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Math Functions Index ...
Arithmetic
BASE - convert an integer to the text representation of that number for a given radix (base)
BASE2DECIMAL - convert the text representation of a number in a given radix (base) to an integer
COMBIN - number of combinations for a given number of items
COMBINA - number of combinations with repitition of n things taken r at a time
DISTANCE - distance between 2 points on the globe
EVEN - number rounded up to the nearest even integer
FACT - factorial of a number
FACTDOUBLE - double factorial of a number
GCD - number rounded up to the nearest even integer
EGCD - greatest common divisor using Euclid’s method
LCM - greatest common divisor of all the values
ELCM - least common multiple using Euclid’s method
MAX - the nth largest distinct value in a dataset
MIN - the nth smallest distinct value in a dataset
MROUND - number rounded to the desired multiple
MULTINOMIAL - ratio of a sum of values to the product of the factorials of those values
MULTINOMIAL_q - ratio of a sum of values to the product of the factorials of those values
ODD - a number rounded up to the nearest odd integer
POWER - float value raised to a power
PRODUCT - product of all the values
PRODUCT38 - product of 2 decimal(38
QUOTIENT - integer portion of a division
QUOTIENT38 - quotient of 2 decimal(38
SERIESSUM - sum of a power series
SERIESSUM_q - sum of a power series
SUMSQ - sum of the squares of all the values
WAVG - weighted average
Equalities
GREATEROF - greater of two values passed into the function
LESSEROF - lesser of two values passed into the function
Formatting
ROMAN - Arabic numeral converted to a Roman numeral
Rounding
CEILING - number rounded up
FLOOR - a number rounded down
INT - number rounded down
ROUNDDOWN - number rounded down
ROUNDUP - number rounded up
TRUNC - number truncated to an integer by removing the fractional part of the number
Numerical Integration
QUAD - evaluate an infinite integral
QUADDE - evaluate an infinite integral
QUADGK - evaluate a finite integral
QUADOSC - evaluate an infinite integral
QUADTS - evaluate a finite integral
Interpolation
BILINEARINTERP - interpolate on a regular 2-dimensional grid
INTERP - straight-line interpolated value of y given x in the array (x
INTERP_q - straight-line interpolated value of y given x in the array (x
INTERP2 - interpolate on a 2-dimensional grid in 3rd normal form
LINEAR - straight-line interpolated value of y given x in the array (x
MONOSPLINE - interpolated value of y given x in the array (x
POLYCOEF - obtain a specific coefficient value from an approximating polynomial for a set of x- and y-values
POLYFIT - coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
POLYFIT_q - coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
POLYINTERP - interpolated value of y given x in the array (x
POLYRSQ - goodness of fit for an approximating polynomial calculated from a series of x- and y-values for a specified number of degrees
POLYVAL - new y-value given a new x-value using the coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
SPLINE - interpolated value of y given x in the array (x
SPLINE_q - interpolated value of y given x in the array (x
Matrix Factorization
LU - LU factorization of an N x N matrix A using partial pivoting
LUdecomp - LU factorization of an N x N matrix A using partial pivoting
LUdecomp_q - LU factorization of an N x N matrix A using partial pivoting
LUdecompN - LU factorization of an N x N matrix A using partial pivoting
LUdecompN_q - LU factorization of an N x N matrix A using partial pivoting
MSYMMEIG - D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix
QR - decompose a string representation of an N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
QRdecomp - decompose a de-normalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
QRdecomp_q - decompose a de-normalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
SYMMEIG - D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix
Matrix Helper Functions
DIAG - vector of the diagonal of the string representation of a matrix
EYE - m-by-n identity matrix
MAPPEND - add columns or rows to an existing matrix variable
MATRIX2STRING - turn table data into a string representation of a matrix
MATRIX2STRING_q - turn table data into a string representation of a matrix
MCOLS - find the number of columns in the string representation of a matrix
MCOLUMN - column from the string representation of a matrix
MINDEX - intersection of a row and a column from the string representation of a matrix
MROW - row from the string representation of a matrix
MROWS - find the number of rows in the string representation of a matrix
MUPDATE - change the values in the string representation of a matrix or to perform element-wise operations on a matrix or some portion of a matrix
NMATRIX2STRING - turn third-normal form table data into a string representation of a matrix
NMATRIX2STRING_q - turn third-normal form table data into a string representation of a matrix
ONES - m-by-n matrix of ones
VANDERMONDE - string representation of a Vandermonde matrix
ZERO - m-by-n matrix of zeroes
Matrix Math
BKSUB - solution to the equation A*x=b
CORRM - correlation matrix
COVM - sample covariance matrix
CROSSPROD - matrix cross-product of 2 matrices
FWDSUB - solution to the equation A*x=b
MATADD - add a value to every element of a matrix or to add 2 matrices of the same dimensions together
MATINVERSE - matrix inverse of a square (N x N) matrix
MATMULT - product of two matrixes or to multiply a matrix by a constant
MATSUB - subtract a value from every element of a matrix or to calculate the difference between 2 matrices of the same dimensions
MCORR - correlation matrix
MCOV - sample covariance matrix
MCROSS - matrix cross-product of 2 matrices
MDETERM - determinant of an N x N matrix
MDETERM_q - determinant of an N x N matrix
MDETERMN - determinant of an N x N matrix
MDETERMN_q - determinant of an N x N matrix
MINVERSE - matrix inverse of a square (N x N) matrix
MINVERSE_q - matrix inverse of a square (N x N) matrix
MINVERSEN - matrix inverse of a square (N x N) matrix
MINVERSEN_q - matrix inverse of a square (N x N) matrix
MMULT - matrix product of two arrays
MMULT_q - matrix product of two arrays
MMULTN - matrix product of two arrays in third-normal form
MMULTN_q - matrix product of two arrays in third-normal form
MNORM - 1-norm
MRANK - rank of a matrix
MTRACE - trace of a de-normalized matrix
MTRACE_q - trace of a de-normalized matrix
MTRACEN - trace of a matrix in third-normal form
MTRACEN_q - trace of a matrix in third-normal form
MTRIL - lower triangular part of the string representation of a matrix
MTRIU - upper triangular part of the string representation of a matrix
SPECRAD - spectral radius of a square matrix
SUMX2MY2 - sum of the differences of the squares in the corresponding elements in 2 matrices
SUMX2PY2 - sum of the sum of the squares in the corresponding elements in 2 matrices
SUMXMY2 - sum of the sqaure of the differences in the corresponding elements in 2 matrices
SUMPRODUCT - sum of the elementwise multiplication of 1 or more matrices
SVD - economy-sized singular value decomposition of an m-x-n matrix A
SVdecomp - economy-sized singular value decomposition of an m-x-n matrix A
TCROSSPROD - matrix cross-product of 2 matrices
TMCROSS - matrix cross-product of 2 matrices
TRANSPOSE - transposed matrix
Matrix Randomization
MRAND - m-by-n matrix of pseudo-random numbers greater than or equal to zero and less than one
MRANDN - m-by-n matrix of pseudo-random numbers from the standard normal distribution
MRORTHO - an m-by-m random orthogonal matrix
Random Number Functions
RAND - random number greater than or equal to zero and less than one
RANDBETWEEN - random integer number between the numbers you specify
RANDNORM - pseudo-random number based on a normal distribution for the given mean and standard deviation
Random Number Generators
RANDBETA - q sequence of random numbers from the beta distribution with two positive shape parameters alpha and beta
RANDBINOM - sequence of random integers from the binomial distribution for a given probability of success and a given number of trials
RANDCAUCHY - sequence of random numbers from a Cauchy distribution for a given location parameter and scale
RANDCHISQ - generate a sequence of random numbers from a chi-squared distribution for a specified degrees of freedom
RANDEXP - sequence of random numbers from an exponential distribution with rate lambda
