Transcendental

Arrhenius

Syntax: y = Arrhenius( tempC )

Description: Returns the non-specific component of the Arrhenius relationship that is then multiplied by the activation energy in the Arrhenius equation. Returns 11604.5181215503 / (tempC + 273.15).

JMP Version Added: Before version 14

Arrhenius( 100 );

Arrhenius Inv

Syntax: tempC = Arrhenius Inv( y )

Description: Returns the inverse of the Arrhenius function, which is (11604.5181215503 / y) - 273.15.

JMP Version Added: Before version 14

Arrhenius Inv( 100 );

Beta

Syntax: z = Beta( x, y )

Description: Returns Beta function of x and y, defined as Gamma( x ) * Gamma( y ) / Gamma( x + y ).

JMP Version Added: Before version 14

Beta( 5, 4 );

Box Cox Inverse Transform

Syntax: x = Box Cox Inverse Transform( y, lambda )

Description: Returns the inverse Box-Cox transformation of the argument.

JMP Version Added: 19

Box Cox Inverse Transform( 3, 2 );

Box Cox Transform

Syntax: y = Box Cox Transform( x, lambda )

Description: Returns the Box-Cox transformation of the argument.

JMP Version Added: 19

Box Cox Transform( 3, 2 );

Cytometry Logicle

Syntax: y = Cytometry Logicle( x, T, W, M, A )

Description: Compute cytometry logicle transformation.

JMP Version Added: Before version 14

Cytometry Logicle( 100, 10000, .15, .45, 0 );

Cytometry Logicle Inverse

Syntax: x = Cytometry Logicle Inverse( y, T, W, M, A )

Description: Compute inverse cytometry logicle transformation.

JMP Version Added: Before version 14

Cytometry Logicle Inverse( 100, 10000, .15, .45, 0 );

Digamma

Syntax: y = Digamma( x )

Description: Returns the digamma function evaluated at x, where the digamma function is the derivative of the logarithm of the gamma function.

JMP Version Added: Before version 14

Digamma( 5 );

Exp

Syntax: y = Exp( <x=1> )

Description: Returns e raised to the x power. Argument can be a number, matrix, or list of numbers.

JMP Version Added: Before version 14

Round( Exp( 1 ), 5 );

ExpM1

Syntax: y = ExpM1( x )

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

JMP Version Added: Before version 14

Show( ExpM1( 1.1e-18 ), Exp( 1.1e-18 ) - 1 );

FFT

Syntax: ret = FFT( L, <<inverse( 0 ), <<multivariate( 0 ), <<scale( 1.0 ) )

Description: Conducts Fast Fourier Transformation (FFT) on argument L, a required list consisting of real and imaginary parts of the data in matrix forms. If L consists of only one matrix, the matrix is considered to be the real part. If L consists of two matrices, the first is the real part, and the second is the imaginary part. The two matrices must have the same dimensions and must have more than one row. There are three optional arguments. The inverse argument determines whether to conduct inverse FFT. The multivariate argument determines whether to conduct spatial or multivariate FFT. The scale argument determines the constant by which the return values should be multiplied. Return value is a list of two matrices with the same dimensions as the first input argument.

JMP Version Added: Before version 14

FFT( {[1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 2, 3, 6, 6, 2, 2, 2, 3, 3, 3]} );
A = [1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 2, 3, 6, 6, 2, 2, 2, 3, 3, 3];
res = FFT( {A} );
res = FFT( {A}, <<Inverse( 1 ) );
res = FFT( {A}, <<multivariate( 1 ) );
res = FFT( FFT( {A} ), <<Inverse( 1 ), <<scale( 1 / 20 ) );
B = FFT( {A} );
FFT( B, <<Inverse( 1 ), <<scale( 1 / 20 ) );
Afun = Function( {},
    [1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 2, 3, 6, 6, 2, 2, 2, 3, 3, 3]
);
FFT( FFT( {Afun()} ), <<Inverse( 1 ), <<scale( 1 / 20 ) );
Afun = Function( {},
    {[1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 2, 3, 6, 6, 2, 2, 2, 3, 3, 3]}
);
FFT( FFT( Afun() ), <<Inverse( 1 ), <<scale( 1 / 20 ) );
A = [1 3, 2 4, 3 1, 4 3, 4 5, 5 2, 5 7, 6 9, 7 5, 7 3, 2 7, 3 4, 6 7, 6 4, 2 7, 2 4, 2 6, 3 5,
3 6, 3 1];
res = FFT( {A} );
res = FFT( {A}, <<multivariate( 1 ) );
res = FFT( FFT( {A} ), <<Inverse( 1 ), <<scale( 1 / 40 ) );
res = FFT(
    FFT( {A}, <<multivariate( 1 ) ),
    <<multivariate( 1 ),
    <<Inverse( 1 ),
    <<scale( 1 / 20 )
);
A = [1 3 1,
2 4 3,
3 1 2,
4 3 3,
4 5 9,
5 2 8,
5 7 6,
6 9 5,
7 5 3,
7 3 2,
2 7 1,
3 4 3,
6 7 3,
6 4 2,
2 7 4,
2 4 1,
2 6 5,
3 5 1,
3 6 2,
3 1 9];
res = FFT( {A} );
res = FFT( {A}, <<multivariate( 1 ) );
FFT( FFT( {A} ), <<Inverse( 1 ), <<scale( 1 / 60 ) );
fin = FFT(
    FFT( {A}, <<multivariate( 1 ) ),
    <<Inverse( 1 ),
    <<multivariate( 1 ),
    <<scale( 1 / 20 )
);
Show( fin );

