Matlib

object Matlib extends Mathematics with Probabilities with Statistics with Trigonometry

Since: 2012-06-07

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Trigonometry, Statistics, Probabilities, Mathematics, AnyRef, Any

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final def !=(arg0: Any): Boolean
Definition Classes
AnyRef → Any
final def ##(): Int
Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean
Definition Classes
AnyRef → Any
val HALF_PI: Double
Definition Classes
Trigonometry
def Schrödinger[A, B](a: A, b: B): Either[A, B]
Is the cat dead or alive?
Is the cat dead or alive?
A
The type of the alive cat
B
The type of the dead cat
a
The alive cat
b
The deat bat
returns
A box ... is the cat dead or alive?
Definition Classes
Probabilities
val TAU: Double
Definition Classes
Trigonometry
def add(a: Array[Double], b: Array[Double]): Array[Double]
Element by element addition
Element by element addition
a
THe first array
b
The second array
returns
An array that is the element by element summation of a to b
Definition Classes
Mathematics
final def asInstanceOf[T0]: T0
Definition Classes
Any
def clone(): AnyRef
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws(classOf[java.lang.CloneNotSupportedException]) @native() @HotSpotIntrinsicCandidate()
def combinations(n: BigInt, c: BigInt): BigInt
Computes the possible number of distinct combinations of n items into groups of c items
Computes the possible number of distinct combinations of n items into groups of c items
n
The number of items
c
The number of items in a set
returns
The number of combinations of n items in c sets.
Definition Classes
Probabilities
def corr(x: Array[Double], y: Array[Double]): Double
Calculate Pearson's correlation coefficient.
Calculate Pearson's correlation coefficient. This is also known as the Correlation Coefficient or the Pearson product-moment correlation coefficient
x
x values
y
y values
returns
correlation coefficient
Definition Classes
Mathematics
def corrcoef(x: Array[Double], y: Array[Double]): Double
Definition Classes
Mathematics
def cot(radians: Double): Double
Cotangent
Cotangent
Definition Classes
Trigonometry
def csc(radians: Double): Double
Cosecant
Cosecant
Definition Classes
Trigonometry
def cumsum(data: Array[Double]): Array[Double]
Cumulative sum of elements
Cumulative sum of elements
data
values
returns
An array containing the cumulative sum of data
Definition Classes
Mathematics
def diff(x: Array[Double]): Array[Double]
Definition Classes
Mathematics
def divide(a: Array[Double], b: Array[Double]): Array[Double]
Element by element division
Element by element division
a
THe first array
b
The second array
returns
An array that is the element by element summation of a to b
Definition Classes
Mathematics
def dot(a: Array[Double], b: Array[Double]): Double
Calculates the dot product between 2 arrays (The dot is the project of b onto a).
Calculates the dot product between 2 arrays (The dot is the project of b onto a). a and b must be the same size
a
The first array
b
THe second array (b will be projected onto a)
returns
The dot product. (b projected onto a)
Definition Classes
Mathematics
final def eq(arg0: AnyRef): Boolean
Definition Classes
AnyRef
def equals(arg0: AnyRef): Boolean
Definition Classes
AnyRef → Any
def extrap1(x: Array[Double], y: Array[Double], xi: Array[Double]): Array[Double]
Linear Extrapolation.
Linear Extrapolation. Recipe is from
x
array of x values
y
array of y values
xi
array of x values to interpolate to
returns
array of y values at xi
Definition Classes
Mathematics
See also
https://stackoverflow.com/questions/32076041/extrapolation-in-java
def factorial(n: BigInt, result: BigInt = 1): BigInt
Computes factorial.
Computes factorial. We need this for imaging in order because the number of permutations of n distinct objects is equal to the factorial of n
n
The value for the factorial
result
The accumulator of the previous iteration of factorial. Normally developers do not supply this value. Instead the default value of 1 is used.
returns
factorial of n
Definition Classes
Probabilities
def fft(data: Array[Double]): Array[Complex[Double]]
Discrete Fourier transform
Discrete Fourier transform
data
values
returns
The fft of data
Definition Classes
Mathematics
def fibonacci(x: Int): BigInt
x
The integer of interest
returns
The fibonacci value for the given integer
Definition Classes
Mathematics
