Transcendental Functions

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JSL Syntax Reference • JSL Functions • Transcendental Functions

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Transcendental Functions

Converts the temperature n to the value of explanatory variable in Arrhenius model.

11605/(n+273.15)

Temperature in Celsius.

This is frequently used as a transformation.

Arrhenius Inv(n)

The inverse of the Arrhenius function. Converts the value n to the temperature in Celsius.

11605/(n-273.15)

The value of the converted explanatory variable in Arrhenius model.

This is frequently used as a transformation.

Returns the beta function.

The derivative of the log of the gamma function (LGamma).

The digamma function evaluated at n.

Raises e to the power a.

ea.

Equivalent Expression

e()^a

Returns a more accurate calculation of Exp(x)-1 when x is very small.

Multiplies all numbers 1 through n, inclusive

One and only one argument must be specified.

FFT(list, <named arguments>)

Conducts a Fast Fourier Transformation (FFT) on a list of matrices.

The function takes one matrix, or a list of matrices for complex numbers. The returned value is a list of two matrices with the same dimensions as the first argument.

A list of one or two matrices. If one is provided, it is considered to be the real part. If two are provided, the first is the real part and the second is the imaginary part. Both matrices must have the same dimensions, and both must have more than one row.

Named Arguments

All named arguments are optional.

<<inverse(Boolean)

If true (1), an inverse FFT is conducted.

<<multivariate(Boolean)

If true (1), a multivariate FFT is conducted. If false(0), a spatial FFT is conducted.

<<scale(number)

Multiplies the return values by the specified number.

Fit Transform To Normal(Distribution("name"), Y(vector), <Freq(vector))

Fits a transformation to normality for a vector of data. This includes the Johnson Sl, Johnson Sb, Johnson Su, and GLog distributions.

A list that contains parameter estimates, the covariance matrix, the log-likelihood, AICc, a convergence message, and the transformed values.

Gamma(t, <limit>)

The gamma function of x, or for each row if x is a column:

Gamma(t, limit) is the same integral as Gamma(t) but with the limit of integration that is defined instead of infinity.

a number or a column

optional limit. The default is infinity.

Returns the log gamma function for t, which is the natural log of gamma.

Returns the natural logarithm (base e logarithm) of n.

This function is intended for internal use by derivatives. The Ln(n) function is recommended instead.

Returns the natural logarithm (base e logarithm) of n. An optional second argument lets you specify a different base. For example, Log(n,3) for the base 3 logarithm of n. The Log argument can be any numeric expression. The expression Log(e()) evaluates as 1, and Log(32,2) is 5.

Returns the common (base 10) logarithm of n.

Same as Log(1 + x), except that it is more accurate when x is very small.

Returns log(p/(1-p)).

N Choose K(n, k)

This function returns the number of n things taken k at a time (“n choose k”) and is computed in the standard way using factorials, as

. For example, NChooseK(5,2) evaluates as 10.

This is implemented internally in JMP using lGamma functions. The result is not always an integer.

Raises a to the power of b.

The product of a multiplied by itself b times.

Can be a variable, number, or matrix.

Optional. Can be a variable or a number.

For Power(), the second argument (b) is optional, and the default value is 2. Power(a) returns a2.

Returns the rth root of n, where r defaults to 2 for square root.

SbInv(z, gamma, delta, theta, sigma)

Johnson Sb inverse transformation. If argument is normal, the result is Johnson Sb.

SbTrans(x, gamma, delta, theta, sigma)

Johnson Sb transformation from a doubly bound variable to a standard normal (0, 1) distribution.

Scheffe Cubic(x1, x2)

Returns x1*x2*(x1-x2). This function supports notation for cubic mixture models.

SlInv(z, gamma, delta, theta, sigma)

Johnson Sl inverse transformation. If argument is normal, the result is Johnson Sl.

SlTrans(x, gamma, delta, theta, sigma)

Johnson Sl transformation from a doubly bound variable to a standard normal (0, 1) distribution.

Returns the square root of n.

An efficient computation of the function 1/ [1 + exp(expr)].

Equivalent to Squash(-expr), or

.

SuInv(z, gamma, delta, theta, sigma)

Johnson Su inverse transformation. If argument is normal, the result is Johnson Su.

SuTrans(x, gamma, delta, theta, sigma)

Johnson Su transformation from a doubly bound variable to a standard normal (0, 1) distribution.

Returns the trigamma function evaluated at n. The trigamma function is the derivative of the digamma function.