diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html index 659472b8..d5ca9c87 100644 --- a/docs/pyerrors/linalg.html +++ b/docs/pyerrors/linalg.html @@ -311,8 +311,6 @@ """Computes the matrix to scalar operation op to a given matrix of Obs.""" def _mat(x, **kwargs): dim = int(np.sqrt(len(x))) - if np.sqrt(len(x)) != dim: - raise Exception('Input has to have dim**2 entries') mat = [] for i in range(dim): @@ -325,8 +323,6 @@ if isinstance(obs, np.ndarray): raveled_obs = (1 * (obs.ravel())).tolist() - elif isinstance(obs, list): - raveled_obs = obs else: raise TypeError('Unproper type of input.') return derived_observable(_mat, raveled_obs, **kwargs) @@ -346,10 +342,7 @@ A[n, m] = entry B[n, m] = 0.0 big_matrix = np.block([[A, -B], [B, A]]) - if kwargs.get('num_grad') is True: - op_big_matrix = _num_diff_mat_mat_op(op, big_matrix, **kwargs) - else: - op_big_matrix = derived_observable(lambda x, **kwargs: op(x), [big_matrix], array_mode=True)[0] + op_big_matrix = derived_observable(lambda x, **kwargs: op(x), [big_matrix], array_mode=True)[0] dim = op_big_matrix.shape[0] op_A = op_big_matrix[0: dim // 2, 0: dim // 2] op_B = op_big_matrix[dim // 2:, 0: dim // 2] @@ -358,15 +351,11 @@ res[n, m] = CObs(op_A[n, m], op_B[n, m]) return res else: - if kwargs.get('num_grad') is True: - return _num_diff_mat_mat_op(op, obs, **kwargs) return derived_observable(lambda x, **kwargs: op(x), [obs], array_mode=True)[0] def eigh(obs, **kwargs): """Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.""" - if kwargs.get('num_grad') is True: - return _num_diff_eigh(obs, **kwargs) w = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[0], obs) v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs) return w, v @@ -374,235 +363,21 @@ def eig(obs, **kwargs): """Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.""" - if kwargs.get('num_grad') is True: - return _num_diff_eig(obs, **kwargs) - # Note: Automatic differentiation of eig is implemented in the git of autograd - # but not yet released to PyPi (1.3) w = derived_observable(lambda x, **kwargs: anp.real(anp.linalg.eig(x)[0]), obs) return w def pinv(obs, **kwargs): """Computes the Moore-Penrose pseudoinverse of a matrix of Obs.""" - if kwargs.get('num_grad') is True: - return _num_diff_pinv(obs, **kwargs) return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs) def svd(obs, **kwargs): """Computes the singular value decomposition of a matrix of Obs.""" - if kwargs.get('num_grad') is True: - return _num_diff_svd(obs, **kwargs) u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs) s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs) vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs) return (u, s, vh) - - -# Variants for numerical differentiation - -def _num_diff_mat_mat_op(op, obs, **kwargs): - """Computes the matrix to matrix operation op to a given matrix of Obs elementwise - which is suitable for numerical differentiation.""" - def _mat(x, **kwargs): - dim = int(np.sqrt(len(x))) - if np.sqrt(len(x)) != dim: - raise Exception('Input has to have dim**2 entries') - - mat = [] - for i in range(dim): - row = [] - for j in range(dim): - row.append(x[j + dim * i]) - mat.append(row) - - return op(np.array(mat))[kwargs.get('i')][kwargs.get('j')] - - if isinstance(obs, np.ndarray): - raveled_obs = (1 * (obs.ravel())).tolist() - elif isinstance(obs, list): - raveled_obs = obs - else: - raise TypeError('Unproper type of input.') - - dim = int(np.sqrt(len(raveled_obs))) - - res_mat = [] - for i in range(dim): - row = [] - for j in range(dim): - row.append(derived_observable(_mat, raveled_obs, i=i, j=j, **kwargs)) - res_mat.append(row) - - return np.array(res_mat) @ np.identity(dim) - - -def _num_diff_eigh(obs, **kwargs): - """Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh - elementwise which is suitable for numerical differentiation.""" - def _mat(x, **kwargs): - dim = int(np.sqrt(len(x))) - if np.sqrt(len(x)) != dim: - raise Exception('Input has to have dim**2 entries') - - mat = [] - for i in range(dim): - row = [] - for j in range(dim): - row.append(x[j + dim * i]) - mat.append(row) - - n = kwargs.get('n') - res = np.linalg.eigh(np.array(mat))[n] - - if n == 0: - return res[kwargs.get('i')] - else: - return res[kwargs.get('i')][kwargs.get('j')] - - if isinstance(obs, np.ndarray): - raveled_obs = (1 * (obs.ravel())).tolist() - elif isinstance(obs, list): - raveled_obs = obs - else: - raise TypeError('Unproper type of input.') - - dim = int(np.sqrt(len(raveled_obs))) - - res_vec = [] - for i in range(dim): - res_vec.append(derived_observable(_mat, raveled_obs, n=0, i=i, **kwargs)) - - res_mat = [] - for i in range(dim): - row = [] - for j in range(dim): - row.append(derived_observable(_mat, raveled_obs, n=1, i=i, j=j, **kwargs)) - res_mat.append(row) - - return (np.array(res_vec) @ np.identity(dim), np.array(res_mat) @ np.identity(dim)) - - -def _num_diff_eig(obs, **kwargs): - """Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig - elementwise which is suitable for numerical differentiation.""" - def _mat(x, **kwargs): - dim = int(np.sqrt(len(x))) - if np.sqrt(len(x)) != dim: - raise Exception('Input has to have dim**2 entries') - - mat = [] - for i in range(dim): - row = [] - for j in range(dim): - row.append(x[j + dim * i]) - mat.append(row) - - n = kwargs.get('n') - res = np.linalg.eig(np.array(mat))[n] - - if n == 0: - # Discard imaginary part of eigenvalue here - return np.real(res[kwargs.get('i')]) - else: - return res[kwargs.get('i')][kwargs.get('j')] - - if isinstance(obs, np.ndarray): - raveled_obs = (1 * (obs.ravel())).tolist() - elif isinstance(obs, list): - raveled_obs = obs - else: - raise TypeError('Unproper type of input.') - - dim = int(np.sqrt(len(raveled_obs))) - - res_vec = [] - for i in range(dim): - # Note: Automatic differentiation of eig is implemented in the git of autograd - # but not yet released to PyPi (1.3) - res_vec.append(derived_observable(_mat, raveled_obs, n=0, i=i, **kwargs)) - - return np.array(res_vec) @ np.identity(dim) - - -def _num_diff_pinv(obs, **kwargs): - """Computes the Moore-Penrose pseudoinverse of a matrix of Obs elementwise which is suitable - for numerical differentiation.""" - def _mat(x, **kwargs): - shape = kwargs.get('shape') - - mat = [] - for i in range(shape[0]): - row = [] - for j in range(shape[1]): - row.append(x[j + shape[1] * i]) - mat.append(row) - - return np.linalg.pinv(np.array(mat))[kwargs.get('i')][kwargs.get('j')] - - if isinstance(obs, np.ndarray): - shape = obs.shape - raveled_obs = (1 * (obs.ravel())).tolist() - else: - raise TypeError('Unproper type of input.') - - res_mat = [] - for i in range(shape[1]): - row = [] - for j in range(shape[0]): - row.append(derived_observable(_mat, raveled_obs, shape=shape, i=i, j=j, **kwargs)) - res_mat.append(row) - - return np.array(res_mat) @ np.identity(shape[0]) - - -def _num_diff_svd(obs, **kwargs): - """Computes the singular value decomposition of a matrix of Obs elementwise which - is suitable for numerical differentiation.""" - def _mat(x, **kwargs): - shape = kwargs.get('shape') - - mat = [] - for i in range(shape[0]): - row = [] - for j in range(shape[1]): - row.append(x[j + shape[1] * i]) - mat.append(row) - - res = np.linalg.svd(np.array(mat), full_matrices=False) - - if kwargs.get('n') == 1: - return res[1][kwargs.get('i')] - else: - return res[kwargs.get('n')][kwargs.get('i')][kwargs.get('j')] - - if isinstance(obs, np.ndarray): - shape = obs.shape - raveled_obs = (1 * (obs.ravel())).tolist() - else: - raise TypeError('Unproper type of input.') - - mid_index = min(shape[0], shape[1]) - - res_mat0 = [] - for i in range(shape[0]): - row = [] - for j in range(mid_index): - row.append(derived_observable(_mat, raveled_obs, shape=shape, n=0, i=i, j=j, **kwargs)) - res_mat0.append(row) - - res_mat1 = [] - for i in range(mid_index): - res_mat1.append(derived_observable(_mat, raveled_obs, shape=shape, n=1, i=i, **kwargs)) - - res_mat2 = [] - for i in range(mid_index): - row = [] - for j in range(shape[1]): - row.append(derived_observable(_mat, raveled_obs, shape=shape, n=2, i=i, j=j, **kwargs)) - res_mat2.append(row) - - return (np.array(res_mat0) @ np.identity(mid_index), np.array(res_mat1) @ np.identity(mid_index), np.array(res_mat2) @ np.identity(shape[1])) @@ -956,8 +731,6 @@ Obs valued. View Source 
def eigh(obs, **kwargs):
     """Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
-    if kwargs.get('num_grad') is True:
-        return _num_diff_eigh(obs, **kwargs)
     w = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[0], obs)
     v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
     return w, v
@@ -982,10 +755,6 @@ Obs valued.
             View Source
             
def eig(obs, **kwargs):
     """Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig."""
-    if kwargs.get('num_grad') is True:
-        return _num_diff_eig(obs, **kwargs)
-        # Note: Automatic differentiation of eig is implemented in the git of autograd
-        # but not yet released to PyPi (1.3)
     w = derived_observable(lambda x, **kwargs: anp.real(anp.linalg.eig(x)[0]), obs)
     return w
 

@@ -1009,8 +778,6 @@ Obs valued.
             View Source
             
def pinv(obs, **kwargs):
     """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
-    if kwargs.get('num_grad') is True:
-        return _num_diff_pinv(obs, **kwargs)
     return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
 

 
@@ -1033,8 +800,6 @@ Obs valued.
             View Source
             
def svd(obs, **kwargs):
     """Computes the singular value decomposition of a matrix of Obs."""
-    if kwargs.get('num_grad') is True:
-        return _num_diff_svd(obs, **kwargs)
     u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
     s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
     vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs)