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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
All Wiki Pages
Home
ACOSH
ACOT
ACOTH
ASINH
ATANH
BASE
BASE2DECIMAL
BFGS
BILINEARINTERP
BKSUB
BRENT
CEILING
COMBIN
COMBINA
CORRM
COSH
COTH
COVM
CROSSPROD
CSC
CSCH
DIAG
DISTANCE
EGCD
ELCM
EVEN
EYE
FACT
FACTDOUBLE
FDERIV
FLOOR
FWDSUB
GCD
GRAD
GREATEROF
HESSIAN
INT
INTERP
INTERP - 2008
INTERP_q
INTERP2 - 2008
JACOBIAN
LCM
LESSEROF
LINEAR
LINEAR - 2008
LU
LUdecomp
LUdecomp_q
LUdecompN
LUdecompN_q
MAPPEND
MATADD
MATINVERSE
MATMULT
MATRIX2STRING
MATRIX2STRING_q
MATSUB
MAX - 2008
MCOLS
MCOLUMN
MCORR
MCOV
MCOV_q
MCOVN
MCOVN_q
MCROSS
MDETERM
MDETERM_q
MDETERMN
MDETERMN_q
MIN - 2008
MINDEX
MINVERSE
MINVERSE_q
MINVERSEN
MINVERSEN_q
MMULT
MMULT_q
MMULTN
MMULTN_q
MNORM
MONOSPLINE - 2008
MRAND
MRANDN
MRANK
MRORTHO
MROUND
MROW
MROWS
MSYMMEIG
MTRACE
MTRACE_q
MTRACEN
MTRACEN_q
MTRIL
MTRIU
MULTINOMIAL
MULTINOMIAL_q
MUPDATE
NEWTON
NLMIN
NMATRIX2STRING
NMATRIX2STRING - 2008
NMATRIX2STRING_q
ODD
ONES
POLYCOEF - 2008
POLYFIT
POLYFIT_q
POLYINTERP - 2008
POLYRSQ - 2008
POLYVAL - 2008
POWER
PRODUCT
PRODUCT38
QR
QRdecomp
QRdecomp_q
QUAD
QUADDE
QUADGK
QUADOSC
QUADTS
QUOTIENT
QUOTIENT38
RAND
RANDBETA
RANDBETWEEN
RANDBINOM
RANDCAUCHY
RANDCHISQ
RANDEXP
RANDFDIST
RANDGAMMA
RANDLAPLACE
RANDLOGISTIC
RANDNORM
RANDNORMAL
RANDPOISSON
RANDSNORMAL
RANDTDIST
RANDWEIBULL
ROMAN
ROUNDDOWN
ROUNDUP
SEC
SECANT
SECH
SeriesDate
SeriesFloat
SeriesInt
SERIESSUM
SERIESSUM_q
SINH
SPECRAD
SPLINE
SPLINE - 2008
SPLINE_q
SUMPRODUCT
SUMSQ
SUMX2MY2
SUMX2PY2
SUMXMY2
SVD
SVdecomp
SYMMEIG
TANH
TCROSSPROD
TMCROSS
TRANSPOSE
TRUNC
VANDERMONDE
WAVG - 2008
XLDB_MATH_VERSION
ZERO