Title: GSL::Vector class

See also GSL::Vector::Complex.

1 Class methods

GSL::Vector.alloc(ary)
GSL::Vector.new(ary)
GSL::Vector.new(range)
GSL::Vector.new(size)
GSL::Vector.new(elm0, elm1, ....)
GSL::Vector[elm0, elm1, ....]

Constructors.

Ex:

irb(main):002:0> v1 = Vector.alloc(5)
=> GSL::Vector: [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 ]
irb(main):003:0> v2 = Vector.alloc(1, 3, 5, 2)
=> GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
irb(main):004:0> v3 = Vector[1, 3, 5, 2]
=> GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
irb(main):005:0> v4 = Vector.alloc([1, 3, 5, 2])
=> GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
irb(main):006:0> v5 = Vector[1..6]
=> GSL::Vector: [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 6.000e+00 ]
GSL::Vector.calloc(size)
This method creates a vector object, and initializes all the elements to zero.
GSL::Vector.linspace(min, max, n = 10)

Creates an GSL::Vector with n linearly spaced elements between min and max. If min is greater than max, the elements are stored in decreasing order. This mimics the linspace function of GNU Octave.

Ex:

irb(main):002:0> x = Vector.linspace(0, 10, 5)
[ 0.000e+00 2.500e+00 5.000e+00 7.500e+00 1.000e+01 ]
irb(main):003:0> y = Vector.linspace(10, 0, 5)
[ 1.000e+01 7.500e+00 5.000e+00 2.500e+00 0.000e+00 ]
GSL::Vector.logspace(min, max, n)

Similar to GSL::Vector#linspace except that the values are logarithmically spaced from 10^min to 10^max.

Ex:

irb(main):007:0* x = Vector.logspace(1, 3, 5)
[ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
irb(main):008:0> x = Vector.logspace(3, 1, 5)
[ 1.000e+03 3.162e+02 1.000e+02 3.162e+01 1.000e+01 ]
GSL::Vector.logspace2(min, max, n)

Similar to GSL::Vector#linspace except that the values are logarithmically spaced from min to max.

Ex:

irb(main):010:0* x = Vector.logspace2(10, 1000, 5)
[ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
irb(main):011:0> x = Vector.logspace2(1000, 10, 5)
[ 1.000e+03 3.162e+02 1.000e+02 3.162e+01 1.000e+01 ]
GSL::Vector.indgen(n, start=0, step=1)

This creates a vector of length n with elements from start with interval step (mimics NArray#indgen).

Ex:

irb(main):019:0> v = Vector::Int.indgen(5)
=> GSL::Vector::Int: 
[ 0 1 2 3 4 ]
irb(main):020:0> v = Vector::Int.indgen(5, 3)
=> GSL::Vector::Int: 
[ 3 4 5 6 7 ]
irb(main):021:0> v = Vector::Int.indgen(5, 3, 2)
=> GSL::Vector::Int: 
[ 3 5 7 9 11 ]
GSL::Vector.filescan(filename)

Reads a formatted ascii file and returns an array of vectors. For a data file a.dat as

1 5 6 5
3 5 6 7
5 6 7 9

then a, b, c, d = Vetor.filescan("a.dat") yields

a = [1, 3, 5]
b = [5, 5, 6]
c = [6, 6, 7]
d = [5, 7, 9]

1.1 NArray Extension

If an NArray object is given, a newly allocated vector is created.

Ex:

na = NArray[1.0, 2, 3, 4, 5]
p na                <----- NArray.float(5): 
                           [ 1.0, 2.0, 3.0, 4.0, 5.0]
v = Vector.new(na)  
p v                 <----- [ 1 2 3 4 5 ]

See also here.

2 NOTE:

In Ruby/GSL, vector lendth is limited within the range of Fixnum. For 32-bit CPU, the maximum of vector length is 2^30 ~ 1e9.

3 Methods

3.1 Accessing vector elements

GSL::Vector#get(indices)
GSL::Vector#[indices]
Return elements(s) of the vector self.
GSL::Vector#set(i, val)
GSL::Vector#[] =

Set the i-th element of the vector self to val.

