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XLeratorDB/Math Functions Documentation

FUNCTION REFERENCE - Math Functions FUNCTIONS

Trigonometric
ACOSH

Calculate the inverse hyperbolic cosine of a number.

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ACOT

Calculate the arccotangent of a number.

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ACOTH

hyperbolic arccotangent

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ASINH

Calculate the inverse hyperbolic sine of a number.

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ATANH

Calculate the inverse hyperbolic tangent of a number.

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COSH

Calculate the hyperbolic cosine of a number.

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COTH

Calculate hyperbolic cotangent of a number.

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CSC

Calculate the cosecant of the given angle.

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CSCH

Calculate the hyperbolic cosecant of the given angle.

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SEC

Calculate the secant of the given angle.

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SECH

Calculate the hyperbolic secant of the given angle.

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SINH

Calculate the hyperbolic sine of a number.

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TANH

Calculate the hyperbolic tangent of a number.

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ATAN2

Calculate a numeric value between -π and π representing the angle θ of a (x, y) point and positive x-axis

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Arithmetic/algebra
BASE

Convert an integer to the text representation of that number for a given radix (base).

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BASE2DECIMAL

Convert the text representation of a number in a given radix (base) to an integer.

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CEILING

Calculate a number rounded up, away from zero, to the nearest multiple of significance.

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COMBIN

Combinatorial function

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COMBINA

Calculate the number of combinations with repitition of n things taken r at a time.

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DISTANCE

Calculate the distance between 2 points on the globe, using the great circle formula.

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EGCD

Calculate the greatest common divisor using Euclid's method.

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ELCM

Calculate the least common multiple using Euclid's method.

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EVEN

Calculate a number rounded up to the nearest even integer.

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FACT

factorial of a number

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FACTDOUBLE

Calculate the double factorial of a number.

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FLOOR

Calculate a number rounded down, towards zero, to the nearest multiple of significance.

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GCD

Calculate a number rounded up to the nearest even integer.

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GREATEROF

Calculate the greater of two values passed into the function.

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INT

Calculate a number rounded down, towards zero, to the nearest integer.

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LCM

Calculate the least common multiple of all the values, or only the DISTINCT values, in the expression.

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LESSEROF

Calculate the lesser of two values passed into the function.

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MAX

Calculate the nth largest distinct value

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MIN

Calculate the nth smallest distinct value in a dataset.

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MROUND

Calculate a number rounded to the desired multiple.

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MULTINOMIAL

Calculate the ratio of a sum of values to the product of the factorials of those values.

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MULTINOMIAL_q

Calculate the ratio of a sum of values to the product of the factorials of those values.

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ODD

Calculate a number rounded up to the nearest odd integer.

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POWER

Calculate the value of the specified expression to the specified power.

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PRODUCT

Calculate the product of all the values, or only the DISTINCT values, in a dataset.

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PRODUCT38

Calculate the product of 2 decimal(38,18) values as a decimal with precision 38 and scale 18.

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QUOTIENT

Calculate integer portion of a division.

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QUOTIENT38

Calculate the quotient of 2 decimal(38,18) values as a decimal with precision 38 and scale 18.

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ROMAN

Calculate an Arabic numeral converted to a Roman numeral, as text.

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ROUNDDOWN

Calculate a number rounded down, towards zero.

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ROUNDUP

Calculate a number rounded up, away from zero.

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SERIESSUM

Calculate the sum of a power series.

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SERIESSUM_q

Calculate the sum of a power series.

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SUMSQ

Calculate the sum of the squares of all the values, or only the DISTINCT values, in the expression.

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TRUNC

Calculate a number truncated to an integer by removing the fractional part of the number.

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WAVG

Calculate the weighted average.

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Optimization
BFGS

Broyden-Fletcher-Goldfarb-Shanno (BFGS) method to find the minimum of a functionBRENT - Find the root of a continuous function of one variable

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BRENT

Find the root of a continuous function of on variable

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FDERIV

Numerical function differentiation for orders n = 1 to 8 using finite difference approximations

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GRAD

Numerically compute the gradient.

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HESSIAN

Numerically computer the Hessian matrix

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JACOBIAN

Numerically compute the Jacobian matrix

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NEWTON

Find the root of a univariate function

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NLMIN

Nelder-Mead Minimization.

