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Returns the Laplace expansion along given row or column.

Matrix[[7,6], [3,9]].laplace_expansion(column: 1)
# => 45

Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)
# => Vector[3, -2]

Hadamard product

Matrix[[1,2], [3,4]].hadamard_product(Matrix[[1,2], [3,2]])
#  => 1  4
#     9  8

Private. Use Matrix#determinant

Returns the determinant of the matrix, using Bareiss’ multistep integer-preserving gaussian elimination. It has the same computational cost order O(n^3) as standard Gaussian elimination. Intermediate results are fraction free and of lower complexity. A matrix of Integers will have thus intermediate results that are also Integers, with smaller bignums (if any), while a matrix of Float will usually have intermediate results with better precision.

Explicit conversion to a Matrix. Returns self

Deprecated.

Use map(&:to_f)

Deprecated.

Use map(&:to_i)

Deprecated.

Use map(&:to_r)

Returns an angle with another vector. Result is within the [0..Math::PI].

Vector[1,0].angle_with(Vector[0,1])
# => Math::PI / 2

Return a single-column matrix from this vector

mtch.values_at(index, ...)   -> array

Uses each index to access the matching values, returning an array of the corresponding matches.

m = /(.)(.)(\d+)(\d)/.match("THX1138: The Movie")
m.to_a               #=> ["HX1138", "H", "X", "113", "8"]
m.values_at(0, 2, -2)   #=> ["HX1138", "X", "113"]

m = /(?<a>\d+) *(?<op>[+\-*\/]) *(?<b>\d+)/.match("1 + 2")
m.to_a               #=> ["1 + 2", "1", "+", "2"]
m.values_at(:a, :b, :op) #=> ["1", "2", "+"]

Returns the portion of the original string before the current match. Equivalent to the special variable $`.

m = /(.)(.)(\d+)(\d)/.match("THX1138.")
m.pre_match   #=> "T"

Returns the portion of the original string after the current match. Equivalent to the special variable $'.

m = /(.)(.)(\d+)(\d)/.match("THX1138: The Movie")
m.post_match   #=> ": The Movie"

This is similar to PrettyPrint::format but the result has no breaks.

maxwidth, newline and genspace are ignored.

The invocation of breakable in the block doesn’t break a line and is treated as just an invocation of text.

Returns the factorization of value.

For an arbitrary integer:

p_1**e_1 * p_2**e_2 * ... * p_n**e_n,

prime_division returns an array of pairs of integers:

[[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]].

Each pair consists of a prime number – a prime factor – and a natural number – its exponent (multiplicity).

Parameters

value

An arbitrary integer.

generator

Optional. A pseudo-prime generator. generator.succ must return the next pseudo-prime number in ascending order. It must generate all prime numbers, but may also generate non-prime numbers, too.

Exceptions

ZeroDivisionError

when value is zero.

Example

Prime.prime_division(45)  #=> [[3, 2], [5, 1]]
3**2 * 5                  #=> 45

Load the given PStore file. If read_only is true, the unmarshalled Hash will be returned. If read_only is false, a 3-tuple will be returned: the unmarshalled Hash, a checksum of the data, and the size of the data.

Returns the Ruby source filename and line number containing this proc or nil if this proc was not defined in Ruby (i.e. native).