Factorial

Syntax: y = Factorial( x )

Description: Returns the factorial of x, which is the same as Gamma( x + 1 ). If x is an integer, the result is the product 1 * 2 * ... * x.

JMP Version Added: Before version 14

Factorial( 5 );

Fit Transform To Normal

Syntax: result = Fit Transform To Normal( Distribution(name), Y(vector), <Freq(vector)> )

Description: Fits a transformation to normality for a vector of data. This includes the Johnson Sl, Johnson Sb, Johnson Su, and GLog distributions. The function returns a list containing parameter estimates, covariance matrix, log-likelihood, AICc, a convergence message, and transformed values.

JMP Version Added: Before version 14

datavec = [-3.7975076, 0.48221038, -1.3082712, -1.860647, -6.9470789, -17.237024, -19.470857,
-6.1855986, 2.16525629, -30.990061];
freqvec = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2];
As Table( datavec || freqvec );
Column( 1 ) << set name( "x" );
Column( 2 ) << set name( "freq vec" );
Distribution(
    Freq( :freq vec ),
    Continuous Distribution( Column( :x ), Fit Distribution( GLog ) )
);
results = Fit Transform To Normal( Distribution( "glog" ), Y( datavec ), freq( freqvec ) );
Show( results );

Gamma

Syntax: y = Gamma( x, <limit> )

Description: Returns Gamma function of x, defined as the integral of z^(x-1)*exp(-z) dz from 0 to ∞. If limit is present, an incomplete Gamma is computed using that limit of integration.

JMP Version Added: Before version 14

Gamma( 5 );

LGamma

Syntax: y = LGamma( x )

Description: Returns the natural logarithm of the Gamma function of x. Useful when Gamma(x) is too large to use directly.

JMP Version Added: Before version 14

LGamma( 5 );

Ln

Syntax: y = Ln( x )

Description: Returns the natural logarithm of x.

JMP Version Added: Before version 14

Ln( Exp( 2 ) );

Log

Syntax: y = Log( x, <b> )

Description: Returns the base-b logarithm of x or the natural logarithm of x if b is not specified.

JMP Version Added: Before version 14

Log( 256, 2 );

Log10

Syntax: y = Log10( x )

Description: Returns the base 10 logarithm of x.

JMP Version Added: Before version 14

Log10( 100 );

Log1P

Syntax: y = Log1P( x )

Description: Returns a more accurate calculation of Log(1 + x) when x is very small.

JMP Version Added: Before version 14

Log1P( 1e-6 );

Logist

Syntax: y = Logist( x )

Description: Returns 1 / (1 + Exp( -x )), which converts a number in the domain -∞...+∞ into range 0...1. The Logist() function is useful in logistic regression.

JMP Version Added: Before version 14

Logist( 2 );

Logist Percent

Syntax: y = Logist Percent( x )

Description: Logist function with result scaled 0 to 100.

JMP Version Added: Before version 14

Logist Percent( 10 );

Logit

Syntax: y = Logit( p )

Description: Returns the logit of p, which is defined as log(p / (1 - p)).

JMP Version Added: Before version 14

Logit( 0.95 );

Logit Percent

Syntax: y = Logit Percent( p )

Description: Logit function with argument 0 to 100, rather than 0 to 1.

JMP Version Added: Before version 14

Logit Percent( 95.0 );

N Choose K

Syntax: m = N Choose K( n, k )

Description: Returns n! / (k! * (n - k)!), which is the number of ways to choose k items out of n, ignoring order.

