|
Formulas 5. Mathematical functions
|
|
- abs (x)
- absolute value
- round (x)
- nearest integer; round (1.5) = 2
- floor (x)
- round down: highest integer value not greater than x
- ceiling (x)
- round up: lowest integer value not less than x
- sqrt (x)
- square root: √x, x ≥ 0
- min (x, ...)
- the minimum of a series of numbers, e.g. min (7.2, -5, 3) = -5
- max (x, ...)
- the maximum of a series of numbers, e.g. max (7.2, -5, 3) = 7.2
- imin (x, ...)
- the location of the minimum, e.g. imin (7.2, -5, 3) = 2
- imax (x, ...)
- the location of the maximum, e.g. imax (7.2, -5, 3) = 1
- sin (x)
- sine
- cos (x)
- cosine
- tan (x)
- tangent
- arcsin (x)
- arcsine, -1 ≤ x ≤ 1
- arccos (x)
- arccosine, -1 ≤ x ≤ 1
- arctan (x)
- arctangent
- arctan2 (y, x)
- argument angle
- sinc (x)
- sinus cardinalis: sin (x) / x
- sincpi (x)
- sincπ: sin (πx) / (πx)
- exp (x)
- exponentiation: ex; same as e^x
- ln (x)
- natural logarithm, base e
- log10 (x)
- logarithm, base 10
- log2 (x)
- logarithm, base 2
- sinh (x)
- hyperbolic sine: (ex - e-x) / 2
- cosh (x)
- hyperbolic cosine: (ex + e-x) / 2
- tanh (x)
- hyperbolic tangent: sinh (x) / cosh (x)
- arcsinh (x)
- inverse hyperbolic sine: ln (x + √(1+x2))
- arccosh (x)
- inverse hyperbolic cosine: ln (x + √(x2−1))
- arctanh (x)
- inverse hyperbolic tangent
- sigmoid (x)
- R → (0,1): 1 / (1 + e−x) or 1 − 1 / (1 + ex)
- invSigmoid (x)
- (0,1) → R: ln (x / (1 − x))
- erf (x)
- the error function: 2/√π 0∫x exp(-t2) dt
- erfc (x)
- the complement of the error function: 1 - erf (x)
- randomUniform (min, max)
- a uniform random real number between min (inclusive) and max (exclusive)
- randomInteger (min, max)
- a uniform random integer number between min and max (inclusive)
- randomGauss (μ, σ)
- a Gaussian random real number with mean μ and standard deviation σ
- randomPoisson (mean)
- a Poisson random real number
- randomGamma (shape, rate)
- a random number drawn from a Gamma distribution with shape parameter α and rate parameter β, which is defined as f(x; α, β) = (1 / Γ (α)) βα xα−1 e−β x, for x > 0, α > 0 and β > 0, following the method by Marsaglia & Tsang (2000)
- random_initializeWithSeedUnsafelyButPredictably (seed)
- can be used in a script to create a reproducible sequence of random numbers (warning: this exceptional situation will continue to exist throughout Praat until you call the following function)
- random_initializeSafelyAndUnpredictably ()
- undoes the exceptional situation caused by the previous function
- lnGamma (x)
- logarithm of the Γ function
- gaussP (z)
- the area under the Gaussian distribution between −∞ and z
- gaussQ (z)
- the area under the Gaussian distribution between z and +∞: the one-tailed "statistical significance p" of a value that is z standard deviations away from the mean of a Gaussian distribution
- invGaussQ (q)
- the value of z for which
gaussQ (z) = q
- chiSquareP (
chiSquare, df)
- the area under the χ2 distribution between 0 and chiSquare, for
df degrees of freedom
- chiSquareQ (
chiSquare, df)
- the area under the χ2 distribution between
chiSquare and +∞, for df degrees of freedom: the "statistical significance p" of the χ2 difference between two distributions in df+1 dimensions
- invChiSquareQ (q, df)
- the value of χ2 for which
chiSquareQ (χ2, df) = q
- studentP (t, df)
- the area under the student T-distribution from -∞ to t
- studentQ (t, df)
- the area under the student T-distribution from t to +∞
- invStudentQ (q, df)
- the value of t for which
studentQ (t, df) = q
- fisherP (f, df1, df2)
- the area under Fisher's F-distribution from 0 to f
- fisherQ (f, df1, df2)
- the area under Fisher's F-distribution from f to +∞
- invFisherQ (q, df1, df2)
- the value of f for which
fisherQ (f, df1, df2) = q
- binomialP (p, k, n)
- the probability that in n experiments, an event with probability p will occur at most k times
binomialQ (p, k, n)
- the probability that in n experiments, an event with probability p will occur at least k times; equals 1 -
binomialP (p, k - 1, n)
- invBinomialP (P, k, n)
- the value of p for which
binomialP (p, k, n) = P
invBinomialQ (Q, k, n)
- the value of p for which
binomialQ (p, k, n) = Q
- hertzToBark (x)
- from acoustic frequency to Bark-rate (perceptual spectral frequency; place on basilar membrane): 7 ln (x/650 + √(1 + (x/650)2))
- barkToHertz (x)
- 650 sinh (x / 7)
- hertzToMel (x)
- from acoustic frequency to perceptual pitch: 550 ln (1 + x / 550)
- melToHertz (x)
- 550 (exp (x / 550) - 1)
- hertzToSemitones (x)
- from acoustic frequency to a logarithmic musical scale, relative to 100 Hz: 12 ln (x / 100) / ln 2
- semitonesToHertz (x)
- 100 exp (x ln 2 / 12)
- erb (f)
- the perceptual equivalent rectangular bandwidth (ERB) in hertz, for a specified acoustic frequency (also in hertz): 6.23·10-6 f2 + 0.09339 f + 28.52
- hertzToErb (x)
- from acoustic frequency to ERB-rate: 11.17 ln ((x + 312) / (x + 14680)) + 43
- erbToHertz (x)
- (14680 d - 312) / (1 - d) where d = exp ((x - 43) / 11.17)
phonToDifferenceLimens (x)
- from perceptual loudness (intensity sensation) level in phon, to the number of intensity difference limens above threshold: 30 · ((61/60) x − 1).
differenceLimensToPhon (x)
- the inverse of the previous: ln (1 + x / 30) / ln (61 / 60).
- beta (x, y)
- besselI (n, x)
- besselK (n, x)
For functions with arrays, see Scripting 5.7. Vectors and matrices.
Links to this page
© ppgb 20200801