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SECANT

Find the root of single-variable continuous function.

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Interpolation
BILINEARINTERP

Interpolate on a regular 2-dimensional grid.

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INTERP

Calculate the straight-line interpolated value of y given x in the array (x, y).

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INTERP_q

Calculate the straight-line interpolated value of y given x in the array (x, y).

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INTERP2

Interpolate on a 2-dimensional grid in 3rd normal form.

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LINEAR

Calculate the straight-line interpolated value of y given x in the array (x, y).

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MONOSPLINE

Calculate the interpolated value of y given x in the array (x, y).

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POLYCOEF

Obtain a specific coefficient value from an approximating polynomial for a set of x- and y-values.

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POLYFIT

Calculate the coefficients of a polynomial p(x) of degree that fits the x- and y-values supplied to the function.

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POLYFIT_q

Calculate the coefficients of a polynomial p(x) of degree n ;that fits the x- and y-values supplied to the function.

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POLYINTERP

Calculate the interpolated value of y given x in the array (x, y).

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POLYRSQ

Calculate the goodness of fit for an approximating polynomial calculated from a series of x- and y-values for a specified number of degrees.

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POLYVAL

Calculate a new y-value given a new x-value using the coefficients of a polynomial p(x) of degree that fits the x- and y-values supplied to the function.

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SPLINE

Calculate the interpolated value of y given x in the array (x, y).

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SPLINE_q

Calculate the interpolated value of y given x in the array (x, y).

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Matrix Functions
BKSUB

Return a solution to the equation A*x=b, when A is an upper-triangular matrix.

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CORRM

Table-valued function to calculate the correlation matrix

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COVM

Table-valued function to calculate the covariance matrix

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CROSSPROD

scalar function to calculate A' * A or A' * B

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DIAG

Return the vector of the diagonal of the string representation of a matrix.

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EYE

Generate an m-by-n identity matrix.

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FWDSUB

Return a solution to the equation A*x=b, when A is a lower-triangular matrix.

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LU

LU factorization with partial pivoting

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LUdecomp

Calculate the LU factorization of an N x N matrix using partial pivoting.

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LUdecomp_q

Calculate the LU factorization of an N x N matrix using partial pivoting.

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LUdecompN

Calculate the LU factorization of an N x N matrix using partial pivoting.

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LUdecompN_q

Calculate the LU factorization of an N x N matrix using partial pivoting.

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MAPPEND

append rows or columns to a matrix

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MATADD

Add a value to every element of a matrix or to add 2 matrices of the same dimensions together.

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MATINVERSE

Calculate the matrix inverse of a square (N x N) matrix.

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MATMULT

matrix multiplication for string representations of matrices

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MATRIX2STRING

Turn table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semi-colons.

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MATRIX2STRING_q

Turn table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semi-colons.

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MATSUB

Subtract a value from every element of a matrix or to calculate the difference between 2 matrices of the same dimensions.

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MCOLS

Find the number of columns in the string representation of a matrix.

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MCOLUMN

Return a column from the string representation of a matrix.

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MCORR

Correlation matrix using a formatted matrix as input

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MCOV

Calculate a sample covariance matrix.

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MCROSS

table-valued function to calculate A' * A or A' * B

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MDETERM

matrix determinant function

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MDETERM_q

Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.

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MDETERMN

Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.

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MDETERMN_q

Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.

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MINDEX

Return the intersection of a row and a column from the string representation of a matrix.

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MINVERSE

Calculate the matrix inverse of a square (N x N) matrix.

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MINVERSE_q

Calculate the matrix inverse of a square (N x N) matrix.

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MINVERSEN

Calculate the matrix inverse of a square (N x N) matrix.

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MINVERSEN_q

Calculate the matrix inverse of a square (N x N) matrix.

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MMULT

Matrix Mulitplication

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MMULT_q

Calculate the matrix product of two arrays.

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MMULTN

Matrix Mulitplication

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MMULTN_q

Calculate the matrix product of two arrays in third-normal form.

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MNORM

calculate matrix norms

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MRAND

Generate an m-by-n matrix of pseudo-random numbers greater than or equal to zero and less than one.