JMP Version Added: Before version 14

N Choose K( 5, 3 );

Power

Syntax: z = x ^ y; z = Power( x, <y=2> )

Description: Returns x raised to the y power. If x is negative, y must be an integer.

JMP Version Added: Before version 14

Power( 2, 5 );

Root

Syntax: y = Root( x, <n=2> )

Description: Returns the nth root of x.

JMP Version Added: Before version 14

Round( Root( 2, 3 ), 4 ) /* cube root */;

SHASHInv

Syntax: x = SHASHInv( z, gamma, delta, theta, sigma )

Description: Transforms a standard normal variable to a sinh-arcsinh (SHASH) distributed variable.

JMP Version Added: 14

gamma = 1;
delta = .5;
theta = -1;
sigma = 2;
x = 3;
result1 = SHASHTrans( x, gamma, delta, theta, sigma );
x1 = SHASHInv( result1, gamma, delta, theta, sigma );
x2 = SinH( (ArcSinH( result1 ) - gamma) / delta ) * sigma + theta;
Show( x1, x2 );

SHASHTrans

Syntax: z = SHASHTrans( x, gamma, delta, theta, sigma )

Description: Transforms a sinh-arcsinh (SHASH) distributed variable to a standard normal distributed variable. The SHASH transformation can be used to create more normally distributed data.

JMP Version Added: 14

gamma = 1;
delta = .5;
theta = -1;
sigma = 2;
x = 3;
result1 = SHASHTrans( x, gamma, delta, theta, sigma );
result2 = SinH( gamma + delta * ArcSinH( (x - theta) / sigma ) );
Show( result1, result2 );

SbInv

Syntax: x = SbInv( z, gamma, delta, theta, sigma )

Description: Transforms a standard normal variable to a double bounded Johnson variable.

JMP Version Added: Before version 14

SbInv( 1.96, 1.5, 2, 1, 2 );

SbTrans

Syntax: z = SbTrans( x, gamma, delta, theta, sigma )

Description: Transforms a double bounded Johnson variable to a standard normal variable.

JMP Version Added: Before version 14

Round( SbTrans( 2.114, 1.5, 2, 1, 2 ), 2 );

Scheffe Cubic

Syntax: y = Scheffe Cubic( x1, x2 )

Description: Evaluates as x1x2(x1-x2); used to support modeling notation for cubic mixture models.

JMP Version Added: Before version 14

Scheffe Cubic( [1, -1, 1, -1, 1], [-1, -1, 1, 1, -1] );

SlInv

Syntax: x = SlInv( z, gamma, delta, theta, <sigma=1> )

Description: Transforms a standard normal variable to a Johnson SL variable.

JMP Version Added: Before version 14

SlInv( 1.96, 1.5, 2, 1 );

SlTrans

Syntax: z = SlTrans( x, gamma, delta, theta, <sigma=1> )

Description: Transforms a Johnson SL variable to a standard normal variable.

JMP Version Added: Before version 14

Round( SlTrans( 2.259, 1.5, 2, 1 ), 2 );

Sqrt

Syntax: y = Sqrt( x )

Description: Returns the positive square root of the x argument, which can be a number, matrix, or list of numbers.

JMP Version Added: Before version 14

Round( Sqrt( 2 ), 4 );

Squash

Syntax: y = Squash( x )

Description: Returns 1 / (1 + Exp( x )), which converts a number in the domain -∞...+∞ into range 1...0. The Squash() function is useful in logistic regression.

JMP Version Added: Before version 14

Squash( 10 );

Squish

Syntax: y = Logist( x )

Description: Returns 1 / (1 + Exp( -x )), which converts a number in the domain -∞...+∞ into range 0...1. The Logist() function is useful in logistic regression.

JMP Version Added: Before version 14

Logist( 2 );

SuInv

Syntax: x = SuInv( z, gamma, delta, theta, sigma )

Description: Transforms a standard normal variable to an unbounded Johnson variable.

JMP Version Added: Before version 14

SuInv( 1.96, 1.5, 2, 1, 2 );

SuTrans

Syntax: z = SuTrans( x, gamma, delta, theta, sigma )

Description: Transforms an unbounded Johnson variable to a standard normal variable.

JMP Version Added: Before version 14

Round( SuTrans( 1.46, 1.5, 2, 1, 2 ), 2 );

Trigamma

Syntax: y = Trigamma( x )

Description: Returns the trigamma function evaluated at x, where the trigamma function is the derivative of the digamma function.

JMP Version Added: Before version 14

Trigamma( 5 );