Ex:

irb(main):001:0> require("gsl")
=> true
irb(main):002:0> v = Vector[0..5]
=> GSL::Vector: [ 0.000e+00 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 ]
irb(main):003:0> v[2]
=> 2.0
irb(main):004:0> v[1, 3, 4]
=> GSL::Vector: [ 1.000e+00 3.000e+00 4.000e+00 ]
irb(main):005:0> v[1..3]
=> GSL::Vector::View: [ 1.000e+00 2.000e+00 3.000e+00 ]
irb(main):006:0> v[3] = 9
=> 9
irb(main):007:0> v[-1] = 123
=> 123
irb(main):008:0> v
=> GSL::Vector: [ 0.000e+00 1.000e+00 2.000e+00 9.000e+00 4.000e+00 1.230e+02 ]

3.2 Initializing vector elements

GSL::Vector#set_all(x)
This method sets all the elements of the vector to the value x.
GSL::Vector#set_zero
This method sets all the elements of the vector to zero.
GSL::Vector#set_basis!(i)

This method makes a basis vector by setting all the elements of the vector to zero except for the i-th element, which is set to one. For a vector v of size 10, the method

v.set_basis!(4)

sets the vector v to a basis vector [0, 0, 0, 0, 1, 0, 0, 0, 0, 0].

GSL::Vector#set_basis(i)

This method returns a new basis vector by setting all the elements of the vector to zero except for the i-th element which is set to one. For a vector v of size 10, the method

vb = v.set_basis(4)

creates a new vector vb with elements [0, 0, 0, 0, 1, 0, 0, 0, 0, 0]. The vector v is not changed.

GSL::Vector#indgen!(start=0, step=1)
GSL::Vector#indgen(start=0, step=1)
Mimics NArray#indgen!.

3.3 Iterators

GSL::Vector#each

An iterator for each of the vector elements, used as

v.each do |x|
  p x
end
GSL::Vector#each_index
Another iterator.
GSL::Vector#collect { |item| .. }

Creates a new vector by collecting the vector elements modified with some operations.

Ex:

irb(main):003:0> a = Vector::Int[0..5]
=> GSL::Vector::Int
[ 0 1 2 3 4 5 ]
irb(main):004:0> b = a.collect {|v| v*v}
=> GSL::Vector::Int
[ 0 1 4 9 16 25 ]
irb(main):005:0> a
=> GSL::Vector::Int
[ 0 1 2 3 4 5 ]
GSL::Vector#collect! { |item| .. }

Ex:

irb(main):006:0> a = Vector::Int[0..5]
=> GSL::Vector::Int
[ 0 1 2 3 4 5 ]
irb(main):007:0> a.collect! {|v| v*v}
=> GSL::Vector::Int
[ 0 1 4 9 16 25 ]
irb(main):008:0> a
=> GSL::Vector::Int
[ 0 1 4 9 16 25 ]

3.4 IO

GSL::Vector#print
GSL::Vector#fprintf(io, format = "%e")
GSL::Vector#fprintf(filename, format = "%e")
GSL::Vector#fscanf(io)
GSL::Vector#fscanf(filename)
GSL::Vector#fwrite(io)
GSL::Vector#fwrite(filename)
GSL::Vector#fread(io)
GSL::Vector#fread(filename)
Methods for writing or reading the vector. The first argument is an IO or a String object.

3.5 Copying vectors

GSL::Vector#clone
GSL::Vector#duplicate
Create a new vector of the same elements.

3.6 Vector views

The GSL::Vector::View class is defined to be used as "references" to vectors. Since the Vector::View class is a subclass of Vector, an instance of the View class created by slicing a Vector object can be used same as the original vector. A View object shares the data with the original vector, i.e. any changes in the elements of the View object affect to the original vector.

GSL::Vector#subvector
GSL::Vector#subvector(n)
GSL::Vector#subvector(offset, n)
GSL::Vector#subvector(offset, stride, n)
Create a Vector::View object slicing n elements of the vector self from the offset offset. If called with one argument n, offset is set to 0. With no arguments, a view is created with the same length of the original vector.
GSL::Vector#subvector_with_stride(offset, n, stride)
Return a Vector::View object of a subvector of another vector self with an additional stride argument. The subvector is formed in the same way as for Vector#subvector but the new vector view has n elements with a step-size of stride from one element to the next in the original vector.
GSL::Vectir#matrix_view(n1, n2)
This creates a Matrix::View object from the vector self. It enables to use the vector as a Matrix object.

