我们从Python开源项目中，提取了以下9个代码示例，用于说明如何使用tensorflow.matrix_determinant()。
def exKxz_pairwise(self, Z, Xmu, Xcov): """ <x_t K_{x_{t-1}, Z}>_q_{x_{t-1:t}} :param Z: MxD inducing inputs :param Xmu: X mean (N+1xD) :param Xcov: 2x(N+1)xDxD :return: NxMxD """ msg_input_shape = "Currently cannot handle slicing in exKxz_pairwise." assert_input_shape = tf.assert_equal(tf.shape(Xmu)[1], self.input_dim, message=msg_input_shape) assert_cov_shape = tf.assert_equal(tf.shape(Xmu), tf.shape(Xcov)[1:3], name="assert_Xmu_Xcov_shape") with tf.control_dependencies([assert_input_shape, assert_cov_shape]): Xmu = tf.identity(Xmu) N = tf.shape(Xmu)[0] - 1 D = tf.shape(Xmu)[1] Xsigmb = tf.slice(Xcov, [0, 0, 0, 0], tf.stack([-1, N, -1, -1])) Xsigm = Xsigmb[0, :, :, :] # NxDxD Xsigmc = Xsigmb[1, :, :, :] # NxDxD Xmum = tf.slice(Xmu, [0, 0], tf.stack([N, -1])) Xmup = Xmu[1:, :] lengthscales = self.lengthscales if self.ARD else tf.zeros((D,), dtype=settings.float_type) + self.lengthscales scalemat = tf.expand_dims(tf.matrix_diag(lengthscales ** 2.0), 0) + Xsigm # NxDxD det = tf.matrix_determinant( tf.expand_dims(tf.eye(tf.shape(Xmu)[1], dtype=settings.float_type), 0) + tf.reshape(lengthscales ** -2.0, (1, 1, -1)) * Xsigm) # N vec = tf.expand_dims(tf.transpose(Z), 0) - tf.expand_dims(Xmum, 2) # NxDxM smIvec = tf.matrix_solve(scalemat, vec) # NxDxM q = tf.reduce_sum(smIvec * vec, [1]) # NxM addvec = tf.matmul(smIvec, Xsigmc, transpose_a=True) + tf.expand_dims(Xmup, 1) # NxMxD return self.variance * addvec * tf.reshape(det ** -0.5, (N, 1, 1)) * tf.expand_dims(tf.exp(-0.5 * q), 2)
def exKxz(self, Z, Xmu, Xcov): """ It computes the expectation: <x_t K_{x_t, Z}>_q_{x_t} :param Z: MxD inducing inputs :param Xmu: X mean (NxD) :param Xcov: NxDxD :return: NxMxD """ msg_input_shape = "Currently cannot handle slicing in exKxz." assert_input_shape = tf.assert_equal(tf.shape(Xmu)[1], self.input_dim, message=msg_input_shape) assert_cov_shape = tf.assert_equal(tf.shape(Xmu), tf.shape(Xcov)[:2], name="assert_Xmu_Xcov_shape") with tf.control_dependencies([assert_input_shape, assert_cov_shape]): Xmu = tf.identity(Xmu) N = tf.shape(Xmu)[0] D = tf.shape(Xmu)[1] lengthscales = self.lengthscales if self.ARD else tf.zeros((D,), dtype=settings.float_type) + self.lengthscales scalemat = tf.expand_dims(tf.matrix_diag(lengthscales ** 2.0), 0) + Xcov # NxDxD det = tf.matrix_determinant( tf.expand_dims(tf.eye(tf.shape(Xmu)[1], dtype=settings.float_type), 0) + tf.reshape(lengthscales ** -2.0, (1, 1, -1)) * Xcov) # N vec = tf.expand_dims(tf.transpose(Z), 0) - tf.expand_dims(Xmu, 2) # NxDxM smIvec = tf.matrix_solve(scalemat, vec) # NxDxM q = tf.reduce_sum(smIvec * vec, [1]) # NxM addvec = tf.matmul(smIvec, Xcov, transpose_a=True) + tf.expand_dims(Xmu, 1) # NxMxD return self.variance * addvec * tf.reshape(det ** -0.5, (N, 1, 1)) * tf.expand_dims(tf.exp(-0.5 * q), 2)