RANDFDIST - sequence of random numbers from an F-distribution with the degree of freedom parameters df1 and df2
RANDGAMMA - sequence of random numbers from a gamma distribution for the supplied shape and scale parameters
RANDLAPLACE - sequence of random numbers from a LaPlace distribution with supplied location and scales parameters
RANDLOGISTIC - sequence of random numbers from a logistic distribution of the supplied location and scale parameters
RANDNORMAL - a sequence of random numbers from the normal distribution with mean μ and standard deviation σ
RANDPOISSON - sequence of random integers from the Poisson distribution for a given λ
RANDSNORMAL - generate a sequence of random numbers from the standard normal distribution
RANDTDIST - sequence of random numbers from Student's t distribution with for the supplied degrees of freedom
RANDWEIBULL - sequence of random numbers from w Weibull distribution with parameters shape(λ) and scale(κ)
Series Generators
SeriesInt - range of integer values
SeriesFloat - range of floating point values
SeriesDate - range of date values
Trigonometric
ACOSH - inverse hyperbolic cosine of a number
ACOT - arccotangent of a number
ACOTH - hyperbolic arccotangent of a number
ASINH - inverse hyperbolic sine of a number
ATANH - inverse hyperbolic tangent of a number
COSH - hyperbolic cosine of a number
COTH - hyperbolic cotangent of a number
CSC - cosecant of the given angle
CSCH - hyperbolic cosecant of the given angle
SEC - secant of the given angle
SECH - hyperbolic secant of the given angle
SINH - hyperbolic sine of a number
TANH - hyperbolic tangent of a number
Optimization
BFGS - minimum of a function using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method
BRENT - root of a continuous function of one variable
FDERIV - numerical function differentiation for orders n = 1 to 4
GRAD - numerically compute the gradient
HESSIAN - numerically computer the hessian matrix
JACOBIAN - numerically computer the jacobian matrix
NEWTON - root of a univariate function
NLMIN - Nelder-Mead Minimization
SECANT - root of single-variable continuous function
Misc Functions
XLDB_MATH_VERSION - display version information for the XLeratorDB/math module
ALL FUNCTIONS (alpahbetical)
ACOSH - inverse hyperbolic cosine of a number
ACOT - arccotangent of a number
ACOTH - hyperbolic arccotangent of a number
ASINH - inverse hyperbolic sine of a number
ATANH - inverse hyperbolic tangent of a number
BASE - convert an integer to the text representation of that number for a given radix (base)
BASE2DECIMAL - convert the text representation of a number in a given radix (base) to an integer
BFGS - minimum of a function using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method
BILINEARINTERP - interpolate on a regular 2-dimensional grid
BKSUB - solution to the equation A*x=b
BRENT - root of a continuous function of one variable
CEILING - number rounded up
COMBIN - number of combinations for a given number of items
COMBINA - number of combinations with repitition of n things taken r at a time
CORRM - correlation matrix
COSH - hyperbolic cosine of a number
COTH - hyperbolic cotangent of a number
COVM - sample covariance matrix
CROSSPROD - matrix cross-product of 2 matrices
CSC - cosecant of the given angle
CSCH - hyperbolic cosecant of the given angle
DIAG - vector of the diagonal of the string representation of a matrix
DISTANCE - distance between 2 points on the globe
EGCD - greatest common divisor using Euclid’s method
ELCM - least common multiple using Euclid’s method
EVEN - number rounded up to the nearest even integer
EYE - m-by-n identity matrix
FACT - factorial of a number
FACTDOUBLE - double factorial of a number
FDERIV - numerical function differentiation for orders n = 1 to 4
FLOOR - a number rounded down
FWDSUB - solution to the equation A*x=b
GCD - number rounded up to the nearest even integer
GRAD - numerically compute the gradient
GREATEROF - greater of two values passed into the function
HESSIAN - numerically computer the hessian matrix
INT - number rounded down
INTERP - straight-line interpolated value of y given x in the array (x
INTERP_q - straight-line interpolated value of y given x in the array (x
INTERP2 - interpolate on a 2-dimensional grid in 3rd normal form