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MRANDN

Generate an m-by-n matrix of pseudo-random numbers from the standard normal distribution.

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MRANK

Calculate the rank of a matrix.

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MRORTHO

Generate an m-by-m random orthogonal matrix.

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MROW

Return a row from the string representation of a matrix.

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MROWS

Find the number of rows in the string representation of a matrix.

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MSYMMEIG

Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.

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MTRACE

Calculate the trace of a de-normalized matrix.

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MTRACE_q

Calculate the trace of a de-normalized matrix.

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MTRACEN

Calculate the trace of a matrix in third-normal form.

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MTRACEN_q

Calculate the trace of a matrix in third-normal form.

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MTRIL

Return the lower triangular part of the string representation of a matrix.

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MTRIU

Return the upper triangular part of the string representation of a matrix.

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MUPDATE

perform elementwise operations on a matrix

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NMATRIX2STRING

Turn third-normal form table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semi-colons.

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NMATRIX2STRING_q

Turn third-normal form table data into a string representation of a matrix, where the columns are separated by commas and the rows are separated by semi-colons.

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ONES

create an m-by-n matrix of ones

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QR

QR decomposition

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QRdecomp

Decompose a de-normalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q, such that A = QR.

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QRdecomp_q

Decompose a de-normalized N x N matrix into the product of an upper triangular matrix R and an orthogonal matrixQ, such that A = QR.

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SPECRAD

Calculate the spectral radius of a square matrix.

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SUMPRODUCT

calculate the sum of elementwise multiplication on a group of matrices

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SUMX2MY2

the sum of the square of the elementwise differences of 2 matrices

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SUMX2PY2

the sum of the sum of the squares for corresponding elements in 2 matrices

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SUMXMY2

Calculate the sum of the sqaure of the differences in the corresponding elements in 2 matrices.

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SVD

Economy-sized singular value decomposition using a formatted matrix as input

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SVdecomp

Calculate the economy-sized singular value decomposition of an m-x-n matrix A.

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SYMMEIG

Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.

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TCROSSPROD

scalar function to calculate A * A' or A * B'

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TMCROSS

table-valued function to calculate A * A' or A * B'

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TRANSPOSE

scalar function to convert A to A'

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VANDERMONDE

Return the Vandermonde matrix.

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ZERO

Generate an m-by-n matrix of zeroes.

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MATRIX

Convert the string representation of a matrix into 3rd-normal form.

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CHOLESKY

Calculate the Cholesky decomposition of a symmetric positive-definite matrix

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Numerical Integration
QUAD

Gauss-Kronrod 15-point quadrature

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QUADDE

Double Exponential quadrature for non-periodic functions

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QUADGK

Gauss-Kronrod 21-point quadrature

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QUADOSC

Double exponential quadrature for periodic functions

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QUADTS

Evaluate a finite integral.

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Number/series Generators
RAND

Calculate a random number greater than or equal to zero and less than one.

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RANDBETA

Random numbers from a beta distribution

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RANDBETWEEN

Calculate a random integer number between the numbers you specify.

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RANDBINOM

Random numbers from a binomial distribution

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RANDCAUCHY

Random numbers from a Cauchy distribution

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RANDCHISQ

Random numbers from a chi-squared distribution

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RANDEXP

Random numbers from an exponential distribution

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RANDFDIST

Random numbers from an F-distribution

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RANDGAMMA

Random numbers from a gamma distribution

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RANDLAPLACE

Random numbers from a LaPlace distribution

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RANDLOGISTIC

Random numbers from a logistic distribution

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RANDNORM

Calculate a pseudo-random number based on a normal distribution for the given mean and standard deviation.

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RANDNORMAL

Random numbers from the normal distribution

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RANDPOISSON

Random numbers from a Poisson distribution

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RANDSNORMAL

Random numbers from the standard normal distribution

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RANDTDIST

Random numbers from Student's t distribution

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RANDWEIBULL

Generate a sequence of random numbers from w Weibull distribution with parameters shape (?) and scale (?).

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SeriesDate

Generate a range of date values.

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SeriesFloat

Generate a range of floating point values.

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SeriesInt

Generate a range of integer values.

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