3.7 Vector operations

GSL::Vector#swap_elements(i, j)
This method exchanges the i-th and j-th elements of the vector in-place.
GSL::Vector#reverse

Reverses the order of the elements of the vector.

irb(main):025:0> v = Vector::Int[1..5]
=> GSL::Vector::Int: 
[ 1 2 3 4 5 ]
irb(main):026:0> v.reverse
=> GSL::Vector::Int: 
[ 5 4 3 2 1 ]
GSL::Vector#trans
GSL::Vector#transpose
GSL::Vector#col
GSL::Vector#row

Transpose the vector from a row vector into a column vector and vice versa.

irb(main):029:0> v = Vector::Int[1..5]
=> GSL::Vector::Int: 
[ 1 2 3 4 5 ]
irb(main):030:0> v.col
=> GSL::Vector::Int::Col: 
[ 1 
  2 
  3 
  4 
  5 ]
GSL::Vector#add(b)
Adds the elements of vector b to the elements of the vector self. A new vector is created, and the vector self is not changed.
GSL::Vector#sub(b)
Subtracts the element of vector b from the elements of self. A new vector is created, and the vector self is not changed.
GSL::Vector#mul(b)
Multiplies the elements of vector self by the elements of vector b.
GSL::Vector#div(b)
Divides the elements of vector self by the elements of vector b.
GSL::Vector#scale(x)
GSL::Vector#scale!(x)
This method multiplies the elements of vector self by the constant factor x.
GSL::Vector#add_constant(x)
GSL::Vector#add_constant!(x)
Adds the constant value x to the elements of the vector self.
GSL::Vector#+(b)
For b,
GSL::Vector#-(b)
For b,
GSL::Vector#/(b)
For b,
GSL::Vector#*(b)
Vector multiplication.
  1. Scale

    irb(main):027:0> v = Vector[1, 2]
    [ 1 2 ]
    irb(main):028:0> v*2
    [ 2 4 ]                           
  2. Element-by-element multiplication

    irb(main):018:0> a = Vector[1, 2]; b = Vector[3, 4]
    [ 3 4 ]
    irb(main):020:0> a*b
    [ 3 8 ]                             
  3. Inner product

    irb(main):023:0> a = Vector[1, 2]; b = Vector[3, 4]
    [ 3 
      4 ]
    irb(main):024:0> a*b.col
    => 11.0                        
  4. Vector::Col*Vector -> Matrix

    irb(main):025:0> a = Vector::Col[1, 2]; b = Vector[3, 4]
    [ 3 4 ]
    irb(main):026:0> a*b
    [ 3 4 
      6 8 ]
  5. Matrix*Vector::Col -> Vector::Col

    irb(main):029:0> a = Vector[1, 2]; m = Matrix[[2, 3], [4, 5]]
    [ 2 3 
      4 5 ]
    irb(main):030:0> m*a          <--- Error
    TypeError: Operation with GSL::Vector is not defined (GSL::Vector::Col expected)
            from (irb):30:in `*'
            from (irb):30
    irb(main):031:0> m*a.col
    [ 8 
      14 ]
GSL::Vector#add!(b)
GSL::Vector#sub!(b)
GSL::Vector#mul!(b)
GSL::Vector#div!(b)
In-place operations with a vector b.
GSL::Vector#swap_elements(i, j)
This exchanges the i-th and j-th elements of the vector self in-place.
GSL::Vector#clone
GSL::Vector#duplicate
These create a copy of the vector self.
GSL::Vector.connect(v1, v2, v3, ...)
GSL::Vector#connect(v2, v3, ...)

