GSL::Vector class¶ ↑

Contents:

1. Class methods

2. Notes

3. Methods

   1. Accessing vector elements

   2. Initializing vector elements

   3. Iterators

   4. IO

   5. Copying vectors

   6. Vector views

   7. Vector operations

   8. Vector operations with size changes

   9. Finding maximum and minimum elements of vectors

   10. Vector properties

   11. Element-wise vector comparison

   12. Histogram

   13. Sorting

   14. BLAS methods

   15. Data type conversions

4. NArray

5. GNU graph interface

See also GSL::Vector::Complex.

Class methods¶ ↑

• GSL::Vector.alloc(ary)

• GSL::Vector.alloc(ary)

• GSL::Vector.alloc(range)

• GSL::Vector.alloc(size)

• GSL::Vector.alloc(elm0, elm1, .…)

• GSL::Vector[elm0, elm1, .…]

  Constructors.

  Ex:

  >> v1 = GSL::Vector.alloc(5)
  => GSL::Vector: [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 ]
  >> v2 = GSL::Vector.alloc(1, 3, 5, 2)
  => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
  >> v3 = GSL::Vector[1, 3, 5, 2]
  => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
  >> v4 = GSL::Vector.alloc([1, 3, 5, 2])
  => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
  >> v5 = GSL::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:

  >> x = GSL::Vector.linspace(0, 10, 5)
  [ 0.000e+00 2.500e+00 5.000e+00 7.500e+00 1.000e+01 ]
  >> y = GSL::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:

  >> x = GSL::Vector.logspace(1, 3, 5)
  [ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
  >> x = GSL::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:

  >> x = GSL::Vector.logspace2(10, 1000, 5)
  [ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
  >> x = GSL::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:

  >> v = GSL::Vector::Int.indgen(5)
  => GSL::Vector::Int:
  [ 0 1 2 3 4 ]
  >> v = GSL::Vector::Int.indgen(5, 3)
  => GSL::Vector::Int:
  [ 3 4 5 6 7 ]
  >> v = GSL::Vector.indgen(4, 1.2, 0.3)
  => GSL::Vector
  [ 1.200e+00 1.500e+00 1.800e+00 2.100e+00 ]

• 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]
  

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 = GSL::Vector.alloc(na)
p v                 <----- [ 1 2 3 4 5 ]

See also here.

NOTE:¶ ↑

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

Methods¶ ↑

Accessing vector elements¶ ↑

• GSL::Vector#get(args)

• GSL::Vector#[args]

  Returns elements(s) of the vector self if args is a single Fixnum, a single Array of Fixnums, or a single GSL::Permutation (or GSL::Index). For all other args, the arguments are treated as with Vector#subvector and a Vector::View is returned.

• GSL::Vector#set(args, val)

• GSL::Vector#[args] = val

  If args is empty, behaves as #set_all and val must be a Numeric.

  If args is a single Fixnum, i, sets the i-th element of the vector self to val, which must be a Numeric.

  All other args specify a subvector (as with #subvector) whose elements are assigned from val. In this case, val can be an Array, Range, GSL::Vector, or Numeric.

  NOTE: GSL does not provide a vector copy function that properly copies data across overlapping memory regions, so watch out if assigning to part of a Vector from another part of itself (see example below).

  Ex:

  >> require 'gsl'
  => true
  >> v = GSL::Vector[0..5]
  => GSL::Vector
  [ 0.000e+00 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 ]
  >> v[2]
  => 2.0
  >> v[1,2,3]
  => GSL::Vector::View
  [ 1.000e+00 3.000e+00 5.000e+00 ]
  >> v[[1,2,3]]
  => GSL::Vector
  [ 1.000e+00 2.000e+00 3.000e+00 ]
  >> v[3] = 9
  => 9
  >> v[-1] = 123
  => 123
  >> v
  => GSL::Vector
  [ 0.000e+00 1.000e+00 2.000e+00 9.000e+00 4.000e+00 1.230e+02 ]
  >> v[2,3] = 0
  => 0
  >> v
  => GSL::Vector
  [ 0.000e+00 1.000e+00 0.000e+00 0.000e+00 0.000e+00 1.230e+02 ]
  >> v[2,3] = [4,5,6]
  => [4, 5, 6]
  >> v
  => GSL::Vector
  [ 0.000e+00 1.000e+00 4.000e+00 5.000e+00 6.000e+00 1.230e+02 ]
  >> v[1,4] = v[0,4] # !!! Overlapping !!!
  => GSL::Vector::View
  [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 ]
  >> v
  => GSL::Vector
  [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 1.230e+02 ]

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!.

