Mathematics
General Mathematical Functions
Returns the absolute value of x.
Computes the conjugate transpose of a matrix.
Computes the trace of a matrix or a tensor contraction on a multidimensional array.
Standard Library function that returns the average value of an array. Optionally, it can return the average value of one dimension of an array.
Standard Library function that creates an array containing values calculated using a bilinear interpolation to solve for requested points interior to an input grid specified by the input array.
Returns and clears the accumulated math error status.
Returns the complex conjugate of the input variable.
Convolves an array with a kernel (or another array).
Standard Library function that calculates a simple correlation coefficient for two arrays.
Standard Library function that returns the cross product of two three-element vectors.
Computes the cumulative sum over an array or over one dimension of an array.
Standard Library function that computes curvatures on a parametrically defined surface.
Standard Library function that performs a nonlinear least-squares fit to a function of an arbitrary number of parameters.
Standard Library function that calculates the first derivative of a function in x and y.
Differentiates a function represented by an array.
Standard Library function that calculates the determinant of a square, two-dimensional input variable.
Standard Library function that transforms the Euclidean metric for a Jacobian j = Jacobian( f )
Performs general exponentiation.
Returns the prime factorization of an integer greater than 1.
Returns the Fast Fourier Transform for the input variable.
Returns a value indicating if the input variable is finite or not.
Standard Library function that fits a Gaussian curve through a data set.
Returns the greatest common divisor of some integers greater than 0.
Greatest Integer Function. Standard Library function that returns the greatest integer less than or equal to the passed value. Also known as the Floor Function.
Standard Library function that constructs a Hilbert transformation matrix.
Returns the imaginary part of a complex number.
Returns an inverted copy of a square array.
Computes elements of the inter-quartile range for the Tukey Box Plot as defined in "The Elements of Graphing Data," Cleveland, W.S., Hobart Press, 1994, pp. 139-142.
Performs the bit shift operation on bytes, integers, and longwords.
Standard Library function that computes the Jacobian of a function represented by n m-dimensional arrays.
Determines the coefficients for a Lagrange interpolating polynomial associated with a given set of abscissa points and function values.
Returns the least common multiple of some integers greater than 1.
Solves the set of n linear equations Ax =b. (LUBKSB must be used with the procedure LUDCMP to do this.)
Replaces an n-by-n matrix, a, with the LU decomposition of a row-wise permutation of itself.
Iteratively improves the solution vector, x, of a linear set of equations, Ax =b. (You must call the LUDCMP procedure before calling MPROVE.)
Computes binomial coefficients, often stated in words as "N choose K"
Converts input to the nearest integer.
Standard Library function that computes unit normals on a parametrically defined surface.
Standard Library function that evaluates a polynomial function of a variable.
Standard Library function that returns the area of an n-sided polygon, given the vertices of the polygon.
Standard Library function that fits an n-degree polynomial curve through a set of data points using the least-squares method.
Standard Library function that fits an n-degree polynomial curve through a set of data points using the least-squares method.
Returns all positive primes less than or equal to a scalar input.
Returns the product of all elements in an array.
Computes quantiles in a distribution.
Returns one or more normally distributed floating-point pseudo-random numbers with a mean of zero and a standard deviation of 1.
Returns one or more uniformly distributed floating-point pseudo-random numbers over the range 0 < Y < 1.0.
Standard Library function that fits a curve to data using the multiple linear regression method.
Rounds a scalar or an array of FLOAT, DOUBLE, COMPLEX, or DCOMPLEX values to the specified number of decimal points.
Returns the sign of passed values.
Standard Library function that calculates the standard deviation value of an array. (Optionally, it can also calculate the standard deviation over one dimension of an array as a function of the other dimensions.)
Smallest Integer Function. Standard Library function that returns the smallest integer greater than or equal to the passed value. Also known as Ceiling Function.
Performs a Sobel edge enhancement of an image.
Standard Library function that performs a cubic spline interpolation.
Standard Library function that computes the standard deviation and (optionally) the mean of the input array.
Sums an array of n dimensions over one of its dimensions.
Standard Library function that determines the polynomial fit to a surface.
Uses “back substitution” to solve the set of simultaneous linear equations Ax = b, given the u, w, and v arrays created by the SVD procedure from the matrix a.
Performs a singular value decomposition on a matrix.
Standard Library function that uses singular value decomposition method of least-squares curve fitting to fit polynomial function to data.
Compute the generalized tensor product of two arrays.
Sums the elements of an input array.
Uses the QL algorithm with implicit shifts to determine the eigenvalues and eigenvectors of a real, symmetric, tridiagonal matrix.
Reduces a real, symmetric matrix to tridiagonal form, using Householder’s method.
Solves tridiagonal systems of linear equations.
Applies a binary operator to a vector and each vector along one dimension of an array.
Finds the roots of the m-degree complex polynomial, using Laguerre’s method.
Optimization and Regression Routines
Standard Library function that performs a nonlinear least-squares fit to a function of an arbitrary number of parameters.
Calculates the efficient frontier (a set of optimal portfolios).
Standard Library function that fits a Gaussian curve through a data set.
Determines the coefficients for a Lagrange interpolating polynomial associated with a given set of abscissa points and function values.
Minimizes a real valued function of n real variables.
Standard Library function that fits an n-degree polynomial curve through a set of data points using the least-squares method.
Standard Library function that fits an n-degree polynomial curve through a set of data points using the least-squares method.
Standard Library function that fits a curve to data using the multiple linear regression method.
Standard Library function that uses the singular value decomposition method of least-squares curve fitting to fit a polynomial function to data.
Special Mathematical Functions
Calculates the Bessel I function for the input parameter.
Calculates the Bessel J function for the input parameter.
Calculates the Bessel Y function for the input parameter.
Calculates the standard error function of the input variable.
Calculates the gamma function of the input variable.
Evaluates the integral of the Gaussian probability function.
Transcendental Mathematical Functions
Returns the arccosine of x.
Returns the inverse hyperbolic cosine of x.
Returns the natural logarithm of x.
Returns the logarithm to the base 10 of x.
Returns the arcsine of x.
Returns the inverse hyperbolic sine of x.
Calculates the arctangent of the input variable (s).
Returns the inverse hyperbolic tangent of x.
Calculates the cosine of the input variable.
Calculates the hyperbolic cosine of the input variable.
Raises e to the power of the value of the input variable.
Returns the sine of the input variable.
Returns the hyperbolic sine of the input variable.
Calculates the square root of the input variable.
Returns the tangent of the input variable.
Returns the hyperbolic tangent of the input variable.
