| ARITHMETIC/ALGEBRA |
| Arithmetic |
BASE
|
Convert an integer to the text representation of that number for a given radix (base).†
Available in XLeratorDB/math 2008 only |
BASE2DECIMAL
|
Convert the text representation of a number in a given radix (base) to an integer.†
Available in XLeratorDB/math 2008 only |
COMBIN
|
Calculate the number of combinations for a given number of items.
|
COMBINA
|
Calculate the number of combinations with repitition of n things taken r at a time.†
Available in XLeratorDB/math 2008 only |
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
|
Calculate the factorial of a number.
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FACTDOUBLE
|
Calculate the double factorial of a number.
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GCD
|
Calculate a number rounded up to the nearest even integer.
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LCM
|
Calculate the greatest common divisor of all the values, or only the DISTINCT values, in the expression.
|
MAX
|
Calculate the nth largest distinct value in a dataset.
Available in XLeratorDB/math 2008 only |
MIN
|
Calculate the nth smallest distinct value in a dataset.
Available in XLeratorDB/math 2008 only |
MROUND
|
Calculate a number rounded to the desired multiple.
|
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.
Available in XLeratorDB/math 2008 only |
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.
|
SERIESSUM
|
Calculate the sum of a power series.†
|
SERIESSUM_q
|
Calculate the sum of a power series.†
|
SUMSQ
|
Calculate the sum of the squares of all the values, or only the DISTINCT values, in the expression.
|
WAVG
|
Calculate the weighted average.
Available in XLeratorDB/math 2008 only |
| |
| Equalities |
GREATEROF
|
Calculate the greater of two values passed into the function.
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LESSEROF
|
Calculate the lesser of two values passed into the function.
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| |
| Rounding |
CEILING
|
Calculate a number rounded up, away from zero, to the nearest multiple of significance.
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FLOOR
|
Calculate a number rounded down, towards zero, to the nearest multiple of significance.
|
INT
|
Calculate a number rounded down, towards zero, to the nearest integer.
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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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TRUNC
|
Calculate a number truncated to an integer by removing the fractional part of the number.
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| |
| Formatting |
ROMAN
|
Calculate an Arabic numeral converted to a Roman numeral, as text.
|
| |
| TRIGONOMETRIC |
ACOSH
|
Calculate the inverse hyperbolic cosine of a number.
|
ACOT
|
Calculate the arccotangent of a number.†
Available in XLeratorDB/math 2008 only |
ACOTH
|
Calculate the hyperbolic arccotangent of a number.†
Available in XLeratorDB/math 2008 only |
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.†
Available in XLeratorDB/math 2008 only |
CSC
|
Calculate the cosecant of the given angle.
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CSCH
|
Calculate the hyperbolic cosecant of the given angle.†
Available in XLeratorDB/math 2008 only |
SEC
|
Calculate the secant of the given angle.
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SECH
|
Calculate the hyperbolic secant of the given angle.†
Available in XLeratorDB/math 2008 only |
SINH
|
Calculate the hyperbolic sine of a number.
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TANH
|
Calculate the hyperbolic tangent of a number.
|
| |
| NUMERICAL INTEGRATION |
QUAD
|
Evaluate an infinite integral.
|
QUADDE
|
Evaluate an infinite integral.
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QUADGK
|
Evaluate a finite integral.
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QUADOSC
|
Evaluate an infinite integral.
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QUADTS
|
Evaluate a finite integral.
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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.
Available in XLeratorDB/math 2008 only |
LINEAR
|
Calculate the straight-line interpolated value of y given x in the array (x, y).
|
MONOSPLINE
|
Calculate the interpolated value of y given x in the array (x, y).
Available in XLeratorDB/math 2008 only |
POLYCOEF
|
Obtain a specific coefficient value from an approximating polynomial for a set of x- and y-values.
Available in XLeratorDB/math 2008 only |
POLYFIT
|
Calculate the coefficients of a polynomial p(x) of degree that fits the x- and y-values supplied to the function.†
(table-valued function) |
POLYFIT_q
|
Calculate the coefficients of a polynomial p(x) of degree n ;that fits the x- and y-values supplied to the function.†
(table-valued function) |
POLYINTERP
|
Calculate the interpolated value of y given x in the array (x, y).
Available in XLeratorDB/math 2008 only |
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.
Available in XLeratorDB/math 2008 only |
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.
