.TRANSFORM.Math

Contents

NameDescription
ComplexMath
Examples
cubicRoots_RealAnalytical solution for the real roots of a cubic equation (a*x^3+b*x^2+c*x+d=0)
cubicRoots_SingleRealReturns a single real root within the user defined range for a cubic equation (a*x^3+b*x^2+c*x+d=0)
spliceSigmoidSmoothing algorithm using the sigmoid function
Sigmoid
spliceTanhSpline interpolation of two functions using the hyperbolic tangent
spliceTanh_derDerivative of spliceTanh
smoothMax
smoothMax_der
logspaceCreate log spaced vector
logspace_dxCreate log spaced vector and only return the spacing between points
BesselJ
BesselY
gamma_LanczosGamma function using the Lanczos approximation
factorialCalculates the factorial of integer n
regRoot_cinterpSquare root function with cubic interpolation near 0
regRoot_cinterp_der
QuadraticCoefficientsReturns the coefficients of a quadritic equation a*x + b*x^2 + c*x^3 from three number pairs (x,y)
variableFactorCalcutes a matrix f from 0 to 1 that relates a ratio of variable to fixed values
meanFactorCalcutes a matrix fA and f that returns the calculates a mean value based on a ratio of variable to fixed values using variableFactor
interpolate_wLimitInterpolate in a vector
interpolate2DInterpolate a 2D data table
linspace_1DCreate a linearly spaced 1D array and the special case when n = 1 the average is returned
linspaceRepeat_1DCreate [m] linearly spaced 1D arrays stored in a [n,m] matrix and the special case when n = 1 the average is returned
linspaceRepeat_1D_multiCreate [m] linearly spaced 1D arrays stored in a [n,m] matrix and the special case when n = 1 the average is returned
linspace_2DcornerCreate a linearly spaced 2D matrix from the linear interpolation of 4 corner values
linspace_2DedgeCreate a linearly spaced 2D matrix from the linear interpolation of 4 edge values
linspaceRepeat_2DedgeCreate [m] linearly spaced 2D matrix stored in a [n1,n2,m] matrix from the linear interpolation of 4 edge values
fillArray_1Dcreate a matrix from an array of values (i.e., fill(val[:],n)) for 1 dimension
fillArray_1D_2nscreate a matrix from an array of values (i.e., fill(val[:],n,n2)) for 1 dimension
fillArray_2Dcreate a matrix from an array of values (i.e., fill(val[:],n1,n2)) for 2 dimensions
fillArray_3Dcreate a matrix from an array of values (i.e., fill(val[:],n1,n2,n3)) for 3 dimensions
ArrheniusEquationArrehnius equation y = A*exp(-(Ea/RT)^b)
cumulativeSum
mean
cubicHermiteSpline
cubicHermiteSplineLinearExtrapolationInterpolate using a cubic Hermite spline with linear extrapolation
splineDerivativesFunction to compute the derivatives for cubic hermite spline interpolation
isMonotonicReturns true if the argument is a monotonic sequence
smoothMax_spliceOnce continuously differentiable approximation to the maximum function using splice
smoothMin_spliceOnce continuously differentiable approximation to the minimum function using a splice function
regStepApproximation of a general step, such that the approximation is continuous and differentiable
replaceArrayValuesReplace array values with user specified values at specified index
indexFilterReturn array of indices from source contained or not contained in target
integral_TrapezoidalRuleIntegral of array y(x) using the trapezoidal rule