Title: Matrices

1 Class methods

GSL::Matrix.new(n)

GSL::Matrix.new(size1, size2)

GSL::Matrix.new(array)

GSL::Matrix.new(arrays)

These methods create a GSL::Matrix object.

ex1:

irb(main):002:0> m = Matrix.new([1, 2, 3], [4, 5, 6], [7, 8, 9])
[ 1.000e+00 2.000e+00 3.000e+00 
  4.000e+00 5.000e+00 6.000e+00 
  7.000e+00 8.000e+00 9.000e+00 ]
=> #<GSL::Matrix:0x6e9644>

ex2: With an array and rows&cols,

m = Matrix.new([1, 2, 3, 4, 5, 6, 7, 8, 9], 3, 3)

ex3: With range objects,

irb(main):002:0> m = Matrix.new(1..3, 4..6, 7..9)
[ 1.000e+00 2.000e+00 3.000e+00 
  4.000e+00 5.000e+00 6.000e+00 
  7.000e+00 8.000e+00 9.000e+00 ]
=> #<GSL::Matrix:0x6eb1ec>
irb(main):004:0> m2 = Matrix.new(1..6, 2, 3)
[ 1.000e+00 2.000e+00 3.000e+00 
  4.000e+00 5.000e+00 6.000e+00 ]
=> #<GSL::Matrix:0x6e51c0>

GSL::Matrix.eye(n, val = 1.0)

GSL::Matrix.diagonal(n, val = 1.0)

Create diagonal matrix of dimensions n*n, of values val.

GSL::Matrix.identity(n)

GSL::Matrix.unit(n)

GSL::Matrix.I(n)

Create diagonal matrix of dimensions n*n, of values 1.0.

1.1 NOTE:

Matrix dimensions are limited within the range of Fixnum. For 32-bit CPU, the maximum of matrix dimension is 2^30 ~ 1e9.

2 Methods

GSL::Matrix#set(argv)

This method sets elements of the matrix in various manners.

with two integers and a number,

m.set(1, 2, 3.2)         -> the (1, 2) element is set to 3.2

with arrays,

m.set([6, 5, 6], [4, 5, 7], [8, 5, 21])	
   ->
        6   5   6
        4   5   7
        8   5  21

with an array and sizes,

m.set([4, 5, 6, 8, 98, 6, 4, 3, 1], 3, 3)
   ->
        4   5   6
        8  98   6
        4   3   1

GSL::Matrix#get(i, j)

This method returns the (i,j)-th element of the matrix self.

GSL::Matrix#set_all(x)

This method sets all the elements of the matrix self to the value x.

GSL::Matrix#set_zero

This method sets all the elements of the matrix to zero.

GSL::Matrix#set_identity

This method sets the elements of the matrix to the corresponding elements of the identity matrix, i.e. a unit diagonal with all off-diagonal elements zero. This applies to both square and rectangular matrices.

2.1 IO

GSL::Matrix#fwrite(io)
GSL::Matrix#fwrite(filename)
GSL::Matrix#fread(io)
GSL::Matrix#fread(filename)
GSL::Matrix#fprintf(io, format = "%e")
GSL::Matrix#fprintf(filename, format = "%e")
GSL::Matrix#fscanf(io)
GSL::Matrix#fscanf(filename)

2.2 Matrix views

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

GSL::Matrix#submatrix(k1, k2, n1, n2)

This returns a GSL::Matirx::View object, a submatrix of the matrix self. The upper-left element of the submatrix is the element (k1,k2) of the original matrix. The submatrix has n1 rows and n2 columns.

GSL::Vectir#matrix_view(n1, n2)

This creates a Matrix::View object from the vector self.

ex:

v2 = Vector.new([1, 2, 3, 4, 5, 6, 7, 8, 9])
mview = v2.matrix_view(3, 3)
p mview.class            <----- GSL::Matrix::View
mview.print              <----- [ 1 2 3 
                                  4 5 6 
                                  7 8 9 ]
mview.set(2, 1, 99.9)
mview.print              <----- [ 1 2 3 
                                  4 5 6 
                                  7 99.9 9 ]
v2.print                 
    <----- [ 1 2 3 4 5 6 7 99.9 9 ]

2.3 Creating row and column views

GSL::Matrix#row(i): This method returns a vector view of the i-th row of the matrix.
GSL::Matrix#column(i)
GSL::Matrix#col(i): These methods return a vector view of the j-th column of the matrix.
GSL::Matrix#diagonal: This method returns a vector view of the diagonal of the matrix. The matrix is not required to be square. For a rectangular matrix the length of the diagonal is the same as the smaller dimension of the matrix.
GSL::Matrix#subdiagonal(k): Returns a vector view view of the k-th subdiagonal of the matrix self. The matrix is not required to be square. The diagonal of the matrix corresponds to k = 0.
GSL::Matrix#superdiagonal(k): Returns a vector view of the k-th superdiagonal of the matrix self. The matrix is not required to be square. The diagonal of the matrix corresponds to k = 0.

