create_tensor
Creates a new tensor based on a given name, shape, and values, and adds it to the tensor store. For the purposes of this server, tensors are vectors and matrices.
view_tensor
Display the contents of a tensor from the store.
delete_tensor
Deletes a tensor based on its name in the tensor store.
add_matrices
Adds two matrices with the provided names, if compatible.
subtract_matrices
Subtracts two matrices with the provided names, if compatible.
multiply_matrices
Multiplies two matrices with the provided names, if compatible.
scale_matrix
Scales a matrix of the provided name by a certain factor, in-place by default.
matrix_inverse
Computes the inverse of the matrix with the provided name.
transpose
Computes the transpose of the inverse of the matrix of the provided name.
determinant
Computes the determinant of the matrix of the provided name.
rank
Computes the rank (number of pivots) of the matrix of the provided name.
compute_eigen
Calculates the eigenvectors and eigenvalues of the matrix of the provided name.
qr_decompose
Computes the QR factorization of the matrix of the provided name. The columns of Q are an orthonormal basis for the image of the matrix, and R is upper triangular.
svd_decompose
Computes the Singular Value Decomposition of the matrix of the provided name.
find_orthonormal_basis
Finds an orthonormal basis for the matrix of the provided name. The vectors returned are all pair-wise orthogonal and are of unit length.
change_basis
Computes the matrix of the provided name in the new basis.
vector_project
Projects a vector in the tensor store to the specified vector in the same vector space.
vector_dot_product
Computes the dot product of two vectors in the tensor stores based on their provided names.
vector_cross_product
Computes the cross product of two vectors in the tensor stores based on their provided names.
gradient
Computes the gradient of a multivariable function based on the input function. Example call: gradient("x^2 + 2xyz + zy^3"). Do NOT include the function name (like f(x, y, z) = ...).
curl
Computes the curl of a vector field based on the input vector field. The input string must be formatted as a python list. Example call: curl("[3xy, 2z^4, 2y]").
divergence
Computes the divergence of a vector field based on the input vector field. The input string must be formatted as a python list. Example call: divergence("[3xy, 2z^4, 2y]").
laplacian
Computes the laplacian of a scalar function (as the divergence of the gradient) or a vector field (where a component-wise laplacian is computed). If a scalar function is the input, it must be input in the same format as in the gradient tool. If the input is a vector field, it must be input in the same manner as the curl/divergence tools.
directional_deriv
Computes the directional derivative of a function in a given direction u. By default, the tool normalizes u before computing the directional derivative, as specified by the unit parameter.
plot_vector_field
Plots a vector field (specified in the same format as in the curl/divergence functions). Currently, only 3d vector fields are supported. A 2d png perspective image of the vector field is returned. By default, the bounds of the graph are from -1 to 1 on each axis.
plot_function
Plots a function in 2d or 3d (based on the input variables), specified in the same format as in the gradient tool. Only the variables x and y can be used.