我们从Python开源项目中，提取了以下12个代码示例，用于说明如何使用tensorflow.matrix_solve()。
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 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_solve(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) # Work with 5 simultaneous systems. 5 is arbitrary. x = self._rng.randn(*(batch_shape + (k, 5))) self._compare_results( expected=tf.matrix_solve(mat, x).eval(), actual=operator.solve(x))
def test_sqrt_solve(self): # Square roots are not unique, but we should still have # S^{-T} S^{-1} x = A^{-1} x. # In our case, we should have S = S^T, so then S^{-1} S^{-1} x = A^{-1} x. 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) # Work with 5 simultaneous systems. 5 is arbitrary. x = self._rng.randn(*(batch_shape + (k, 5))) self._compare_results( expected=tf.matrix_solve(mat, x).eval(), actual=operator.sqrt_solve(operator.sqrt_solve(x)))
def testSolve(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) # Work with 5 simultaneous systems. 5 is arbitrary. x = self._rng.randn(*(batch_shape + (k, 5))) self._compare_results( expected=tf.matrix_solve(mat, x).eval(), actual=operator.solve(x))
def testSqrtSolve(self): # Square roots are not unique, but we should still have # S^{-T} S^{-1} x = A^{-1} x. # In our case, we should have S = S^T, so then S^{-1} S^{-1} x = A^{-1} x. 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) # Work with 5 simultaneous systems. 5 is arbitrary. x = self._rng.randn(*(batch_shape + (k, 5))) self._compare_results( expected=tf.matrix_solve(mat, x).eval(), actual=operator.sqrt_solve(operator.sqrt_solve(x)))
def block_CG(A_,B_): """ block version of CG. Get solution to matrix equation AX = B, ie X = A^-1 * B. Will be much faster than Cholesky for large-scale problems. """ n = tf.shape(B_)[0] m = tf.shape(B_)[1] X = tf.zeros((n,m)) V_ = tf.zeros((n,m)) R = B_ R_ = tf.matrix_set_diag(tf.zeros((n,m)),tf.ones([m])) #somewhat arbitrary again, may want to check sensitivity CG_EPS = tf.cast(n/1000,"float") MAX_ITER = tf.div(n,250) + 3 def cond(i,X,R_,R,V_): return tf.logical_and(i < MAX_ITER, tf.norm(R) > CG_EPS) def body(i,X,R_,R,V_): S = tf.matrix_solve(tf.matmul(tf.transpose(R_),R_), tf.matmul(tf.transpose(R),R)) V = R + tf.matmul(V_,S) T = tf.matrix_solve(tf.matmul(tf.transpose(V),tf.matmul(A_,V)), tf.matmul(tf.transpose(R),R)) X = X + tf.matmul(V,T) V_ = V R_ = R R = R - tf.matmul(A_,tf.matmul(V,T)) return i+1,X,R_,R,V_ i = tf.constant(0) i,X,_,_,_ = tf.while_loop(cond,body,[i,X,R_,R,V_]) return X
def test_MatrixSolve(self): t = tf.matrix_solve(*self.random((2, 3, 3, 3), (2, 3, 3, 1)), adjoint=False) self.check(t) t = tf.matrix_solve(*self.random((2, 3, 3, 3), (2, 3, 3, 1)), adjoint=True) self.check(t)
def genPerturbations(opt): with tf.name_scope("genPerturbations"): X = np.tile(opt.canon4pts[:,0],[opt.batchSize,1]) Y = np.tile(opt.canon4pts[:,1],[opt.batchSize,1]) dX = tf.random_normal([opt.batchSize,4])*opt.pertScale \ +tf.random_normal([opt.batchSize,1])*opt.transScale dY = tf.random_normal([opt.batchSize,4])*opt.pertScale \ +tf.random_normal([opt.batchSize,1])*opt.transScale O = np.zeros([opt.batchSize,4],dtype=np.float32) I = np.ones([opt.batchSize,4],dtype=np.float32) # fit warp parameters to generated displacements if opt.warpType=="homography": A = tf.concat([tf.stack([X,Y,I,O,O,O,-X*(X+dX),-Y*(X+dX)],axis=-1), tf.stack([O,O,O,X,Y,I,-X*(Y+dY),-Y*(Y+dY)],axis=-1)],1) b = tf.expand_dims(tf.concat([X+dX,Y+dY],1),-1) pPert = tf.matrix_solve(A,b)[:,:,0] pPert -= tf.to_float([[1,0,0,0,1,0,0,0]]) else: if opt.warpType=="translation": J = np.concatenate([np.stack([I,O],axis=-1), np.stack([O,I],axis=-1)],axis=1) if opt.warpType=="similarity": J = np.concatenate([np.stack([X,Y,I,O],axis=-1), np.stack([-Y,X,O,I],axis=-1)],axis=1) if opt.warpType=="affine": J = np.concatenate([np.stack([X,Y,I,O,O,O],axis=-1), np.stack([O,O,O,X,Y,I],axis=-1)],axis=1) dXY = tf.expand_dims(tf.concat([dX,dY],1),-1) pPert = tf.matrix_solve_ls(J,dXY)[:,:,0] return pPert # make training batch
def solve_linear_tf(model): """ Linearly solve the structure. """ Logger.info('Solving linear model with %d DOFs using TensorFlow...'%model.DOF) K_bar,F_bar,index=model.K_,model.F_,model.index K_bar=K_bar.astype(np.float32) F_bar=F_bar.astype(np.float32) Dvec=model.D #Begin a new graph if 'sess' in locals() and sess is not None: print('Close interactive session') sess.close() # with tf.device('/cpu:0'): K_init = tf.placeholder(tf.float32, shape=(model.DOF, model.DOF)) K_ = tf.Variable(K_init) # K_ = tf.constant(K_bar,name="stiffness") F_ = tf.Variable(np.array([F_bar.astype(np.float32)]),name="force") # with tf.device('/cpu:0'): D_=tf.matrix_solve(K_,tf.transpose(F_),name='displacement') sess = tf.Session(config=tf.ConfigProto(log_device_placement=True)) print(type(K_bar),K_bar.dtype,K_bar.shape) sess.run(tf.global_variables_initializer(),feed_dict={K_init:K_bar}) # run the op. delta=sess.run(D_) n_nodes=model.node_count #fill original displacement vector prev = 0 for idx in index: gap=idx-prev if gap>0: delta=np.insert(delta,prev,[0]*gap) prev = idx + 1 if idx==index[-1] and idx!=n_nodes-1: delta = np.insert(delta,prev, [0]*(n_nodes*6-prev)) delta += Dvec model.is_solved=True return delta