Creates a new vector by connecting all the elements of the given vectors.

irb(main):031:0> v1 = Vector::Int[1, 3]
=> GSL::Vector::Int: 
[ 1 3 ]
irb(main):032:0> v2 = Vector::Int[4, 3, 5]
=> GSL::Vector::Int: 
[ 4 3 5 ]
irb(main):033:0> v1.connect(v2)
=> GSL::Vector::Int: 
[ 1 3 4 3 5 ]
GSL::Vector#abs

Creates a new vector, with elements fabs(x_i).

irb(main):034:0> v = Vector::Int[-3, 2, -5, 4]
=> GSL::Vector::Int: 
[ -3 2 -5 4 ]
irb(main):035:0> v.abs
=> GSL::Vector::Int: 
[ 3 2 5 4 ]
GSL::Vector#square
GSL::Vector#abs2

Create a new vector, with elements x_i*x_i.

irb(main):036:0> v = Vector::Int[1..4]
=> GSL::Vector::Int: 
[ 1 2 3 4 ]
irb(main):037:0> v.square
=> GSL::Vector::Int: 
[ 1 4 9 16 ]
GSL::Vector#sqrt
Creates a new vector, with elements sqrt(x_i).
GSL::Vector#floor
GSL::Vector#ceil
GSL::Vector#round

Ex:

irb(main):002:0> v = Vector[1.1, 2.7, 3.5, 4.3]
=> GSL::Vector
[ 1.100e+00 2.700e+00 3.500e+00 4.300e+00 ]
irb(main):003:0> v.floor
=> GSL::Vector::Int
[ 1 2 3 4 ]
irb(main):004:0> v.ceil
=> GSL::Vector::Int
[ 2 3 4 5 ]
irb(main):005:0> v.round
=> GSL::Vector::Int
[ 1 3 4 4 ]
GSL::Vector#normalize(nrm = 1.0)
Creates a new vector of norm nrm, by scaling the vector self.
GSL::Vector#normalize!(nrm = 1.0)

This normalizes the vector self in-place.

Ex:

tcsh> irb
irb(main):001:0> require("gsl")
=> true
irb(main):002:0> a = Vector[-1, -2, -3, -4]
=> GSL::Vector: 
[ -1.000e+00 -2.000e+00 -3.000e+00 -4.000e+00 ]
irb(main):003:0> b = a.abs
=> GSL::Vector: 
[ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
irb(main):004:0> b.sqrt
=> GSL::Vector: 
[ 1.000e+00 1.414e+00 1.732e+00 2.000e+00 ]
irb(main):005:0> b.square
=> GSL::Vector: 
[ 1.000e+00 4.000e+00 9.000e+00 1.600e+01 ]
irb(main):006:0> c = b.normalize(2)
=> GSL::Vector: 
[ 2.582e-01 5.164e-01 7.746e-01 1.033e+00 ]
irb(main):007:0> c.square.sum
=> 2.0
GSL::Vector#decimate(n)
Creates a new vector by averaring every n points of the vector self down to one point.
GSL::Vector#diff(k = 1)
Calculate k-th differences of a vector self.

3.8 Vector operations with size changes

The methods below change vector length of self.

GSL::Vector#pop
Removes the last element from self and returns it, or nil if empty.
GSL::Vector#shift
Returns the first element from self and removes it. Returns nil if empty.
GSL::Vector#push(x)
GSL::Vector#concat(x)
GSL::Vector#<<(x)
Append x (Numeric or GSL::Vector) to the end of self.
GSL::Vector#unshift(x)
Prepends x to the front of self.
GSL::Vector#delete_at(i)
Deletes the element at the specified index i, returning that element, or nil if the index is out of range.
GSL::Vector#delete_if { |x| ... }
Deletes every element of self for which block evaluates to true and returns a new vector of deleted elements.

3.9 Finding maximum and minimum elements of vectors

GSL::Vector#max
This method returns the maximum value in the vector.
GSL::Vector#min
This method returns the minimum value in the vector.
GSL::Vector#minmax
This method returns an array of two elements, the minimum and the maximum values in the vector self.
GSL::Vector#max_index
This method returns the index of the maximum value in the vector. When there are several equal maximum elements then the lowest index is returned.
GSL::Vector#min_index
This method returns the index of the minimum value in the vector. When there are several equal minimum elements then the lowest index is returned.
GSL::Vector#minmax_index
This method returns an array of two elements which has the indices of the minimum and the maximum values in the vector self.

3.10 Vector Properties

GSL::Vector#size
GSL::Vector#len
Return the vector length.
GSL::Vector#sum
Returns the sum of the vector elements.
GSL::Vector#prod
Returns the product of the vector elements.
GSL::Vector#isnull
Returns 1 if all the elements of the vector self are zero, and 0 otherwise.
GSL::Vector#isnull?
Return true if all the elements of the vector self are zero, and false otherwise.
GSL::Vector#all?
Returns true if all the vector elements are non-zero, and false otherwise. If a block is given, the method returns true if the tests are true for all the elements.
GSL::Vector#any?
Returns true if any the vector elements are non-zero, and false otherwise. If a block is given, the method returns true if the tests are true for any of the elements.
GSL::Vector#none?