def eKzxKxz(self, Z, Xmu, Xcov): """ Also known as Phi_2. :param Z: MxD :param Xmu: X mean (NxD) :param Xcov: X covariance matrices (NxDxD) :return: NxMxM """ # use only active dimensions Xcov = self._slice_cov(Xcov) Z, Xmu = self._slice(Z, Xmu) M = tf.shape(Z)[0] N = tf.shape(Xmu)[0] D = tf.shape(Xmu)[1] lengthscales = self.lengthscales if self.ARD else tf.zeros((D,), dtype=settings.float_type) + self.lengthscales Kmms = tf.sqrt(self.K(Z, presliced=True)) / self.variance ** 0.5 scalemat = tf.expand_dims(tf.eye(D, dtype=settings.float_type), 0) + 2 * Xcov * tf.reshape(lengthscales ** -2.0, [1, 1, -1]) # NxDxD det = tf.matrix_determinant(scalemat) mat = Xcov + 0.5 * tf.expand_dims(tf.matrix_diag(lengthscales ** 2.0), 0) # NxDxD cm = tf.cholesky(mat) # NxDxD vec = 0.5 * (tf.reshape(tf.transpose(Z), [1, D, 1, M]) + tf.reshape(tf.transpose(Z), [1, D, M, 1])) - tf.reshape(Xmu, [N, D, 1, 1]) # NxDxMxM svec = tf.reshape(vec, (N, D, M * M)) ssmI_z = tf.matrix_triangular_solve(cm, svec) # NxDx(M*M) smI_z = tf.reshape(ssmI_z, (N, D, M, M)) # NxDxMxM fs = tf.reduce_sum(tf.square(smI_z), [1]) # NxMxM return self.variance ** 2.0 * tf.expand_dims(Kmms, 0) * tf.exp(-0.5 * fs) * tf.reshape(det ** -0.5, [N, 1, 1])
def Linear_RBF_eKxzKzx(self, Ka, Kb, Z, Xmu, Xcov): Xcov = self._slice_cov(Xcov) Z, Xmu = self._slice(Z, Xmu) lin, rbf = (Ka, Kb) if isinstance(Ka, Linear) else (Kb, Ka) if not isinstance(lin, Linear): TypeError("{in_lin} is not {linear}".format(in_lin=str(type(lin)), linear=str(Linear))) if not isinstance(rbf, RBF): TypeError("{in_rbf} is not {rbf}".format(in_rbf=str(type(rbf)), rbf=str(RBF))) if lin.ARD or type(lin.active_dims) is not slice or type(rbf.active_dims) is not slice: raise NotImplementedError("Active dims and/or Linear ARD not implemented. " "Switching to quadrature.") D = tf.shape(Xmu)[1] M = tf.shape(Z)[0] N = tf.shape(Xmu)[0] if rbf.ARD: lengthscales = rbf.lengthscales else: lengthscales = tf.zeros((D, ), dtype=settings.float_type) + rbf.lengthscales lengthscales2 = lengthscales ** 2.0 const = rbf.variance * lin.variance * tf.reduce_prod(lengthscales) gaussmat = Xcov + tf.matrix_diag(lengthscales2)[None, :, :] # NxDxD det = tf.matrix_determinant(gaussmat) ** -0.5 # N cgm = tf.cholesky(gaussmat) # NxDxD tcgm = tf.tile(cgm[:, None, :, :], [1, M, 1, 1]) vecmin = Z[None, :, :] - Xmu[:, None, :] # NxMxD d = tf.matrix_triangular_solve(tcgm, vecmin[:, :, :, None]) # NxMxDx1 exp = tf.exp(-0.5 * tf.reduce_sum(d ** 2.0, [2, 3])) # NxM # exp = tf.Print(exp, [tf.shape(exp)]) vecplus = (Z[None, :, :, None] / lengthscales2[None, None, :, None] + tf.matrix_solve(Xcov, Xmu[:, :, None])[:, None, :, :]) # NxMxDx1 mean = tf.cholesky_solve( tcgm, tf.matmul(tf.tile(Xcov[:, None, :, :], [1, M, 1, 1]), vecplus)) mean = mean[:, :, :, 0] * lengthscales2[None, None, :] # NxMxD a = tf.matmul(tf.tile(Z[None, :, :], [N, 1, 1]), mean * exp[:, :, None] * det[:, None, None] * const, transpose_b=True) return a + tf.transpose(a, [0, 2, 1])
def test_determinants(self): with self.test_session(): for batch_shape in [(), (2, 3,)]: for k in [1, 4]: operator, mat = self._build_operator_and_mat(batch_shape, k) expected_det = tf.matrix_determinant(mat).eval() self._compare_results(expected_det, operator.det()) self._compare_results(np.log(expected_det), operator.log_det())