Iterators¶ ↑

• GSL::Vector#each

• GSL::Vector#reverse_each

  An iterator for each of the vector elements, used as

  v.each do |x|    # Show all the elements
    p x
  end
  

• GSL::Vector#each_index

• GSL::Vector#reverse_each_index

  Iterators

• GSL::Vector#collect { |item| .. }

• GSL::Vector#map { |item| .. }

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

  Ex:

  >> a = GSL::Vector::Int[0..5]
  => GSL::Vector::Int
  [ 0 1 2 3 4 5 ]
  >> b = a.collect {|v| v*v}
  => GSL::Vector::Int
  [ 0 1 4 9 16 25 ]
  >> a
  => GSL::Vector::Int
  [ 0 1 2 3 4 5 ]

• GSL::Vector#collect! { |item| .. }

• GSL::Vector#map! { |item| .. }

  Ex:

  >> a = GSL::Vector::Int[0..5]
  => GSL::Vector::Int
  [ 0 1 2 3 4 5 ]
  >> a.collect! {|v| v*v}
  => GSL::Vector::Int
  [ 0 1 4 9 16 25 ]
  >> a
  => GSL::Vector::Int
  [ 0 1 4 9 16 25 ]

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.

Copying vectors¶ ↑

• GSL::Vector#clone

• GSL::Vector#duplicate

  Create a new vector of the same elements.

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)

• GSL::Vector#subvector(range, stride=1)

  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. If called with a range parameter (and optional stride), a view is created for that range (and stride). Note the n, if given, is the length of the returned View.

  • Example:

    #!/usr/bin/env ruby
    require("gsl")
    
    v = GSL::Vector[1, 2, 3, 4, 5, 6]
    view = v.subvector(1, 4)
    p view.class         <----- GSL::Vector::View
    view.print           <----- [ 2 3 4 5 ]
    
    view[2] = 99
    view.print           <----- [ 2 3 99 5 ]
    v.print              <----- [ 1 2 3 99 5 6 ]

• GSL::Vector#subvector_with_stride(stride)

• GSL::Vector#subvector_with_stride(offset, stride)

• GSL::Vector#subvector_with_stride(offset, stride, n)

  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. Note that n, if given, is the length of the returned View.

• GSL::Vector#matrix_view(n1, n2)

  This creates a Matrix::View object from the vector self. It enables to use the vector as a Matrix object.

  • Ex:

    >> v = GSL::Vector::Int.alloc(1..9)
    => GSL::Vector::Int:
    [ 1 2 3 4 5 6 7 8 9 ]
    >> m = v.matrix_view(3, 3)
    => GSL::Matrix::Int::View:
    [ 1 2 3
      4 5 6
      7 8 9 ]
    >> m[1][2] = 99
    => 99
    >> v
    => GSL::Vector::Int:
    [ 1 2 3 4 5 99 7 8 9 ]

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.

  >> v = GSL::Vector::Int[1..5]
  => GSL::Vector::Int:
  [ 1 2 3 4 5 ]
  >> 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.

  >> v = GSL::Vector::Int[1..5]
  => GSL::Vector::Int:
  [ 1 2 3 4 5 ]
  >> 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,

  * a Number: ---> <tt>self.add_constanb(b)</tt>
  * a Vector: ---> <tt>self.add(b)</tt>

• GSL::Vector#-(b)

  For b,

  * a Number: ---> <tt>self.add_constanb(-b)</tt>
  * a Vector: ---> <tt>self.sub(b)</tt>

• GSL::Vector#/(b)

  For b,

  * a Number: ---> <tt>self.scale(1/b)</tt>
  * a Vector: ---> <tt>self.div(b)</tt>

• GSL::Vector#*(b)

  Vector multiplication.