Returns true if all the elements of the vector self are zero, and false otherwise (just as GSL::Vector#isnull?). If a block is given, the method returns true if the tests are false for all the elements.

Ex:

irb(main):009:0> a = Vector[1, 2, 3]
irb(main):010:0> b = Vector[1, 2, 0]
irb(main):011:0> c = Vector[0, 0, 0]
irb(main):012:0> a.all?
=> true
irb(main):013:0> b.all?
=> false
irb(main):014:0> b.any?
=> true
irb(main):015:0> c.any?
=> false
irb(main):016:0> a.none?
=> false
irb(main):017:0> c.none?
=> true
GSL::Vector#equal?(other, eps = 1e-10)
GSL::Vector#==(other, eps = 1e-10)
Returns true if the vectors have same size and elements equal to absolute accurary eps for all the indices, and false otherwise.

3.11 Element-wise vector comparison

GSL::Vector#eq(other)
GSL::Vector#ne(other)
GSL::Vector#gt(other)
GSL::Vector#ge(other)
GSL::Vector#lt(other)
GSL::Vector#le(other)

Return a Block::Byte object with elements 0/1 by comparing the two vectors self and other. Note that the values returned are 0/1, not true/false, thus all of the elements are "true" in Ruby.

Ex:

irb(main):003:0> a = Vector[1, 2, 3]
irb(main):004:0> b = Vector[1, 2, 5]
irb(main):005:0> a.eq(b)
[ 1 1 0 ]
irb(main):006:0> a.ne(b)
[ 0 0 1 ]
irb(main):007:0> a.gt(b)
[ 0 0 0 ]
irb(main):008:0> a.ge(b)
[ 1 1 0 ]
irb(main):009:0> a.eq(3)
[ 0 0 1 ]
irb(main):010:0> a.ne(2)
[ 1 0 1 ]
irb(main):011:0> a.ge(2)
[ 0 1 1 ]
GSL::Vector#and(other)
GSL::Vector#or(other)
GSL::Vector#xor(other)
GSL::Vector#not

Ex:

irb(main):033:0> a = Vector[1, 0, 3, 0]
irb(main):034:0> b = Vector[3, 4, 0, 0]
irb(main):035:0> a.and(b)
[ 1 0 0 0 ]
irb(main):036:0> a.or(b)
[ 1 1 1 0 ]
irb(main):037:0> a.xor(b)
[ 0 1 1 0 ]
irb(main):038:0> a.not
[ 0 1 0 1 ]
irb(main):039:0> b.not
[ 0 0 1 1 ]
GSL::Vector#where
GSL::Vector#where { |elm| ... }

Returns the vector indices where the tests are true. If all the test failed nil is returned.

Ex:

irb(main):003:0> v = Vector::Int[0, 3, 0, -2, 3, 5, 0, 3]
irb(main):004:0> v.where
[ 1 3 4 5 7 ]                   # where elements are non-zero
irb(main):007:0> v.where { |elm| elm == -2 }
[ 3 ]
irb(main):008:0> a = Vector[0, 0, 0]
irb(main):009:0> a.where
=> nil

3.12 Histogram

GSL::Vector#histogram(n)
GSL::Vector#histogram(ranges)
GSL::Vector#histogram(n, min, max)
GSL::Vector#histogram(n, [min, max])

Creates a histogram filling the vector self.

