local M = { [matrix.new] = [[ matrix.new(r, c[, finit]) Returns a new matrix of "r" rows and "c" columns. If "finit" is not given, the matrix is initialized to 0. If "finit" is provided, the function "finit(i, j)" is called for all elements, with the i arguments equal to the row index and j equal to the column index. The value returned by the function is assigned to the respective matrix elements. ]], [matrix.cnew] = [[ matrix.cnew(r, c[, finit]) Returns a new complex matrix. The meaning of its arguments is the same of the function "new". ]], [matrix.def] = [[ matrix.def(t) Convert the table t into a matrix. The table should be in the form "{{row1_v1, row1_v2, ...}, {row2_v1, row2_v2, ...}, ...}" where each term is a number. You should also ensure that all the lines contain the same number of elements. ]], [matrix.vec] = [[ matrix.vec(t) Convert the table t into a column matrix. In GSL Shell, column matrices are considered vectors. The table should be in the form "{v1, v2, v3, ...}". ]], [matrix.dim] = [[ matrix.dim(m) Returns two values: the number of rows and the number of columns of the matrix. ]], [matrix.copy] = [[ matrix.copy(m) Returns a copy of the matrix. ]], [matrix.transpose] = [[ matrix.transpose(m) Return the transpose of the matrix. ]], [matrix.hc] = [[ matrix.hc(m) Returns the hermitian conjugate of the matrix. ]], [matrix.diag] = [[ matrix.diag(t) Given a table "t" of length "n", returns a diagonal matrix whose diagonal elements are equal to the elements of "t". ]], [matrix.unit] = [[ matrix.unit(n) Return the unit matrix of dimension n by n. ]], [matrix.set] = [[ matrix.set(a, b) Set the matrix "a" to be equal to the matrix "b". An error is raised if the dimensions of the matrices are different. Please note that it is different from the statement "a = b" because the latter simply makes the variable "a" refer to the same matrix as "b". With the "set" function, you set each element of an existing matrix "a" to the same value as the corresponding element of "b". ]], [matrix.fset] = [[ matrix.fset(m, f) Set the elements of the matrix "m" to the value given by "f(i, j)" where "i" and "j" are, respectively, the row and column indexes of the matrix. Note that this function has the same semantics as the "new" function, with the difference that "fset" operates on a matrix that already exists instead of creating a new one. ]], ['matrix'] = [[ A matrix of real numbers. Ordinary arithmetic operators can be used on matrix to perform matrix addition or multiplication. Arithmetic operations can also mix matrix and scalars of both real or complex type. The length '#' operator can be used to retrieve the number of columns. The form m[k] with an integer index can be used to retrieve a row in column form. Methods: dim(), returns the dimensions of the matrix: (rows), (columns) col(j), returns a column of the matrix (reference) row(i), returns a row of the matrix (reference) get(i, j), returns the element in the row "i" and column "j" set(i, j, x), set the element in position (i, j) to the value x copy(), returns a copy of the matrix norm(), returns the Frobenius norm of the matrix slice(i, j, r, c), returns the submatrix of dimension (r,c) starting at position (i,j) (reference) show(), returns the string representation of the matrix ]], ['complex'] = [[ A complex number. Normal arithmetic operations can be used by mixing complex or real numbers or matrices. The general mathematical functions to operate on complex numbers are available in the "complex" module. The cartesian components of a complex or real number can be retrieved with the function "complex.rect". ]], } return M