dtmm.linalg

Numba optimized linear algebra functions for 4x4 matrices and 2x2 matrices.

Module Contents

dtmm.linalg.eig(matrix, overwrite_x=False)

Computes eigenvalues and eigenvectors of 3x3 matrix using numpy.linalg.eig. Eigenvalues are sorted so that eig[2] is the most distinct (extraordinary).

Parameters

• matrix ((..,3,3) array) – A 3x3 matrix.

• overwrite_x (bool, optional) – Ifset, the function will write eigenvectors as rows in the input array.

Returns

• w ((…, 3) array) – The eigenvalues, each repeated according to its multiplicity. The eigenvalues are ordered so that the third eigenvalue is most distinct and first two are least distinct

• v ((…, 3, 3) array) – The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].

dtmm.linalg.tensor_eig(tensor, overwrite_x=False)

Computes eigenvalues and eigenvectors of a tensor.

Eigenvalues are sorted so that eig[2] is the most distinct (extraordinary).

If tensor is provided as a length 6 matrix, the elements are a[0,0], a[1,1], a[2,2], a[0,1], a[0,2], a[1,2]. If provided as a (3x3) matrix a, the rest of the elements are silently ignored.

Parameters

• tensor ((..,6) or (..,3,3) array) – A length 6 array or 3x3 matrix

• overwrite_x (bool, optional) – If tensor is (…,3,3) array, the function will write eigenvectors as rows in the input array.

Returns

• w ((…, 3) array) – The eigenvalues, each repeated according to its multiplicity. The eigenvalues are ordered so that the third eigenvalue is most distinct and first two are least distinct

• v ((…, 3, 3) array) – The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].

dtmm.linalg.inv(mat, out)

inv(mat), gufunc

Calculates inverse of a 4x4 complex matrix or 2x2 complex matrix

Parameters

mat (ndarray) – Input array

Examples

>>> a = np.random.randn(4,4) + 0j
>>> ai = inv(a)

>>> from numpy.linalg import inv
>>> ai2 = inv(a)

>>> np.allclose(ai2,ai)
True

dtmm.linalg.dotmf(a, b, out=None)

dotmf(a, b)

Computes a dot product of an array of 4x4 (or 2x2) matrix with a field array or an E-array (in case of 2x2 matrices).

dtmm.linalg.dotmm(a, b, out)

dotmm(a, b)

Computes an efficient dot product of a 4x4, 2x2 or a less efficient general matrix multiplication.

dtmm.linalg.dotmd(a, d, out)

dotmd(a, d)

Computes a dot product of a 4x4 (or 2x2) matrix with a diagonal matrix represented by a vector of shape 4 (or 2).

dtmm.linalg.dotmv(a, b, out)

dotmv(a, b)

Computes a dot product of a 4x4 or 2x2 matrix with a vector.

dtmm.linalg.dotmdm(a, d, b, out)

dotmdm(a, d, b)

Computes a dot product of a 4x4 (or 2x2) matrix with a diagonal matrix (4- or 2-vector) and another 4x4 (or 2x2) matrix.

dtmm.linalg.multi_dot(arrays, axis=0, reverse=False)

Computes dot product of multiple 2x2 or 4x4 matrices. If reverse is specified, it is performed in reversed order. Axis defines the axis over which matrices are multiplied.