2.4 Iterators

GSL::Matrix#each_row: Iterator for each of rows in the matrix self.
GSL::Matrix#each_col: Iterator for each of columns in the matrix self.

2.6 Copying rows and columns

GSL::Matrix#get_row(i, v): This method returns a new vector (not a view) which contains the elements of the i-th row of the matrix self.
GSL::Matrix#get_col(j, v): This method returns a new vector (not a view) which contains the elements of the j-th column of the matrix self.
GSL::Matrix#set_row(i, v): This method copies the elements of the vector v into the i-th row of the matrix. The length of the vector must be the same as the length of the row.
GSL::Matrix#set_col(j, v): This method copies the elements of the vector v into the j-th column of the matrix. The length of the vector must be the same as the length of the column.

2.7 Exchanging rows and columns

GSL::Matrix#swap_rows(i, j): This method exchanges the i-th and j-th rows of the matrix in-place.
GSL::Matrix#swap_columns(i, j): This method exchanges the i-th and j-th columns of the matrix in-place.
GSL::Matrix#swap_rowcol(i, j): This method exchanges the i-th row and j-th column of the matrix. The matrix must be square for this operation to be possible.
GSL::Matrix#transpose!: This method returns a matrix of a transpose of the matrix.
GSL::Matrix#transpose_memcpy
GSL::Matrix#transpose: This method replaces the matrix by its transpose by copying the elements of the matrix in-place. The matrix must be square for this operation to be possible.

2.8 Matrix operations

GSL::Matrix#add(b)

GSL::Matrix#+(b)

GSL::Matrix#add!(b)

GSL::Matrix#+=(b)

This method adds the elements of matrix b to the elements of the matrix. The two matrices must have the same dimensions.

If b is a scalar, these methods add it to all the elements of the matrix self (equivalent to the method add_constant).

GSL::Matrix#sub(b)

GSL::Matrix#-(b)

GSL::Matrix#sub!(b)

GSL::Matrix#-=(b)

This method subtracts the elements of matrix b from the elements of the matrix. The two matrices must have the same dimensions.

GSL::Matrix#mul_elements(b)

GSL::Matrix#*(b)

GSL::Matrix#mul_elements!(b)

GSL::Matrix#*=(b)

This method multiplies the elements of the matrix by the elements of matrix b. The two matrices must have the same dimensions.

GSL::Matrix#**(b)

Matrix multiplication

GSL::Matrix#div_elements(b)

GSL::Matrix#/(b)

GSL::Matrix#div_elements!(b)

GSL::Matrix#/=(b)

This method divides the elements of the matrix by the elements of matrix b. The two matrices must have the same dimensions.

GSL::Matrix#scale!(x)

GSL::Matrix#scale(x)

This method multiplies the elements of the matrix by the constant factor x.

GSL::Matrix#add_constant!(x)

GSL::Matrix#add_constant(x)

This method adds the constant value x to the elements of the matrix.

2.9 Finding maximum and minimum elements of matrices

GSL::Matrix#max
GSL::Matrix#min: These methods return the max/min value in the matrix.
GSL::Matrix#minmax: This method returns a two elements array [min, max], which contains the minimum and the maximum values in the matrix.
GSL::Matrix#max_index
GSL::Matrix#min_index: These methods return the index of the max/min value in the matrix.
GSL::Matrix#minmax_index: This method returns a two elements array [imin, imax], which contains the indices of the minimum and the maximum value in the matrix.

2.10 Matrix properties

GSL::Matrix#isnull: This returns 1 if all the elements of the matrix self are zero, and 0 otherwise.
GSL::Matrix#isnull?: This returns true if all the elements of the matrix self are zero, and false otherwise.
GSL:Matrix#trace: This returns trace of the matrix self, the sum of the diagonal elements.

2.11 NArray

GSL::Matrix#to_na: The Matrix object self is converted into an NMatrix object. The matrix data are copied to newly allocated memory.
GSL::Vector.na_to_gm(na)
GSL::Matrix.to_gm(na): A GSL::Vector::View object is created from the NArray object na. The data of na are not copied, thus any modifications to the View object affect on the original NArray object na. The View object can be used as a reference to the NMatrix object.

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