JACOBIAN - numerically computer the jacobian matrix
LCM - greatest common divisor of all the values
LESSEROF - lesser of two values passed into the function
LINEAR - straight-line interpolated value of y given x in the array (x
LU - LU factorization of an N x N matrix A using partial pivoting
LUdecomp - LU factorization of an N x N matrix A using partial pivoting
LUdecomp_q - LU factorization of an N x N matrix A using partial pivoting
LUdecompN - LU factorization of an N x N matrix A using partial pivoting
LUdecompN_q - LU factorization of an N x N matrix A using partial pivoting
MAPPEND - add columns or rows to an existing matrix variable
MATADD - add a value to every element of a matrix or to add 2 matrices of the same dimensions together
MATINVERSE - matrix inverse of a square (N x N) matrix
MATMULT - product of two matrixes or to multiply a matrix by a constant
MATRIX2STRING - turn table data into a string representation of a matrix
MATRIX2STRING_q - turn table data into a string representation of a matrix
MATSUB - subtract a value from every element of a matrix or to calculate the difference between 2 matrices of the same dimensions
MAX - the nth largest distinct value in a dataset
MCOLS - find the number of columns in the string representation of a matrix
MCOLUMN - column from the string representation of a matrix
MCORR - correlation matrix
MCOV - sample covariance matrix
MCROSS - matrix cross-product of 2 matrices
MDETERM - determinant of an N x N matrix
MDETERM_q - determinant of an N x N matrix
MDETERMN - determinant of an N x N matrix
MDETERMN_q - determinant of an N x N matrix
MIN - the nth smallest distinct value in a dataset
MINDEX - intersection of a row and a column from the string representation of a matrix
MINVERSE - matrix inverse of a square (N x N) matrix
MINVERSE_q - matrix inverse of a square (N x N) matrix
MINVERSEN - matrix inverse of a square (N x N) matrix
MINVERSEN_q - matrix inverse of a square (N x N) matrix
MMULT - matrix product of two arrays
MMULT_q - matrix product of two arrays
MMULTN - matrix product of two arrays in third-normal form
MMULTN_q - matrix product of two arrays in third-normal form
MNORM - 1-norm
MONOSPLINE - interpolated value of y given x in the array (x
MRAND - m-by-n matrix of pseudo-random numbers greater than or equal to zero and less than one
MRANDN - m-by-n matrix of pseudo-random numbers from the standard normal distribution
MRANK - rank of a matrix
MRORTHO - an m-by-m random orthogonal matrix
MROUND - number rounded to the desired multiple
MROW - row from the string representation of a matrix
MROWS - find the number of rows in the string representation of a matrix
MSYMMEIG - D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix
MTRACE - trace of a de-normalized matrix
MTRACE_q - trace of a de-normalized matrix
MTRACEN - trace of a matrix in third-normal form
MTRACEN_q - trace of a matrix in third-normal form
MTRIL - lower triangular part of the string representation of a matrix
MTRIU - upper triangular part of the string representation of a matrix
MULTINOMIAL - ratio of a sum of values to the product of the factorials of those values
MULTINOMIAL_q - ratio of a sum of values to the product of the factorials of those values
MUPDATE - change the values in the string representation of a matrix or to perform element-wise operations on a matrix or some portion of a matrix
NEWTON - root of a univariate function
NLMIN - Nelder-Mead Minimization
NMATRIX2STRING - turn third-normal form table data into a string representation of a matrix
NMATRIX2STRING_q - turn third-normal form table data into a string representation of a matrix
ODD - a number rounded up to the nearest odd integer
ONES - m-by-n matrix of ones
POLYCOEF - obtain a specific coefficient value from an approximating polynomial for a set of x- and y-values
POLYFIT - coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
POLYFIT_q - coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
POLYINTERP - interpolated value of y given x in the array (x
POLYRSQ - goodness of fit for an approximating polynomial calculated from a series of x- and y-values for a specified number of degrees