Available in XLeratorDB/math 2008 only |
SPLINE
|
Calculate the interpolated value of y given x in the array (x, y).
|
SPLINE_q
|
Calculate the interpolated value of y given x in the array (x, y).†
|
| |
| MATRIX FUNCTIONS |
| Matrix Factorization |
LU
|
Calculate the LU factorization of an N x N matrix using partial pivoting.
|
LUdecomp
|
Calculate the LU factorization of an N x N matrix using partial pivoting.†
|
LUdecomp_q
|
Calculate the LU factorization of an N x N matrix using partial pivoting.†
|
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.†
|
MSYMMEIG
|
Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.†
Available in XLeratorDB/math 2008 only (table-valued function) |
QR
|
Decompose a string representation of an N x N matrix into the product of an upper triangular matrix and an orthogonal matrix Q, such that A=QR.
|
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 matrix Q, such that A = QR.†
|
SYMMEIG
|
Return the D and V matrices representing the eigenvalues and eigenvectors of a real symmetric matrix.†
Available in XLeratorDB/math 2008 only (table-valued function) |
| |
| Matrix Math |
BKSUB
|
Return a solution to the equation A*x=b, when A is an upper-triangular matrix.
|
CORRM
|
Calculate a correlation matrix.†
(table-valued function) |
COVM
|
Calculate a sample covariance matrix.†
(table-valued function) |
CROSSPROD
|
Calculate the matrix cross-product of 2 matrices.
|
FWDSUB
|
Return a solution to the equation A*x=b, when A is a lower-triangular 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
|
Calculate the product of two matrixes or to multiply a matrix by a constant.
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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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MCORR
|
Calculate a correlation matrix.
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MCOV
|
Calculate a sample covariance matrix.
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MCROSS
|
Calculate the matrix cross-product of 2 matrices.†
(table-valued function) |
MDETERM
|
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.†
|
MDETERM_q
|
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.†
|
MDETERMN
|
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.†
|
MDETERMN_q
|
Calculate the determinant of an N x N matrix, where N specifies the number of columns in the matrix.†
|
MINVERSE
|
Calculate the matrix inverse of a square (N x N) matrix.†
|
MINVERSE_q
|
Calculate the matrix inverse of a square (N x N) matrix.†
|
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.†
|
MMULT
|
Calculate the matrix product of two arrays.†
|
MMULT_q
|
Calculate the matrix product of two arrays.†
|
MMULTN
|
Calculate the matrix product of two arrays in third-normal form.†
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MMULTN_q
|
Calculate the matrix product of two arrays in third-normal form.†
|
MNORM
|
Calculate the 1-norm, 2-norm, Infinity-norm, Frobenius norm, and maximum modulus of a matrix.†
Available in XLeratorDB/math 2008 only |
MRANK
|
Calculate the rank of a matrix.†
Available in XLeratorDB/math 2008 only |
MTRACE
|
Calculate the trace of a de-normalized matrix.†
|
MTRACE_q
|
Calculate the trace of a de-normalized matrix.†
|
MTRACEN
|
Calculate the trace of a matrix in third-normal form.†
|
MTRACEN_q
|
Calculate the trace of a matrix in third-normal form.†
|
MTRIL
|
Return the lower triangular part of the string representation of a matrix.
|
MTRIU
|
Return the upper triangular part of the string representation of a matrix.
|
SPECRAD
|
Calculate the spectral radius of a square matrix.†
Available in XLeratorDB/math 2008 only |
SUMPRODUCT
|
Calculate the sum of the elementwise multiplication of 1 or more matrices.†
Available in XLeratorDB/math 2008 only |
SUMX2MY2
|
Calculate the sum of the differences of the squares in the corresponding elements in 2 matrices.†
Available in XLeratorDB/math 2008 only |
SUMX2PY2
|
Calculate the sum of the sum of the squares in the corresponding elements in 2 matrices.†
Available in XLeratorDB/math 2008 only |
SUMXMY2
|
Calculate the sum of the sqaure of the differences in the corresponding elements in 2 matrices.†
Available in XLeratorDB/math 2008 only |
SVD
|
Calculate the economy-sized singular value decomposition of an m-x-n matrix A.
|
SVdecomp
|
Calculate the economy-sized singular value decomposition of an m-x-n matrix A.†
(table-valued function) |
TCROSSPROD
|
Calculate the matrix cross-product of 2 matrices.
|
TMCROSS
|
Calculate the matrix cross-product of 2 matrices.†
(table-valued function) |
TRANSPOSE
|
Return the transposed matrix.
|
| |
| Matrix Randomization |
MRAND
|
Generate an m-by-n matrix of pseudo-random numbers greater than or equal to zero and less than one.
|
MRANDN
|
Generate an m-by-n matrix of pseudo-random numbers from the standard normal distribution.
|
MRORTHO
|
Generate an m-by-m random orthogonal matrix.