Example:

irb(main):003:0> r = GSL::Rng.new           # Random number generator
=> #<GSL::Rng:0x6d8594>
irb(main):004:0> v = r.gaussian(1, 1000)    # Generate 1000 Gaussian random numbers
=> GSL::Vector
[ 1.339e-01 -8.810e-02 1.674e+00 7.336e-01 9.975e-01 -1.278e+00 -2.397e+00 ... ]
irb(main):005:0> h = v.histogram(50, [-4, 4])  # Creates a histogram of size 50, range [-4, 4)
=> #<GSL::Histogram:0x6d28b0>
irb(main):006:0> h.graph("-T X -C -g 3")    # Show the histogram
=> true

This is equivalent to

h = Histogram.alloc(50, [-4, 4])
h.increment(v)

3.13 Sorting

GSL::Vector#sort
GSL::Vector#sort!
These methods sort the vector self in ascending numerical order.
GSL::Vector#sort_index
This method indirectly sorts the elements of the vector self into ascending order, and returns the resulting permutation. The elements of permutation give the index of the vector element which would have been stored in that position if the vector had been sorted in place. The first element of permutation gives the index of the least element in the vector, and the last element of permutation gives the index of the greatest vector element. The vector self is not changed.
GSL::Vector#sort_smallest(n)
GSL::Vector#sort_largest(n)
GSL::Vector#sort_smallest_index(n)
GSL::Vector#sort_largest_index(n)

Ex:

irb(main):005:0> v = Vector::Int[8, 2, 3, 7, 9, 1, 4]
=> GSL::Vector::Int: 
[ 8 2 3 7 9 1 4 ]
irb(main):006:0> v.sort
=> GSL::Vector::Int: 
[ 1 2 3 4 7 8 9 ]
irb(main):007:0> v.sort_index
=> GSL::Permutation: 
[ 5 1 2 6 3 0 4 ]
irb(main):008:0> v.sort_largest(3)
=> GSL::Vector::Int: 
[ 9 8 7 ]
irb(main):009:0> v.sort_smallest(3)
=> GSL::Vector::Int: 
[ 1 2 3 ]

3.14 BLAS Methods

GSL::Vector#nrm2
GSL::Vector#dnrm2
Compute the Euclidean norm ||x||_2 = sqrt {sum x_i^2} of the vector.
GSL::Vector#asum
GSL::Vector#dasum
Compute the absolute sum \sum |x_i| of the elements of the vector.

3.15 Data type conversions

GSL::Vector#to_a

This method converts the vector into a Ruby array. A Ruby array also can be converted into a GSL::Vector object with the to_gv method. For example,

v = GSL::Vector.alloc([1, 2, 3, 4, 5])
a = v.to_a   -> GSL::Vector to an array
p a          -> [1.0, 2.0, 3.0, 4.0, 5.0]
a[2] = 12.0
v2 = a.to_gv  -> a new GSL::Vector object
v2.print     -> 1.0000e+00 2.0000e+00 1.2000e+01 4.0000e+00 5.0000e+00
GSL::Vector#to_m(nrow, ncol)

Creates a GSL::Matrix object of nrow rows and ncol columns.

irb(main):011:0> v = Vector::Int[1..5]
=> GSL::Vector::Int: 
[ 1 2 3 4 5 ]
irb(main):012:0> v.to_m(2, 3)
=> GSL::Matrix::Int: 
[ 1 2 3 
  4 5 0 ]
irb(main):013:0> v.to_m(2, 2)
=> GSL::Matrix::Int: 
[ 1 2 
  3 4 ]
irb(main):014:0> v.to_m(3, 2)
=> GSL::Matrix::Int: 
[ 1 2 
  3 4 
  5 0 ]
GSL::Vector#to_m_diagonal

Converts the vector into a diagonal matrix. See also GSL::Matrix.diagonal(v).

irb(main):012:0> v = Vector[1..4].to_i
=> GSL::Vector::Int: 
[ 1 2 3 4 ]
irb(main):013:0> v.to_m_diagonal
=> GSL::Matrix::Int: 
[ 1 0 0 0 
  0 2 0 0 
  0 0 3 0 
  0 0 0 4 ]
GSL::Vector#to_m_circulant

Creates a circulant matrix.

irb(main):002:0> v = Vector::Int[1..5]
=> GSL::Vector::Int: 
[ 1 2 3 4 5 ]
irb(main):003:0> v.to_m_circulant
=> GSL::Matrix::Int: 
[ 5 1 2 3 4   
  4 5 1 2 3   
  3 4 5 1 2   
  2 3 4 5 1   
  1 2 3 4 5 ]
GSL::Vector#to_complex
GSL::Vector#to_complex2

