Aman-Amith-Shastry-scientific_computation_mcp

Adds two stored tensors element-wise. Args: name_a (str): The name of the first tensor. name_b (str): The name of the second tensor. Returns: np.ndarray: The result of element-wise addition. Raises: ValueError: If the tensor names are not found or shapes are incompatible.

Changes the basis of a stored square matrix. Args: name (str): Name of the matrix in the tensor store. new_basis (list[list[float]]): Columns are new basis vectors. Returns: np.ndarray: Representation of the matrix in the new basis. Raises: ValueError: If the matrix name is not found or non-invertible.

Computes the eigenvalues and right eigenvectors of a stored square matrix. Args: name (str): The name of the tensor to analyze. Returns: dict: A dictionary with keys: - 'eigenvalues': np.ndarray - 'eigenvectors': np.ndarray Raises: ValueError: If the tensor is not found or is not a square matrix.

Creates a NumPy array (matrix) with a specified shape and values. Args: shape (list[int]): The shape of the resulting array as a tuple(e.g., (2, 3)). values (list[float]): A flat list of values to populate the array. name (str): The name of the tensor to be stored. Returns: np.ndarray: A NumPy array with the specified shape. Raises: ValueError: If the number of values does not match the product of the shape.

Computes the symbolic curl of a vector field, optionally evaluated at a point. Args: f_str (str): A string representing the vector field in list format (e.g., "[x+y, x, 2*z]"). point (list[float], optional): A list of coordinates [x, y, z] to evaluate the curl numerically. Returns: dict: A dictionary with the symbolic curl as a string, and optionally the evaluated vector.

Deletes a tensor from the in-memory tensor store. Args: name (str): The name of the tensor to delete. Raises: ValueError: If the tensor name is not found in the store or if an error occurs during deletion.

Computes the determinant of a stored square matrix. Args: name (str): The name of the matrix. Returns: float: The determinant of the matrix. Raises: ValueError: If the matrix is not found or is not square.

Computes symbolic directional derivative of scalar field along a vector direction. Args: f_str (str): Expression like "x*y*z". u (list[float]): Direction vector [vx, vy, vz]. unit (bool): True if u should be normalized before calculating directional derivative. Set to True by default. Returns: str: Symbolic result as string.

Computes the symbolic divergence of a vector field, optionally evaluated at a point. Args: f_str (str): A string representing the vector field in list format (e.g., "[x+y, x, 2*z]"). point (list[float], optional): A list of coordinates [x, y, z] to evaluate the divergence numerically. Returns: dict: A dictionary with the symbolic divergence as a string, and optionally the evaluated scalar.

Finds an orthonormal basis for the column space of a stored matrix using QR decomposition. Args: name (str): The name of the matrix. Returns: list[list[float]]: A list of orthonormal basis vectors. Raises: ValueError: If the matrix is not found or decomposition fails.

Computes the symbolic gradient of a scalar function. Args: f_str (str): A string representing a scalar function (e.g., "x**2 + y*z"). Returns: str: A string representation of the symbolic gradient as a vector.

Computes the Laplacian of a scalar or vector field symbolically. Args: f_str (str): Scalar function as "x**2 + y*z" or vector "[Fx, Fy, Fz]". is_vector (bool): Set True to compute vector Laplacian. Returns: str: Symbolic result of the Laplacian—scalar or list of 3 components.

Computes the inverse of a stored square matrix. Args: name (str): The name of the tensor to invert. Returns: np.ndarray: The inverse of the matrix. Raises: ValueError: If the matrix is not found, is not square, or is singular (non-invertible).

Performs matrix multiplication between two stored tensors. Args: name_a (str): The name of the first tensor. name_b (str): The name of the second tensor. Returns: np.ndarray: The result of matrix multiplication. Raises: ValueError: If either tensor is not found or their shapes are incompatible.

Plots a 2D or 3D mathematical function from a symbolic expression string. Args: expr_str: string representation of a function in x or x and y, e.g. "x**2" or "sin(sqrt(x**2 + y**2))" xlim: (xmin, xmax) range for x-axis ylim: (ymin, ymax) range for y-axis (used in 2D or 3D) grid: resolution of the plot grid Returns: A rendered Image of the function using Matplotlib. - 2D plot if the expression contains only x - 3D surface plot if the expression contains both x and y

Plots a 3D vector field from a string "[u(x,y,z), v(x,y,z), w(x,y,z)]" Args: f_str: string representation of 3D field, e.g. "[z, -y, x]". bounds: (xmin, xmax, ymin, ymax, zmin, zmax) n: grid resolution per axis Returns: Displayed Matplotlib 3D quiver plot (no image return needed)

Computes the QR decomposition of a stored matrix. Decomposes the matrix A into A = Q @ R, where Q is an orthogonal matrix and R is an upper triangular matrix. Args: name (str): The name of the matrix to decompose. Returns: dict: A dictionary with keys: - 'q': np.ndarray, the orthogonal matrix Q - 'r': np.ndarray, the upper triangular matrix R Raises: ValueError: If the matrix is not found or decomposition fails.

Computes the rank of a stored tensor. Args: name (str): The name of the tensor. Returns: int | list[int]: The rank of the matrix. Raises: ValueError: If the tensor name is not found in the store.

Scales a stored tensor by a scalar factor. Args: name (str): The name of the tensor to scale. scale_factor (float): The scalar value to multiply the tensor by. in_place (bool): If True, updates the stored tensor; otherwise, returns a new scaled tensor. Returns: np.ndarray: The scaled tensor. Raises: ValueError: If the tensor name is not found in the store.

Adds two stored tensors element-wise. Args: name_a (str): The name of the first tensor. name_b (str): The name of the second tensor. Returns: np.ndarray: The result of element-wise subtraction. Raises: ValueError: If the tensor names are not found or shapes are incompatible.

Computes the Singular Value Decomposition (SVD) of a stored matrix. Decomposes the matrix A into A = U @ S @ V^T, where U and V^T are orthogonal matrices, and S is a diagonal matrix of singular values. Args: name (str): The name of the matrix to decompose. Returns: dict: A dictionary with keys: - 'u': np.ndarray, the left singular vectors - 's': np.ndarray, the singular values - 'v_t': np.ndarray, the right singular vectors transposed Raises: ValueError: If the matrix is not found or decomposition fails.

Computes the transpose of a stored tensor. Args: name (str): The name of the tensor to transpose. Returns: np.ndarray: The transposed tensor. Raises: ValueError: If the tensor name is not found in the store.

Computes the cross product of two stored vectors. Args: name_a (str): Name of the first vector in the tensor store. name_b (str): Name of the second vector in the tensor store. Returns: np.ndarray: Vector result of the cross product. Raises: ValueError: If either vector is not found or if the cross product computation fails.

Computes the dot product between two stored vectors. Args: name_a (str): Name of the first vector in the tensor store. name_b (str): Name of the second vector in the tensor store. Returns: np.ndarray: Scalar result of the dot product. Raises: ValueError: If either vector is not found or if the dot product computation fails.

Projects a stored vector onto another vector. Args: name (str): Name of the stored vector to project. new_vector (list[float]): The vector to project onto. Returns: np.ndarray: The projection result vector. Raises: ValueError: If the vector name is not found or projection fails.

Returns an immutable view of a previously stored NumPy tensor from the in-memory tensor store. Args: name (str): The name of the tensor as stored in the in-store dictionary Returns: dict: The in-store dictionary for tensors