def testDeterminants(self): with self.test_session(): for batch_shape in [(), (2, 3,)]: for k in [1, 4]: operator, mat = self._build_operator_and_mat(batch_shape, k) expected_det = tf.matrix_determinant(mat).eval() self._compare_results(expected_det, operator.det()) self._compare_results(np.log(expected_det), operator.log_det())
def test_MatrixDeterminant(self): t = tf.matrix_determinant(self.random(2, 3, 4, 3, 3)) self.check(t)
def determinant(kron_a): """Computes the determinant of a given Kronecker-factorized matrix. Note, that this method can suffer from overflow. Args: kron_a: `TensorTrain` object containing a matrix of size N x N, factorized into a Kronecker product of square matrices (all tt-ranks are 1 and all tt-cores are square). Returns: Number, the determinant of the given matrix. Raises: ValueError if the tt-cores of the provided matrix are not square, or the tt-ranks are not 1. """ if not _is_kron(kron_a): raise ValueError('The argument should be a Kronecker product (tt-ranks ' 'should be 1)') shapes_defined = kron_a.get_shape().is_fully_defined() if shapes_defined: i_shapes = kron_a.get_raw_shape()[0] j_shapes = kron_a.get_raw_shape()[1] else: i_shapes = ops.raw_shape(kron_a)[0] j_shapes = ops.raw_shape(kron_a)[1] if shapes_defined: if i_shapes != j_shapes: raise ValueError('The argument should be a Kronecker product of square ' 'matrices (tt-cores must be square)') pows = tf.cast(tf.reduce_prod(i_shapes), kron_a.dtype) cores = kron_a.tt_cores det = 1 for core_idx in range(kron_a.ndims()): core = cores[core_idx] core_det = tf.matrix_determinant(core[0, :, :, 0]) core_pow = pows / i_shapes[core_idx].value det *= tf.pow(core_det, core_pow) return det
def slog_determinant(kron_a): """Computes the sign and log-det of a given Kronecker-factorized matrix. Args: kron_a: `TensorTrain` object containing a matrix of size N x N, factorized into a Kronecker product of square matrices (all tt-ranks are 1 and all tt-cores are square). Returns: Two numbers, sign of the determinant and the log-determinant of the given matrix. If the determinant is zero, then sign will be 0 and logdet will be -Inf. In all cases, the determinant is equal to sign * np.exp(logdet). Raises: ValueError if the tt-cores of the provided matrix are not square, or the tt-ranks are not 1. """ if not _is_kron(kron_a): raise ValueError('The argument should be a Kronecker product ' '(tt-ranks should be 1)') shapes_defined = kron_a.get_shape().is_fully_defined() if shapes_defined: i_shapes = kron_a.get_raw_shape()[0] j_shapes = kron_a.get_raw_shape()[1] else: i_shapes = ops.raw_shape(kron_a)[0] j_shapes = ops.raw_shape(kron_a)[1] if shapes_defined: if i_shapes != j_shapes: raise ValueError('The argument should be a Kronecker product of square ' 'matrices (tt-cores must be square)') pows = tf.cast(tf.reduce_prod(i_shapes), kron_a.dtype) logdet = 0. det_sign = 1. for core_idx in range(kron_a.ndims()): core = kron_a.tt_cores[core_idx] core_det = tf.matrix_determinant(core[0, :, :, 0]) core_abs_det = tf.abs(core_det) core_det_sign = tf.sign(core_det) core_pow = pows / i_shapes[core_idx].value logdet += tf.log(core_abs_det) * core_pow det_sign *= core_det_sign**(core_pow) return det_sign, logdet
