svd_circle, an Octave code which analyzes a linear map of the unit circle caused by an arbitrary 2x2 matrix A, using the singular value decomposition (SVD).
The singular value decomposition has uses in solving overdetermined or underdetermined linear systems, linear least squares problems, data compression, the pseudoinverse matrix, reduced order modeling, and the accurate computation of matrix rank and null space.
The singular value decomposition of an M by N rectangular matrix A has the form
A(mxn) = U(mxm) * S(mxn) * V'(nxn)
where
The computer code and data files described and made available on this web page are distributed under the MIT license
svd_circle is available in a MATLAB version and an Octave version and a Python version.
svd_basis, an Octave code which computes a reduced basis for a collection of data vectors using the singular value decomposition (SVD).
svd_faces, an Octave code which applies singular value decomposition (SVD) analysis to a set of images.
svd_fingerprint, an Octave code which reads a file containing a fingerprint image and uses the Singular Value Decomposition (SVD) to compute and display a series of low rank approximations to the image.
svd_gray, an Octave code which reads a gray scale image, computes the Singular Value Decomposition (SVD), and constructs a series of low rank approximations to the image.
svd_lls, an Octave code which uses the singular value decomposition (SVD) to construct and plot the best affine and linear relationships in the sense of least square, between two vectors of data.
svd_powers, an Octave code which applies singular value decomposition (SVD) analysis to powers x(i)^(j-1).
svd_snowfall, an Octave code which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD).
svd_sphere, an Octave code which analyzes a linear map of the unit sphere caused by an arbitrary 3x3 matrix A, using the singular value decomposition (SVD).
svd_test, an Octave code which demonstrates the singular value decomposition (SVD) for a simple example.
svd_truncated_test, an Octave code which demonstrates the computation of the reduced or truncated Singular Value Decomposition (SVD) that is useful for cases when one dimension of the matrix is much smaller than the other.