Example:

irb(main):002:0> v = Vector[1..4]
=> GSL::Vector
[ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
irb(main):003:0> v.to_complex
[ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] [3.000e+00 0.000e+00] [4.000e+00 0.000e+00] ]
=> #<GSL::Vector::Complex:0x6d7d24>
irb(main):004:0> v.to_complex2
[ [1.000e+00 2.000e+00] [3.000e+00 4.000e+00] ]
=> #<GSL::Vector::Complex:0x6d6424>
GSL::Vector#to_tensor(rank, dimension)

3.16 GSL::Vector <---> NArray

NArray" -->
GSL::Vector#to_na
The Vector object self is converted into an NArray object. The data are copied to newly allocated memory.
GSL::Vector#to_na2
GSL::Vector#to_na_ref

Create an NArray reference of the vector self.

Example:

irb(main):020:0> v = Vector::Int[1, 2, 3, 4]
=> GSL::Vector::Int
[ 1 2 3 4 ]
irb(main):021:0> na = v.to_na
=> NArray.int(4): 
[ 1, 2, 3, 4 ]
irb(main):022:0> na2 = v.to_na2
=> NArray(ref).int(4): 
[ 1, 2, 3, 4 ]
irb(main):023:0> na[1] = 99
=> 99
irb(main):024:0> v              # na and v are independent
=> GSL::Vector::Int
[ 1 2 3 4 ]
irb(main):025:0> na2[1] = 99    # na2 points to the data of v
=> 99
irb(main):026:0> v
=> GSL::Vector::Int
[ 1 99 3 4 ]
NArray#to_gv
NArray#to_gslv
Create GSL::Vector object from the NArray object self.
NArray#to_gv_view
NArray#to_gv2
NArray#to_gslv_view

A GSL::Vector::View object is created from the NArray object self. This method does not allocate memory for the data: the data of self are not copied, but shared with the View object created, thus any modifications to the View object affect on the original NArray object. In other words, the View object can be used as a reference to the NArray object.

Ex:

tcsh> irb
irb(main):001:0> require("gsl")
=> true
irb(main):002:0> na = NArray[1.0, 2, 3, 4, 5]    
=> NArray.float(5): 
[ 1.0, 2.0, 3.0, 4.0, 5.0 ]
irb(main):003:0> vv = na.to_gv_view   # Create a view sharing the memory
=> GSL::Vector::View 
[ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 ]
irb(main):004:0> vv[3] = 9
=> 9
irb(main):005:0> na
=> NArray.float(5): 
[ 1.0, 2.0, 3.0, 9.0, 5.0 ]           # The data are changed
irb(main):006:0> v = na.to_gv         # A vector with newly allocated memory
=> GSL::Vector 
[ 1.000e+00 2.000e+00 3.000e+00 9.000e+00 5.000e+00 ]
irb(main):007:0> v[1] = 123
=> 123
irb(main):008:0> v
=> GSL::Vector 
[ 1.000e+00 1.230e+02 3.000e+00 9.000e+00 5.000e+00 ]
irb(main):009:0> na                   
=> NArray.float(5): 
[ 1.0, 2.0, 3.0, 9.0, 5.0 ]           # v and na are independent 
irb(main):010:0> na = NArray[1.0, 2, 3, 4, 5, 6]
=> NArray.float(6): 
[ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ]
irb(main):011:0> m = na.to_gv_view.matrix_view(2, 3)
=> GSL::Matrix::View
[  1.000e+00  2.000e+00  3.000e+00 
   4.000e+00  5.000e+00  6.000e+00 ]
irb(main):012:0> m[1][2] = 9
=> 9
irb(main):013:0> na
=> NArray.float(6): 
[ 1.0, 2.0, 3.0, 4.0, 5.0, 9.0 ]

3.17 Graphics

GSL::Vector.graph(y)
GSL::Vector.graph(y, options)
GSL::Vector.graph(x, y)
GSL::Vector.graph(x, y, options)
GSL::Vector#graph(options)
GSL::Vector#graph(x, options)

These methods use the GNU plotutils graph application to plot vector self. The option graph as "-T X -C" is given by a String.

Example:

irb(main):008:0> x = Vector.linspace(0, 2.0*M_PI, 20)
irb(main):009:0> c = Sf::cos(x)
irb(main):010:0> s = Sf::sin(x)
irb(main):011:0> Vector.graph(x, c, s, "-T X -C -L 'cos(x), sin(x)'")

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