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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)