Available in XLeratorDB/math 2008 only |
| |
| Matrix Helper Functions |
DIAG
|
Return the vector of the diagonal of the string representation of a matrix.
|
EYE
|
Generate an m-by-n identity matrix.
|
MAPPEND
|
Add columns or rows to an existing matrix variable.†
Available in XLeratorDB/math 2008 only |
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.†
|
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.†
|
MCOLS
|
Find the number of columns in the string representation of a matrix.
|
MCOLUMN
|
Return a column from the string representation of a matrix.
|
MINDEX
|
Return the intersection of a row and a column from the string representation of a matrix.
|
MROW
|
Return a 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.†
Available in XLeratorDB/math 2008 only |
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.
Available in XLeratorDB/math 2008 only |
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.†
|
ONES
|
Generate an m-by-n matrix of ones.
|
VANDERMONDE
|
Return the Vandermonde matrix.
Available in XLeratorDB/math 2008 only |
ZERO
|
Generate an m-by-n matrix of zeroes.
|
| |
| NUMBER/SERIES GENERATORS |
| Random Number Functions |
RAND
|
Calculate a random number greater than or equal to zero and less than one.
|
RANDBETWEEN
|
Calculate a random integer number between the numbers you specify.
|
RANDNORM
|
Calculate a pseudo-random number based on a normal distribution for the given mean and standard deviation.
|
| |
| Random Number Generators |
RANDBETA
|
Generate q sequence of random numbers from the beta distribution with two positive shape parameters alpha and beta.
(table-valued function) |
RANDBINOM
|
Generate a sequence of random integers from the binomial distribution for a given probability of success and a given number of trials.
(table-valued function) |
RANDCAUCHY
|
Generate a sequence of random numbers from a Cauchy distribution for a given location parameter and scale.
(table-valued function) |
RANDCHISQ
|
Generate a sequence of random numbers from a chi-squared distribution for a specified degrees of freedom.
(table-valued function) |
RANDEXP
|
Generate a sequence of random numbers from an exponential distribution with rate lambda.
(table-valued function) |
RANDFDIST
|
Generate a sequence of random numbers from an F-distribution with the degree of freedom parameters df1 and df2.
(table-valued function) |
RANDGAMMA
|
Generate a sequence of random numbers from a gamma distribution for the supplied shape and scale parameters.
(table-valued function) |
RANDLAPLACE
|
Generate a sequence of random numbers from a LaPlace distribution with supplied location and scales parameters.
(table-valued function) |
RANDLOGISTIC
|
Generate a sequence of random numbers from a logistic distribution of the supplied location and scale parameters.
(table-valued function) |
RANDNORMAL
|
Generate a sequence of random numbers from the normal distribution with mean μ and standard deviation σ.
(table-valued function) |
RANDPOISSON
|
Generate a sequence of random integers from the Poisson distribution for a given λ.
(table-valued function) |
RANDSNORMAL
|
Generate a sequence of random numbers from the standard normal distribution.
(table-valued function) |
RANDTDIST
|
Generate a sequence of random numbers from Student's t distribution with for the supplied degrees of freedom.
(table-valued function) |
RANDWEIBULL
|
Generate a sequence of random numbers from w Weibull distribution with parameters shape (λ) and scale (κ).
(table-valued function) |
| |
| Series Generators |
SeriesInt
|
Generate a range of integer values.
(table-valued function) |
SeriesFloat
|
Generate a range of floating point values.
(table-valued function) |
SeriesDate
|
Generate a range of date values.
(table-valued function) |
| |
| Optimization |
BFGS *!*
|
Find the minimum of a function using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.†
Available in XLeratorDB/math 2008 only |
BRENT *!*
|
Find the root of a continuous function of one variable.†
Available in XLeratorDB/math 2008 only |
FDERIV *!*
|
Numerical function differentiation for orders n = 1 to 4 using finite difference approximations.†
Available in XLeratorDB/math 2008 only |
GRAD *!*
|
Numerically compute the gradient.†
Available in XLeratorDB/math 2008 only |
HESSIAN *!*
|
Numerically computer the Hessian matrix.†
Available in XLeratorDB/math 2008 only |
JACOBIAN *!*
|
Numerically compute the Jacobian matrix.†
Available in XLeratorDB/math 2008 only |
NEWTON *!*
|
Find the root of a univariate function.†
Available in XLeratorDB/math 2008 only |
NLMIN *!*
|
Nelder-Mead Minimization.†
Available in XLeratorDB/math 2008 only (table-valued function) |
SECANT *!*
|
Find the root of single-variable continuous function.†
Available in XLeratorDB/math 2008 only |
| |
| MISC FUNCTIONS |
| |
XLDB_MATH_VERSION
|
Display version information for the XLeratorDB/math module.
|