## Class Matrix-Base

### Part of:

class matrix-structure-base, package lisplab

### Direct Method

./= Generalized /=. Generalized <. Generalized <=. Element-wise test of equality, with presition. Generalized >. Generalized >=. Generialized abs. Inverse cosine function : acos(x). Inverse hyperbolic cosine function : acosh(x). Addes a and b elementwise. Called by .+ Inverse sine function : asin(x). Inverse hyperbolic sine function : asinh(x). Inverse tangent function : atan(x). Inverse hyperbolic tangent function : atanh(x). Hankel function 1. Bessel functions of the third kind : H^(1)_n(x). Hankel function 2. Bessel functions of the third kind : H^(2)_n(x). Modified Bessel functions : I_n(x). Bessel functions of the first kind : J_n(x). Modified Bessel functions : K_n(x). The Neumann function. Bessel functions of the second kind : Y_n(x). Generalized complex. Generalized conjugate. Cosine function : cos(x). Hyperbolic cosine function : cosh(x). Divides a with b elementwise. Called by ./ The error function : erf(x) The complementary error function : erfc(x) Generalizes every. Exponential function : exp(x). Rises a to power b elementwise. Called by .^ The gamma function : gamma(x) Generialized abs. Logarithm function Generialized max. Generialized min. Multiplies a and b elementwise. Called by .* Generialized realpart. Generialized signum. Sine function : sin(x). Hyperbolic sine function : sinh(x). Generalizes some Square. Square root. Subtracts b from a elementwise. Called by .- Tangent function : tan(x). Hyperbolic tangent function : tanh(x). Shifts the matrix with periodic indecices Converts the object to the specified type. Non-destructive. Copies the elements and structure, but ignore shared state, like fill pointers etc. Copies all elements from a to b. Gives a list of all dimension lengths, or the length of the dimension specified. Write matrix to ASCII-delimited file or stream Exports the elements of the matrix to a list. Restructuring of Brillouin zones Inverse restructuring of Brillouin zones Imports the elements of the matrix from a list. Solves the linear system of equations Ax=b. LU-factorization with pivoting. Outputs (L U P) where L is low diagonal with unity at diagnoals,... LU-factorization with pivoting. Destructive. Ouputs a combined LU matrix where the diagonals bel... Solves the linear equation system LUx=b, where LU is an output from LU-factor!. Matrix multiplication. Short for (m* a (minv b)). Retuns the matrix element with largest absolute value Retuns the matrix element closest to zero A matrix is a object whose elements are accesible with mref. Creates a new matrix of the same type and with the same value as the other, but with all element... Extended version of mcreate. Creates a new matrix of the same type and with the same value as th... Matrix conjugate transpose. Matrix determinant. Sets each element to the value. Destructive Matrix inverse. Matrix inverse. Destructive. Generalization of map, where type = t gives output type equals type of m. Generalization of map-into. Calls the operator, e.g., .add, .mul, on the elements of the matrices. Retuns the largest matrix element Retuns the smalles matrix element Retuns a list with (minumum maximum) Reverts elements of matrix or vector. Similar to cl:reverse Sums all matrix elements Matrix transpose. Matrix trace (sum of diagonal elements). Shifts the matrix and pads results The rank is the number of dimensions. Reshapes the object Reshape the object to 2D Reshape the object to 1D Cross product. Must be a vecotors of length 3 Dot product of vectors A vector is a object whose elements are accessible with vref. The vector norm