Scientific Computation MCP

import ast import numpy as np def register_tools(mcp, tensor_store): # Matrix/tensor operations @mcp.tool() def add_matrices(name_a: str, name_b: str) -> np.ndarray: """ 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. """ if name_a not in tensor_store or name_b not in tensor_store: raise ValueError("One or both tensor names not found in the store.") try: result = np.add(tensor_store[name_a], tensor_store[name_b]) except ValueError as e: raise ValueError(f"Error adding tensors: {e}") return result @mcp.tool() def subtract_matrices(name_a: str, name_b: str) -> np.ndarray: """ 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. """ if name_a not in tensor_store or name_b not in tensor_store: raise ValueError("One or both tensor names not found in the store.") try: result = np.subtract(tensor_store[name_a], tensor_store[name_b]) except ValueError as e: raise ValueError(f"Error subtracting tensors: {e}") return result @mcp.tool() def multiply_matrices(name_a: str, name_b: str) -> np.ndarray: """ 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. """ if name_a not in tensor_store or name_b not in tensor_store: raise ValueError("One or both tensor names not found in the store.") try: result = np.matmul(tensor_store[name_a], tensor_store[name_b]) except ValueError as e: raise ValueError(f"Error subtracting tensors: {e}") return result @mcp.tool() def scale_matrix(name: str, scale_factor: float, in_place: bool = True) -> np.ndarray: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") result = tensor_store[name] * scale_factor if in_place: tensor_store[name] = result return result @mcp.tool() def matrix_inverse(name: str) -> np.ndarray: """ 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). """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") try: result = np.linalg.inv(tensor_store[name]) except ValueError as e: raise ValueError(f"Error computing matrix inverse: {e}") return result @mcp.tool() def transpose(name: str) -> np.ndarray: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") return tensor_store[name].T @mcp.tool() def determinant(name: str) -> float: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") try: result = np.linalg.det(tensor_store[name]) except ValueError as e: raise ValueError(f"Error computing determinant: {e}") return result @mcp.tool() def rank(name: str) -> int | list[int]: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") result = np.linalg.matrix_rank(tensor_store[name]) return result @mcp.tool() def compute_eigen(name: str) -> dict: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") try: eigenvalues, eigenvectors = np.linalg.eig(tensor_store[name]) except ValueError as e: raise ValueError(f"Error computing eigenvalues and eigenvectors: {e}") return {"eigenvalues": eigenvalues, "eigenvectors": eigenvectors} # Matrix decompositions @mcp.tool() def qr_decompose(name: str) -> dict: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") try: q, r = np.linalg.qr(tensor_store[name]) except ValueError as e: raise ValueError(f"Error computing QR decomposition: {e}") return {'q': q, 'r': r} @mcp.tool() def svd_decompose(name: str) -> dict: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") try: u, s, v_t = np.linalg.svd(tensor_store[name]) except ValueError as e: raise ValueError(f"Error computing SVD decomposition: {e}") return {'u': u, 's': s, 'v_t': v_t} # Bases @mcp.tool() async def find_orthonormal_basis(name: str) -> list[list[float]]: """ 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. """ try: result = await mcp.call_tool("qr_decompose", arguments={'name': name}) d = ast.literal_eval(result[-1].text) except ValueError as e: raise ValueError(f"Error computing orthonormal basis: {e}") return d['q'] @mcp.tool() def change_basis(name: str, new_basis: list[list[float]]) -> np.ndarray: """ 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. """ if name not in tensor_store: raise ValueError("The tensor name is not found in the store.") new_basis = np.asarray(new_basis) return np.linalg.inv(new_basis) @ tensor_store[name] @ new_basis