1. Scale

   >> v = GSL::Vector[1, 2]
   [ 1 2 ]
   >> v*2
   [ 2 4 ]

2. Element-by-element multiplication

   >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4]
   [ 3 4 ]
   >> a*b
   [ 3 8 ]

3. Inner product

   >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4]
   [ 3
     4 ]
   >> a*b.col
   => 11.0

4. GSL::Vector::Col*Vector -> GSL::Matrix

   >> a = GSL::Vector::Col[1, 2]; b = GSL::Vector[3, 4]
   [ 3 4 ]
   >> a*b
   [ 3 4
     6 8 ]

5. GSL::Matrix*Vector::Col -> GSL::Vector::Col

   >> a = GSL::Vector[1, 2]; m = GSL::Matrix[[2, 3], [4, 5]]
   [ 2 3
     4 5 ]
   >> m*a          <--- Error
   TypeError: Operation with GSL::Vector is not defined (GSL::Vector::Col expected)
           from (irb):30:in `*'
           from (irb):30
   >> 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#pow(p)

• GSL::Vector#**(p)

• GSL::Vector#pow!(p)

  Element-wise calculation of power p.

  Ex)

  >> require("gsl")
  >> v = GSL::Vector[1, 2, 3]
  => GSL::Vector
  [ 1.000e+00 2.000e+00 3.000e+00 ]
  >> v.pow(2)
  => GSL::Vector
  [ 1.000e+00 4.000e+00 9.000e+00 ]
  >> v**2
  => GSL::Vector
  [ 1.000e+00 4.000e+00 9.000e+00 ]
  >> v
  => GSL::Vector
  [ 1.000e+00 2.000e+00 3.000e+00 ]
  >> v.pow!(2)
  => GSL::Vector
  [ 1.000e+00 4.000e+00 9.000e+00 ]
  >> v
  => GSL::Vector
  [ 1.000e+00 4.000e+00 9.000e+00 ]

• 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.

  >> v1 = GSL::Vector::Int[1, 3]
  => GSL::Vector::Int:
  [ 1 3 ]
  >> v2 = GSL::Vector::Int[4, 3, 5]
  => GSL::Vector::Int:
  [ 4 3 5 ]
  >> v1.connect(v2)
  => GSL::Vector::Int:
  [ 1 3 4 3 5 ]

• GSL::Vector#sgn

• GSL::Vector#signum

  Creates a new vector, with elements +1 if x_i > 0, -1 if x_i < 0, otherwise 0. Note that this definition gives the signum of NaN as 0 rather than NaN.

• GSL::Vector#abs

• GSL::Vector#fabs

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

  >> v = GSL::Vector::Int[-3, 2, -5, 4]
  => GSL::Vector::Int:
  [ -3 2 -5 4 ]
  >> 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.

  >> v = GSL::Vector::Int[1..4]
  => GSL::Vector::Int:
  [ 1 2 3 4 ]
  >> 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:

  >> v = GSL::Vector[1.1, 2.7, 3.5, 4.3]
  => GSL::Vector
  [ 1.100e+00 2.700e+00 3.500e+00 4.300e+00 ]
  >> v.floor
  => GSL::Vector::Int
  [ 1 2 3 4 ]
  >> v.ceil
  => GSL::Vector::Int
  [ 2 3 4 5 ]
  >> 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
  >> require("gsl")
  => true
  >> a = GSL::Vector[-1, -2, -3, -4]
  => GSL::Vector:
  [ -1.000e+00 -2.000e+00 -3.000e+00 -4.000e+00 ]
  >> b = a.abs
  => GSL::Vector:
  [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
  >> b.sqrt
  => GSL::Vector:
  [ 1.000e+00 1.414e+00 1.732e+00 2.000e+00 ]
  >> b.square
  => GSL::Vector:
  [ 1.000e+00 4.000e+00 9.000e+00 1.600e+01 ]
  >> c = b.normalize(2)
  => GSL::Vector:
  [ 2.582e-01 5.164e-01 7.746e-01 1.033e+00 ]
  >> 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.

