# # = GSL::Vector class # # Contents: # 1. {Class methods}[link:rdoc/vector_rdoc.html#label-Class+methods] # 1. {Notes}[link:rdoc/vector_rdoc.html#label-NOTE%3A] # 1. {Methods}[link:rdoc/vector_rdoc.html#label-Methods] # 1. {Accessing vector elements}[link:rdoc/vector_rdoc.html#label-Accessing+vector+elements] # 1. {Initializing vector elements}[link:rdoc/vector_rdoc.html#label-Initializing+vector+elements] # 1. {Iterators}[link:rdoc/vector_rdoc.html#label-Iterators] # 1. {IO}[link:rdoc/vector_rdoc.html#label-IO] # 1. {Copying vectors}[link:rdoc/vector_rdoc.html#label-Copying+vectors] # 1. {Vector views}[link:rdoc/vector_rdoc.html#label-Vector+views] # 1. {Vector operations}[link:rdoc/vector_rdoc.html#label-Vector+operations] # 1. {Vector operations with size changes}[link:rdoc/vector_rdoc.html#label-Vector+operations+with+size+changes] # 1. {Finding maximum and minimum elements of vectors}[link:rdoc/vector_rdoc.html#label-Finding+maximum+and+minimum+elements+of+vectors] # 1. {Vector properties}[link:rdoc/vector_rdoc.html#label-Vector+Properties] # 1. {Element-wise vector comparison}[link:rdoc/vector_rdoc.html#label-Element-wise+vector+comparison] # 1. {Histogram}[link:rdoc/vector_rdoc.html#label-Histogram] # 1. {Sorting}[link:rdoc/vector_rdoc.html#label-Sorting] # 1. {BLAS methods}[link:rdoc/vector_rdoc.html#label-BLAS+Methods] # 1. {Data type conversions}[link:rdoc/vector_rdoc.html#label-Data+type+conversions] # 1. {NArray}[link:rdoc/vector_rdoc.html#label-NArray+conversions] # 1. {GNU graph interface}[link:rdoc/vector_rdoc.html#label-Graphics] # # See also {GSL::Vector::Complex}[link:rdoc/vector_complex_rdoc.html]. # # == 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}[https://gnu.org/software/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}[link:rdoc/vector_rdoc.html#label-NArray+conversions]. # # == 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}[link:rdoc/matrix_rdoc.html] 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: ---> self.add_constanb(b) # * a Vector: ---> self.add(b) # --- # * GSL::Vector#-(b) # # For b, # * a Number: ---> self.add_constanb(-b) # * a Vector: ---> self.sub(b) # --- # * GSL::Vector#/(b) # # For b, # * a Number: ---> self.scale(1/b) # * a Vector: ---> self.div(b) # # --- # * GSL::Vector#*(b) # # Vector multiplication. # # 1. Scale # >> v = GSL::Vector[1, 2] # [ 1 2 ] # >> v*2 # [ 2 4 ] # 1. Element-by-element multiplication # >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4] # [ 3 4 ] # >> a*b # [ 3 8 ] # 1. Inner product # >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4] # [ 3 # 4 ] # >> a*b.col # => 11.0 # 1. 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 ] # 1. 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 # => # # >> 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) # => # # >> 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)}[link:rdoc/matrix_rdoc.html]. # # >> 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] ] # => # # >> v.to_complex2 # [ [1.000e+00 2.000e+00] [3.000e+00 4.000e+00] ] # => # # # --- # * 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)'") # # {prev}[link:rdoc/sf_rdoc.html] # {next}[link:rdoc/matrix_rdoc.html] # # {Reference index}[link:rdoc/ref_rdoc.html] # {top}[link:index.html] # #