def fibonacciStream(x: Int): Stream[BigInt]
Create a stream of fibonacci numbers up to the given integer
Create a stream of fibonacci numbers up to the given integer
x
The integer of interest
returns
A Stream of numbers in a fibonacci sequence up to the fibonacci number for x
Definition Classes
Mathematics
def find[A](data: Array[A], predicate: (A) => Boolean): Seq[Int]
def fix(x: Double): Double
Round towards zero
Round towards zero
x
The number
returns
The number rounded towars zero
Definition Classes
Mathematics
def fzero(fn: (Double) => Double, min: Double, max: Double): Double
Single variable nonlinear zero finding over an interval
Single variable nonlinear zero finding over an interval
fn
The function whose zero we're searching for
min
The interval minimum
max
The interval maximum
returns
The x value of zero for the fn
Definition Classes
Mathematics
def fzero(fn: (Double) => Double, start: Double): Double
Single variable nonlinear zero finding
Single variable nonlinear zero finding
fn
The function whose zero we're searching for
start
A starting quess for the location of the zero
returns
The x value of zero for the fn
Definition Classes
Mathematics
def gcd(a: Int, b: Int): Int
Greatest common denominator
Greatest common denominator
Definition Classes
Mathematics
final def getClass(): Class[_ <: AnyRef]
Definition Classes
AnyRef → Any
Annotations
@native() @HotSpotIntrinsicCandidate()
def hashCode(): Int
Definition Classes
AnyRef → Any
Annotations
@native() @HotSpotIntrinsicCandidate()
def hist(data: Array[Double], centers: Array[Double], inclusive: Boolean = false): Array[Double]
Bins elements into bins with specified centers
Bins elements into bins with specified centers
data
The data to bin
centers
The bins where each value represents a center of a bin. They MUST be ordered or the data will not be valid.
inclusive
if true values outside of the centers are excluded from results. The default is false
returns
The histogram of data
Definition Classes
Probabilities
def histc(data: Array[Double], edges: Array[Double]): Array[Double]
Bins elements using specified edges
Bins elements using specified edges
data
The data to bin
edges
array defining the edges of each bin
returns
The histogram of data
Definition Classes
Probabilities
def interp1(x: Array[Double], y: Array[Double], xi: Array[Double]): Array[Double]
Linear interpolation
Linear interpolation
x
array of x values
y
array of y values
xi
array of x values to interpolate to
returns
array of y values at xi
Definition Classes
Mathematics
Exceptions thrown
final def isInstanceOf[T0]: Boolean
Definition Classes
Any
def isprime[A](n: A)(implicit arg0: Numeric[A]): Boolean
returns
true if the number is a prime number. False otherwise
Definition Classes
Mathematics
def linspace(d1: Double, d2: Double, n: Int): Array[Double]
generates n linearly-spaced points between d1 and d2.
generates n linearly-spaced points between d1 and d2.
d1
The min value
d2
The max value
n
The number of points to generated
returns
an array of lineraly space points.
Definition Classes
Mathematics
def logspace(d1: Double, d2: Double, n: Int): Array[Double]
generates n logarithmically-spaced points between d1 and d2.
generates n logarithmically-spaced points between d1 and d2.
d1
The min value
d2
The max value
n
The number of points to generated
returns
an array of lineraly space points.
Definition Classes
Mathematics
def mad(data: Array[Double]): Array[Double]
Mean absolute deviation
Mean absolute deviation
data
data
returns
array of mean absolute deviation
Definition Classes
Statistics
def mean(data: Array[Double]): Double
data
data
returns
mean value of data
Definition Classes
Statistics
def median(data: Array[Double]): Double
data
data
returns
median value of data
Definition Classes
Statistics
def mod(a: Double, b: Double): Double
Modulus after divistion.
Modulus after divistion. THis just calls the % operator; it's included to make porting Matlab code more familiar.
a
a value
b
the other value
returns
the modulus
Definition Classes
Mathematics
def multiply(a: Array[Double], b: Array[Double]): Array[Double]
Element by element multiplication
Element by element multiplication
a
THe first array
b
The second array
returns
An array that is the element by element summation of a to b
Definition Classes
Mathematics
final def ne(arg0: AnyRef): Boolean
Definition Classes
AnyRef
def near(data: Array[Double], key: Double, inclusive: Boolean = true): Int