• GSL::Vector#join(sep = “ ”)

  Converts the vector to a String by joining all the elements with a separator sep.

• GSL::Vector#zip(vec, …)

• GSL::Vector.zip(vec, …)

  Create an Array of vectors by merging the elements of self with corresponding elements from each arguments.

  Ex:

  >> require("gsl")
  >> a = GSL::Vector[4, 5, 6]
  >> b = GSL::Vector[7, 8, 9]
  >> GSL::Vector[1, 2, 3].zip(a, b)
  [[ 1.000e+00 4.000e+00 7.000e+00 ],
   [ 2.000e+00 5.000e+00 8.000e+00 ],
   [ 3.000e+00 6.000e+00 9.000e+00 ]]
  >> GSL::Vector[1, 2].zip(a, b)
  [[ 1.000e+00 4.000e+00 7.000e+00 ],
   [ 2.000e+00 5.000e+00 8.000e+00 ]]
  >> a.zip(GSL::Vector[1, 2], GSL::Vector[8.0])
  [[ 4.000e+00 1.000e+00 8.000e+00 ],
   [ 5.000e+00 2.000e+00 0.000e+00 ],
   [ 6.000e+00 0.000e+00 0.000e+00 ]]

• GSL::Vector#concat(x)

  Returns a new Vector that contains the concatenation self and x, which must be an Array, Fixnum, Bignum, Float, Range, or GSL::Vector.

Vector operations with size changes¶ ↑

The methods below change vector length of self. A Vector's length may not extend past its original allocation. Use of these methods is discouraged. Existing Views may still refer to elements beyond the end of the shortened Vector. These elements remain allocated, but are effectvely unmanaged.

• GSL::Vector#delete(x)

  Deletes items from self that are equal to x. If the item is not found, returns nil, otherwise returns x.

• 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 self.

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.

Vector Properties¶ ↑

• GSL::Vector#size

• GSL::Vector#len

• GSL::Vector#length

  Return the vector length.

• GSL::Vector#stride

  Return the vector stride.

• GSL::Vector#sum

  Returns the sum of the vector elements.

• GSL::Vector#prod

  Returns the product of the vector elements.

• GSL::Vector#cumsum

  Calculate the cumulative sum of elements of self and returns as a new vector.

• GSL::Vector#cumprod

  Calculate the cumulative product of elements of self and returns as a new vector.

• 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#ispos

• GSL::Vector#ispos?

• GSL::Vector#isneg

• GSL::Vector#isneg?

  (GSL-1.9 or later) Return 1 (true) if all the elements of the vector self are zero, strictly positive, strictly negative respectively, and 0 (false) otherwise.

• GSL::Vector#isnonneg

• GSL::Vector#isnonneg?

  (GSL-1.10 or later) Return 1 (true) if all the elements of the vector self are non-negative , and 0 (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:

  >> a = GSL::Vector[1, 2, 3]
  >> b = GSL::Vector[1, 2, 0]
  >> c = GSL::Vector[0, 0, 0]
  >> a.all?
  => true
  >> b.all?
  => false
  >> b.any?
  => true
  >> c.any?
  => false
  >> a.none?
  => false
  >> c.none?
  => true

• GSL::Vector#all

• GSL::Vector#any

• GSL::Vector#none

  Returns 1 or 0.

• 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.

