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__init__.py
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"""Backward compatible with LinearAlgebra from Numeric """ # This module is a lite version of the linalg.py module in SciPy which contains # high-level Python interface to the LAPACK library. The lite version # only accesses the following LAPACK functions: dgesv, zgesv, dgeev, # zgeev, dgesdd, zgesdd, dgelsd, zgelsd, dsyevd, zheevd, dgetrf, dpotrf. __all__ = ['LinAlgError', 'solve_linear_equations', 'inverse', 'cholesky_decomposition', 'eigenvalues', 'Heigenvalues', 'generalized_inverse', 'determinant', 'singular_value_decomposition', 'eigenvectors', 'Heigenvectors', 'linear_least_squares' ] from numpy.core import transpose import numpy.linalg as linalg # Linear equations LinAlgError = linalg.LinAlgError def solve_linear_equations(a, b): return linalg.solve(a,b) # Matrix inversion def inverse(a): return linalg.inv(a) # Cholesky decomposition def cholesky_decomposition(a): return linalg.cholesky(a) # Eigenvalues def eigenvalues(a): return linalg.eigvals(a) def Heigenvalues(a, UPLO='L'): return linalg.eigvalsh(a,UPLO) # Eigenvectors def eigenvectors(A): w, v = linalg.eig(A) return w, transpose(v) def Heigenvectors(A): w, v = linalg.eigh(A) return w, transpose(v) # Generalized inverse def generalized_inverse(a, rcond = 1.e-10): return linalg.pinv(a, rcond) # Determinant def determinant(a): return linalg.det(a) # Linear Least Squares def linear_least_squares(a, b, rcond=1.e-10): """returns x,resids,rank,s where x minimizes 2-norm(|b - Ax|) resids is the sum square residuals rank is the rank of A s is the rank of the singular values of A in descending order If b is a matrix then x is also a matrix with corresponding columns. If the rank of A is less than the number of columns of A or greater than the number of rows, then residuals will be returned as an empty array otherwise resids = sum((b-dot(A,x)**2). Singular values less than s[0]*rcond are treated as zero. """ return linalg.lstsq(a,b,rcond) def singular_value_decomposition(A, full_matrices=0): return linalg.svd(A, full_matrices)