Python scipy.diag方法代碼示例

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_complex_lu(self):
        """Getting factors of complex matrix"""
        umfpack = um.UmfpackContext("zi")

        for A in self.complex_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_real_lu(self):
        """Getting factors of real matrix"""
        umfpack = um.UmfpackContext("di")

        for A in self.real_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_complex_lu(self):
        # Getting factors of complex matrix
        umfpack = um.UmfpackContext("zi")

        for A in self.complex_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_complex_int64_lu(self):
        # Getting factors of complex matrix with long indices
        umfpack = um.UmfpackContext("zl")

        for A in self.complex_int64_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_real_lu(self):
        # Getting factors of real matrix
        umfpack = um.UmfpackContext("di")

        for A in self.real_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def test_real_int64_lu(self):
        # Getting factors of real matrix with long indices
        umfpack = um.UmfpackContext("dl")

        for A in self.real_int64_matrices:
            umfpack.numeric(A)

            (L,U,P,Q,R,do_recip) = umfpack.lu(A)

            L = L.todense()
            U = U.todense()
            A = A.todense()
            if not do_recip:
                R = 1.0/R
            R = matrix(diag(R))
            P = eye(A.shape[0])[P,:]
            Q = eye(A.shape[1])[:,Q]

            assert_array_almost_equal(P*R*A*Q,L*U) 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def _quartimax_obj(self, loadings):
        """
        Quartimax function objective.

        Parameters
        ----------
        loadings : array-like
            The loading matrix

        Returns
        -------
        gradient_dict : dict
            A dictionary with
            - grad : np.array
                The gradient.
            - criterion : float
                The value of the criterion for the objective.
        """
        gradient = -loadings**3
        criterion = -np.sum(np.diag(np.dot((loadings**2).T, loadings**2))) / 4
        return {'grad': gradient, 'criterion': criterion} 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def _oblimin_obj(self, loadings):
        """
        The Oblimin function objective.

        Parameters
        ----------
        loadings : array-like
            The loading matrix

        Returns
        -------
        gradient_dict : dict
            A dictionary with
            - grad : np.array
                The gradient.
            - criterion : float
                The value of the criterion for the objective.
        """
        X = np.dot(loadings**2, np.eye(loadings.shape[1]) != 1)
        if (self.gamma != 0):
            p = loadings.shape[0]
            X = np.diag(np.full(1, p)) - np.dot(np.zeros((p, p)), X)
        gradient = loadings * X
        criterion = np.sum(loadings**2 * X) / 4
        return {'grad': gradient, 'criterion': criterion} 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def ElasticRod(n):
    # Fixed-free elastic rod
    L = 1.0
    le = L/n
    rho = 7.85e3
    S = 1.e-4
    E = 2.1e11
    mass = rho*S*le/6.
    k = E*S/le
    A = k*(diag(r_[2.*ones(n-1),1])-diag(ones(n-1),1)-diag(ones(n-1),-1))
    B = mass*(diag(r_[4.*ones(n-1),2])+diag(ones(n-1),1)+diag(ones(n-1),-1))
    return A,B 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def MikotaPair(n):
    # Mikota pair acts as a nice test since the eigenvalues
    # are the squares of the integers n, n=1,2,...
    x = arange(1,n+1)
    B = diag(1./x)
    y = arange(n-1,0,-1)
    z = arange(2*n-1,0,-2)
    A = diag(z)-diag(y,-1)-diag(y,1)
    return A,B 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def MikotaPair(n):
    # Mikota pair acts as a nice test since the eigenvalues
    # are the squares of the integers n, n=1,2,...
    x = np.arange(1,n+1)
    B = diag(1./x)
    y = np.arange(n-1,0,-1)
    z = np.arange(2*n-1,0,-2)
    A = diag(z)-diag(y,-1)-diag(y,1)
    return A,B 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def _equamax_obj(self, loadings):
        """
        Equamax function objective.

        Parameters
        ----------
        loadings : array-like
            The loading matrix

        Returns
        -------
        gradient_dict : dict
            A dictionary with
            - grad : np.array
                The gradient.
            - criterion : float
                The value of the criterion for the objective.
        """
        p, k = loadings.shape

        N = np.ones(k) - np.eye(k)
        M = np.ones(p) - np.eye(p)

        loadings_squared = loadings**2
        f1 = (1 - self.kappa) * np.sum(np.diag(np.dot(loadings_squared.T,
                                                      np.dot(loadings_squared, N)))) / 4
        f2 = self.kappa * np.sum(np.diag(np.dot(loadings_squared.T,
                                                np.dot(M, loadings_squared)))) / 4

        gradient = ((1 - self.kappa) * loadings * np.dot(loadings_squared, N) +
                    self.kappa * loadings * np.dot(M, loadings_squared))

        criterion = f1 + f2
        return {'grad': gradient, 'criterion': criterion} 

# 需要導入模塊: import scipy [as 別名]
# 或者: from scipy import diag [as 別名]
def _check_fiedler(n, p):
    # This is not necessarily the recommended way to find the Fiedler vector.
    np.random.seed(1234)
    col = np.zeros(n)
    col[1] = 1
    A = toeplitz(col)
    D = np.diag(A.sum(axis=1))
    L = D - A
    # Compute the full eigendecomposition using tricks, e.g.
    # http://www.cs.yale.edu/homes/spielman/561/2009/lect02-09.pdf
    tmp = np.pi * np.arange(n) / n
    analytic_w = 2 * (1 - np.cos(tmp))
    analytic_V = np.cos(np.outer(np.arange(n) + 1/2, tmp))
    _check_eigen(L, analytic_w, analytic_V)
    # Compute the full eigendecomposition using eigh.
    eigh_w, eigh_V = eigh(L)
    _check_eigen(L, eigh_w, eigh_V)
    # Check that the first eigenvalue is near zero and that the rest agree.
    assert_array_less(np.abs([eigh_w[0], analytic_w[0]]), 1e-14)
    assert_allclose(eigh_w[1:], analytic_w[1:])

    # Check small lobpcg eigenvalues.
    X = analytic_V[:, :p]
    lobpcg_w, lobpcg_V = lobpcg(L, X, largest=False)
    assert_equal(lobpcg_w.shape, (p,))
    assert_equal(lobpcg_V.shape, (n, p))
    _check_eigen(L, lobpcg_w, lobpcg_V)
    assert_array_less(np.abs(np.min(lobpcg_w)), 1e-14)
    assert_allclose(np.sort(lobpcg_w)[1:], analytic_w[1:p])

    # Check large lobpcg eigenvalues.
    X = analytic_V[:, -p:]
    lobpcg_w, lobpcg_V = lobpcg(L, X, largest=True)
    assert_equal(lobpcg_w.shape, (p,))
    assert_equal(lobpcg_V.shape, (n, p))
    _check_eigen(L, lobpcg_w, lobpcg_V)
    assert_allclose(np.sort(lobpcg_w), analytic_w[-p:])

    # Look for the Fiedler vector using good but not exactly correct guesses.
    fiedler_guess = np.concatenate((np.ones(n//2), -np.ones(n-n//2)))
    X = np.vstack((np.ones(n), fiedler_guess)).T
    lobpcg_w, lobpcg_V = lobpcg(L, X, largest=False)
    # Mathematically, the smaller eigenvalue should be zero
    # and the larger should be the algebraic connectivity.
    lobpcg_w = np.sort(lobpcg_w)
    assert_allclose(lobpcg_w, analytic_w[:2], atol=1e-14)