Find the index of the array nearest to the value.
Find the index of the array nearest to the value. The values array can contain only unique values. If it doesn't the first occurence of a value in the values array is the one used, subsequent duplicate are ignored. If the value falls outside the bounds of the array, null is returned
data
Values to search through for the nearest point
key
THe value to search for the nearest neighbor in the array
inclusive
If true the key must be within the values array
returns
The index of the array value nearest the value. -1 will be returned if the key is outside the array values
Definition Classes
Mathematics
def norm(x: Array[Double]): Double
Compute the norm.
Compute the norm. Treats the array as a vector of values.
x
The array
returns
The norm (aka magnitude) of the array.
Definition Classes
Mathematics
def normalizeAngle(radians: Double): Double
Adjusts an angle in radians to fall between 0 and 2 * PI
Adjusts an angle in radians to fall between 0 and 2 * PI
returns
The same angle but adjusted so that if falls between 0 and 2 PI
Definition Classes
Trigonometry
final def notify(): Unit
Definition Classes
AnyRef
Annotations
@native() @HotSpotIntrinsicCandidate()
final def notifyAll(): Unit
Definition Classes
AnyRef
Annotations
@native() @HotSpotIntrinsicCandidate()
def prod(data: Array[Double]): Double
data
The data array
returns
The product of the elements of data
Definition Classes
Mathematics
def quantile(data: Array[Double], p: Array[Double], method: Int): Array[Double]
Empirical quantile (percentile).
Empirical quantile (percentile). Like prctile in Matlab's statistics toolbox
data
The data samples
p
The percentiles of interest (0 <= p <= 1)
method
The method for calculating the emperical quantile:
1. Interpolation so that F(X_(k)) == (k-0.5)/n. (DEFAULT) 2. Interpolation so that F(X_(k)) == k/(n+1). 3. Based on the empirical distribution.
Definition Classes
Probabilities
def quantile(data: Array[Double], p: Array[Double]): Array[Double]
Definition Classes
Probabilities
def quantile(data: Array[Double], p: Double, method: Int): Double
Definition Classes
Probabilities
def quantile(data: Array[Double], p: Double): Double
Definition Classes
Probabilities
def relativecdf(y: Array[Double], y0: Array[Double], r: Array[Double]): Array[Double]
Calculate the relative cumulative density between 2 sample sets.
Calculate the relative cumulative density between 2 sample sets. Internally the CDF is calculated using the empirical CDF, tocdf
y
Samples from the comparison outcome space
y0
Samples from a reference outcome space
r
The relative density at r
returns
The relative cumaltive density
See also
‘‘Relative Distribution Methods in the Social Sciences’’ by Mark S. Handcock and Martina Morris, Springer-Verlag, 1999,Springer-Verlag, ISBN 0387987789
def relativepdf(y: Array[Double], y0: Array[Double], r: Array[Double]): Array[Double]
Calculate relative probability density between 2 sample sets.
Calculate relative probability density between 2 sample sets. Internally the PDF is calculated using scilube.probability.KDE.
y
Samples from the comparison outcome space
y0
Samples from a reference outcome space
r
The proportion (e.g. probability of y / y0 values relative to q0(r) where 0 <- r(n) <= 1
returns
The relative density at r
See also
‘‘Relative Distribution Methods in the Social Sciences’’ by Mark S. Handcock and Martina Morris, Springer-Verlag, 1999,Springer-Verlag, ISBN 0387987789
def rem(x: Double, y: Double): Double
x
a value
y
another value
returns
Remainder after division
Definition Classes
Mathematics
def sec(radians: Double): Double
Secant
Secant
Definition Classes
Trigonometry
def sign(x: Double): Int
Signum function
Signum function
x
a value
returns
The sign of x (-1 or 1)
Definition Classes
Mathematics
def sort[A](x: Array[A])(implicit arg0: Ordering[A]): Seq[Int]
This does not actually sort, rather it returns the sort indices of an array.
This does not actually sort, rather it returns the sort indices of an array. This provides sort indices like Matlab's sort method. You can use the returned value to sort the array like so: import scala.math.Ordering._ // import implicit orderings val a = Array(1, 3, 2) val i = Matlab.sort(a) val b = Matlib.subset(a, i);
def sort[A](x: Array[A], lt: (A, A) => Boolean): Seq[Int]
This does not actually sort, rather it returns the sort indices of an array.
