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I need to write a linear least squares program in python 2.7 . Help with modification to compute RMSE too. #linear least squares def lstsq
I need to write a linear least squares program in python 2.7 . Help with modification to compute RMSE too. #linear least squares def lstsq(a, b, rcond=-1): """ Return the least-squares solution to a linear matrix equation. Solves the equation `a x = b` by computing a vector `x` that minimizes the Euclidean 2-norm `|| b - a x ||^2`. The equation may be under, well, or over determined, meaning that the number of linearly independent rows of `a` can be less than, equal to, or greater than its number of linearly independent columns. To plot the data along with the fitted line: >>> import matplotlib.pyplot as plt >>> plt.plot(x, y, 'o', label='Original data', markersize=10) >>> plt.plot(x, m*x + c, 'r', label='Fitted line') >>> plt.legend() >>> plt.show() """ import math a, _ = _makearray(a) b, wrap = _makearray(b) is_1d = len(b.shape) == 1 if is_1d: b = b[:, newaxis] _assertRank2(a, b) m = a.shape[0] n = a.shape[1] n_rhs = b.shape[1] ldb = max(n, m) if m != b.shape[0]: raise LinAlgError('Sorry, incompatible dimensions! Try again ') t, result_t = _commonType(a, b) result_real_t = _realType(result_t) real_t = _linalgRealType(t) bstar = zeros((ldb, n_rhs), t) bstar[:b.shape[0], :n_rhs] = b.copy() a, bstar = _fastCopyAndTranspose(t, a, bstar) a, bstar = _to_native_byte_order(a, bstar) s = zeros((min(m, n),), real_t) nlvl = max( 0, int( math.log( float(min(m, n))/2. ) ) + 1 ) iwork = zeros((3*min(m, n)*nlvl+11*min(m, n),), fortran_int) if isComplexType(t): lapack_routine = lapack_lite.zgelsd lwork = 1 rwork = zeros((lwork,), real_t) work = zeros((lwork,), t) results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0, work, -1, rwork, iwork, 0) lwork = int(abs(work[0])) rwork = zeros((lwork,), real_t) a_real = zeros((m, n), real_t) bstar_real = zeros((ldb, n_rhs,), real_t) results = lapack_lite.dgelsd(m, n, n_rhs, a_real, m, bstar_real, ldb, s, rcond, 0, rwork, -1, iwork, 0) lrwork = int(rwork[0]) work = zeros((lwork,), t) rwork = zeros((lrwork,), real_t) results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0, work, lwork, rwork, iwork, 0) else: lapack_routine = lapack_lite.dgelsd lwork = 1 work = zeros((lwork,), t) results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0, work, -1, iwork, 0) lwork = int(work[0]) work = zeros((lwork,), t) results = lapack_routine(m, n, n_rhs, a, m, bstar, ldb, s, rcond, 0, work, lwork, iwork, 0) if results['info'] > 0: raise LinAlgError('SVD did not converge in Linear Least Squares') resids = array([], result_real_t) if is_1d: x = array(ravel(bstar)[:n], dtype=result_t, copy=True) if results['rank'] == n and m > n: if isComplexType(t): resids = array([sum(abs(ravel(bstar)[n:])**2)], dtype=result_real_t) else: resids = array([sum((ravel(bstar)[n:])**2)], dtype=result_real_t) else: x = array(transpose(bstar)[:n,:], dtype=result_t, copy=True) if results['rank'] == n and m > n: if isComplexType(t): resids = sum(abs(transpose(bstar)[n:,:])**2, axis=0).astype( result_real_t, copy=False) else: resids = sum((transpose(bstar)[n:,:])**2, axis=0).astype( result_real_t, copy=False) st = s[:min(n, m)].astype(result_real_t, copy=True) return wrap(x), wrap(resids), results['rank'], st
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