POLYVAL - new y-value given a new x-value using the coefficients of a polynomial p(x) of degree n that fits the x- and y-values supplied to the function
POWER - float value raised to a power
PRODUCT - product of all the values
PRODUCT38 - product of 2 decimal(38
QR - decompose a string representation of an N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
QRdecomp - decompose a de-normalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
QRdecomp_q - decompose a de-normalized N x N matrix A into the product of an upper triangular matrix R and an orthogonal matrix Q
QUAD - evaluate an infinite integral
QUADDE - evaluate an infinite integral
QUADGK - evaluate a finite integral
QUADOSC - evaluate an infinite integral
QUADTS - evaluate a finite integral
QUOTIENT - integer portion of a division
QUOTIENT38 - quotient of 2 decimal(38
RAND - random number greater than or equal to zero and less than one
RANDBETA - q sequence of random numbers from the beta distribution with two positive shape parameters alpha and beta
RANDBETWEEN - random integer number between the numbers you specify
RANDBINOM - sequence of random integers from the binomial distribution for a given probability of success and a given number of trials
RANDCAUCHY - sequence of random numbers from a Cauchy distribution for a given location parameter and scale
RANDCHISQ - generate a sequence of random numbers from a chi-squared distribution for a specified degrees of freedom
RANDEXP - sequence of random numbers from an exponential distribution with rate lambda
RANDFDIST - sequence of random numbers from an F-distribution with the degree of freedom parameters df1 and df2
RANDGAMMA - sequence of random numbers from a gamma distribution for the supplied shape and scale parameters
RANDLAPLACE - sequence of random numbers from a LaPlace distribution with supplied location and scales parameters
RANDLOGISTIC - sequence of random numbers from a logistic distribution of the supplied location and scale parameters
RANDNORM - pseudo-random number based on a normal distribution for the given mean and standard deviation
RANDNORMAL - a sequence of random numbers from the normal distribution with mean μ and standard deviation σ
RANDPOISSON - sequence of random integers from the Poisson distribution for a given λ
RANDSNORMAL - generate a sequence of random numbers from the standard normal distribution
RANDTDIST - sequence of random numbers from Student's t distribution with for the supplied degrees of freedom
RANDWEIBULL - sequence of random numbers from w Weibull distribution with parameters shape(λ) and scale(κ)
ROMAN - Arabic numeral converted to a Roman numeral
ROUNDDOWN - number rounded down
ROUNDUP - number rounded up
SEC - secant of the given angle
SECANT - root of single-variable continuous function
SECH - hyperbolic secant of the given angle
SeriesDate - range of date values
SeriesFloat - range of floating point values
SeriesInt - range of integer values
SERIESSUM - sum of a power series
SERIESSUM_q - sum of a power series
SINH - hyperbolic sine of a number
SPECRAD - spectral radius of a square matrix
SPLINE - interpolated value of y given x in the array (x
SPLINE_q - interpolated value of y given x in the array (x
SUMPRODUCT - sum of the elementwise multiplication of 1 or more matrices
SUMSQ - sum of the squares of all the values
SUMX2MY2 - sum of the differences of the squares in the corresponding elements in 2 matrices
SUMX2PY2 - sum of the sum of the squares in the corresponding elements in 2 matrices
SUMXMY2 - sum of the sqaure of the differences in the corresponding elements in 2 matrices
SVD - economy-sized singular value decomposition of an m-x-n matrix A
SVdecomp - economy-sized singular value decomposition of an m-x-n matrix A
SYMMEIG - D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix
TANH - hyperbolic tangent of a number
TCROSSPROD - matrix cross-product of 2 matrices
TMCROSS - matrix cross-product of 2 matrices
TRANSPOSE - transposed matrix
TRUNC - number truncated to an integer by removing the fractional part of the number
VANDERMONDE - string representation of a Vandermonde matrix
WAVG - weighted average
XLDB_MATH_VERSION - display version information for the XLeratorDB/math module
ZERO - m-by-n matrix of zeroes
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