This does not actually sort, rather it returns the sort indices of an array. This provides sort indices like Matlab's sort method. You can use the returned value to sort the array like so: val a = Array(1, 3, 2) val i = Matlab.sort(a, (i: Int, j: Int) => i < j) val b = Matlib.subset(a, i);
A
The type of the values to be sorted
x
The array to sort
returns
The indices of the correct sort order
def std(data: Array[Double]): Double
Standard deviation is a statistical measure of spread or variability.The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean.
Standard deviation is a statistical measure of spread or variability.The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean.
std normalizes values by N, where N is the sample size. This the Population Standard Deviation
data
data
returns
standard deviation of data
Definition Classes
Statistics
def subset[A](data: Array[A], idx: Seq[Int])(implicit arg0: ClassTag[A]): Array[A]
Extract a subset of an Array.
Extract a subset of an Array. Example:
```
// MATLAB equivalent:
// a = 1:10
// idx = [2 3 5 6]
// b = a(idx)
val a = (0 to 10).toArray
val idx = Seq(2, 3, 5, 6)
val b = Matlib.subset(a, idx)
```
NOTE: This does no bounds checking!! Makes sure your indices are between 0 and data.size
A
The Type of the data array
data
The array to subset
idx
Indices into data to exist in the subset
returns
An a subset of data (e.g. In Matlab
def subtract(a: Array[Double], b: Array[Double]): Array[Double]
Element by element subtraction
Element by element subtraction
a
THe first array
b
The second array
returns
An array that is the element by element summation of a to b
Definition Classes
Mathematics
def sum(x: Array[Double]): Double
Definition Classes
Mathematics
final def synchronized[T0](arg0: => T0): T0
Definition Classes
AnyRef
def toString(): String
Definition Classes
AnyRef → Any
def tocdf(data: Array[Double]): (Array[Double], Array[Double])
Emperical cumulative density function.
Emperical cumulative density function. This makes no assumptions about the data
data
Data set to generate a CDF for
returns
A tuple of (cdf, x) where cdf is the cumulative density defined over x
def trapz(x: Array[Double], y: Array[Double]): Double
Trapezoidal integration
def unique(a: Array[Double], occurrence: String = "last"): (Array[Double], Array[Int], Array[Int])
Same as Matlab's unique.
Same as Matlab's unique. For performance, if you just need the unique values use
```
a.distinct
```
. This method also returns the order indices.
a.distinct }}} This method also returns the order indices.
a
An array
occurrence
The default value is occurrence = "last", which returns the index of the last occurrence of each repeated value (or row) in A, while occurrence = 'first' returns the index of the first occurrence of each repeated value (or row) in A
returns
A tuple of (c, ia, ic). c is the same values as in A but with no repetitions. C will be sorted. ia and ic are index arrays such that c = a(ia) and a = c(ic)
Definition Classes
Mathematics
def variance(data: Array[Double]): Double
Population Variance (like Matlab's var function but var is a keyword in Scala so I couldn't use it)
Population Variance (like Matlab's var function but var is a keyword in Scala so I couldn't use it)
data
data
returns
variance of data
Definition Classes
Statistics
final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws(classOf[java.lang.InterruptedException])
final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
@throws(classOf[java.lang.InterruptedException]) @native()
final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

def finalize(): Unit
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws(classOf[java.lang.Throwable]) @Deprecated @deprecated
Deprecated
(Since version ) see corresponding Javadoc for more information.

Packages

Matlib

object Matlib extends Mathematics with Probabilities with Statistics with Trigonometry

Value Members

Deprecated Value Members

Inherited from Trigonometry

Inherited from Statistics

Inherited from Probabilities

Inherited from Mathematics

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

Matlib

object Matlib extends Mathematics with Probabilities with Statistics with Trigonometry

Value Members

Deprecated Value Members

Inherited from Trigonometry

Inherited from Statistics

Inherited from Probabilities

Inherited from Mathematics

Inherited from AnyRef

Inherited from Any

Ungrouped

Matlib