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:

  >> a = GSL::Vector[1, 2, 3]
  >> b = GSL::Vector[1, 2, 5]
  >> a.eq(b)
  [ 1 1 0 ]
  >> a.ne(b)
  [ 0 0 1 ]
  >> a.gt(b)
  [ 0 0 0 ]
  >> a.ge(b)
  [ 1 1 0 ]
  >> a.eq(3)
  [ 0 0 1 ]
  >> a.ne(2)
  [ 1 0 1 ]
  >> a.ge(2)
  [ 0 1 1 ]

• GSL::Vector#and(other)

• GSL::Vector#or(other)

• GSL::Vector#xor(other)

• GSL::Vector#not

  Ex:

  >> a = GSL::Vector[1, 0, 3, 0]
  >> b = GSL::Vector[3, 4, 0, 0]
  >> a.and(b)
  [ 1 0 0 0 ]
  >> a.or(b)
  [ 1 1 1 0 ]
  >> a.xor(b)
  [ 0 1 1 0 ]
  >> a.not
  [ 0 1 0 1 ]
  >> 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:

  >> v = GSL::Vector::Int[0, 3, 0, -2, 3, 5, 0, 3]
  >> v.where
  [ 1 3 4 5 7 ]                   # where elements are non-zero
  >> v.where { |elm| elm == -2 }
  [ 3 ]
  >> a = GSL::Vector[0, 0, 0]
  >> a.where
  => nil

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:

  >> r = GSL::Rng.alloc           # Random number generator
  => #<GSL::Rng:0x6d8594>
  >> 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 ... ]
  >> h = v.histogram(50, [-4, 4])  # Creates a histogram of size 50, range [-4, 4)
  => #<GSL::Histogram:0x6d28b0>
  >> h.graph("-T X -C -g 3")    # Show the histogram
  => true

  This is equivalent to

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

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:

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

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.

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.

  >> v = GSL::Vector::Int[1..5]
  => GSL::Vector::Int:
  [ 1 2 3 4 5 ]
  >> v.to_m(2, 3)
  => GSL::Matrix::Int:
  [ 1 2 3
    4 5 0 ]
  >> v.to_m(2, 2)
  => GSL::Matrix::Int:
  [ 1 2
    3 4 ]
  >> 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).

  >> v = GSL::Vector[1..4].to_i
  => GSL::Vector::Int:
  [ 1 2 3 4 ]
  >> 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.

  >> v = GSL::Vector::Int[1..5]
  => GSL::Vector::Int:
  [ 1 2 3 4 5 ]
  >> 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:

  >> v = GSL::Vector[1..4]
  => GSL::Vector
  [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
  >> 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>
  >> 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)

NArray conversions¶ ↑

• GSL::Vector#to_na

  Converts a vector self 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:

  >> v = GSL::Vector::Int[1, 2, 3, 4]
  => GSL::Vector::Int
  [ 1 2 3 4 ]
  >> na = v.to_na
  => NArray.int(4):
  [ 1, 2, 3, 4 ]
  >> na2 = v.to_na2
  => NArray(ref).int(4):
  [ 1, 2, 3, 4 ]
  >> na[1] = 99
  => 99
  >> v              # na and v are independent
  => GSL::Vector::Int
  [ 1 2 3 4 ]
  >> na2[1] = 99    # na2 points to the data of v
  => 99
  >> 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
  >> require("gsl")
  => true
  >> na = NArray[1.0, 2, 3, 4, 5]
  => NArray.float(5):
  [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
  >> 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 ]
  >> vv[3] = 9
  => 9
  >> na
  => NArray.float(5):
  [ 1.0, 2.0, 3.0, 9.0, 5.0 ]           # The data are changed
  >> 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 ]
  >> v[1] = 123
  => 123
  >> v
  => GSL::Vector
  [ 1.000e+00 1.230e+02 3.000e+00 9.000e+00 5.000e+00 ]
  >> na
  => NArray.float(5):
  [ 1.0, 2.0, 3.0, 9.0, 5.0 ]           # v and na are independent
  >> na = NArray[1.0, 2, 3, 4, 5, 6]
  => NArray.float(6):
  [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ]
  >> 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 ]
  >> m[1][2] = 9
  => 9
  >> na
  => NArray.float(6):
  [ 1.0, 2.0, 3.0, 4.0, 5.0, 9.0 ]

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 a vector self. The options of graph as “-T X -C” can be given by a String.

  Example:

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

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