string.
Runtime Errors:
x | bytes |
(returns) | string |
Description: Decode a bytes object as a little endian utf-16 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 latin-1 (ISO-8859-1) bytes.
Runtime Errors:
s | string |
(returns) | bytes |
Description: Encode a string as utf-8 bytes.
Runtime Errors:
s | string |
(returns) | bytes |
Description: Encode a string as utf-16 (byte order identified by optional byte-order mark) bytes.
Details:
Runtime Errors:
s | string |
(returns) | bytes |
Description: Encode a string as big endian utf-16 bytes.
Runtime Errors:
s | string |
(returns) | bytes |
Description: Encode a string as little endian utf-16 bytes.
Runtime Errors:
x | bytes |
(returns) | string |
Description: Convert an arbitrary bytes object to a base64-encoded string.
s | string |
(returns) | bytes |
Description: Convert a base64-encoded string to a bytes object.
Runtime Errors:
x | any fixed A |
(returns) | bytes |
Description: Convert fixed-length, named bytes into arbitrary-length, 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 four-digit 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 four-digit 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 log-likelihood of a Gaussian (normal) distribution parameterized by mu and sigma or a record params.
Parameters:
x | Value at which to compute the log-likelihood. |
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 Chi-squared 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 Chi-squared 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 Chi-squared 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 \(\frac{\Gamma(a + n)}{\Gamma(a)\Gamma(b)} x^{a-1}(1-x)^{b-1}\). |
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 \(\frac{\mathrm{choose}(m, x) \mathrm{choose}(n, k-x)}{\mathrm{choose}(m+n, k)} \). |
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 \(\frac{\Gamma(x+n)}{\Gamma(n) x!} p^{n} (1-p)^{x}\). |
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 Kolmogorov-Smirnov 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 element-wise 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 element-wise subtraction, weighted by element-wise 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 chi-square calculation.
Parameters:
pull | Observation minus prediction divided by uncertainty. If this is a scalar, it will be squared and added to the chi-square. If a vector, each component will be squared and added to the chi-square. |
state | Record of the previous chi2 and dof. |
state | any record A with fields {chi2: double, dof: int} |
(returns) | double |
Description: Return the reduced chi-square, 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 chi-square probability, which is the CDF of the chi-square 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 periodic-plus-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. | ||||||||
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 time-step 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 time-step. |
Details:
Runtime Errors:
n | int |
state | any record A with fields {level: double, trend: double} |
(returns) | array of double |
Description: Forecast n time-steps 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 time-steps. |
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 equal-sized 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 two-dimensional 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 z-value 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 log-likelihood. 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 element-wise 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 element-wise subtraction, weighted by element-wise 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 chi-square calculation.
Parameters:
pull | Observation minus prediction divided by uncertainty. If this is a scalar, it will be squared and added to the chi-square. If a vector, each component will be squared and added to the chi-square. |
state | Record of the previous chi2 and DOF. |
state | any record A with fields {chi2: double, DOF: int} |
(returns) | double |
Description: Return the reduced chi-square, 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 chi-square probability, which is the CDF of the chi-square 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 non-null 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 non-null 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 post-processing. |
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 post-processing. |
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 k-means (Lloyd's algorithm).
Parameters:
data | Sample data. |
clusters | Set of clusters; the record type C may contain additional identifying information for post-processing. |
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 vector-wise 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 vector-wise 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 log-likelihood 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 log-likelihood 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 log-likelihood 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 two-class 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: