Linear System Solver
solve_linear_systemRead-onlyIdempotent
Solve systems of linear equations Ax=b using SciPy's optimized solver. Handles square systems directly and overdetermined systems via least squares for best-fit solutions.
Instructions
Solve systems of linear equations (Ax = b) using SciPy's optimised solver.
Examples:
SQUARE SYSTEM (2 equations, 2 unknowns): coefficients=[[2,3],[1,1]], constants=[8,3], method="direct" Solves: 2x+3y=8, x+y=3 Result: [x=1, y=2]
OVERDETERMINED SYSTEM (3 equations, 2 unknowns): coefficients=[[1,2],[3,4],[5,6]], constants=[5,6,7], method="least_squares" Finds best-fit x minimizing ||Ax-b|| Result: [x≈-6, y≈5.5]
3x3 SYSTEM: coefficients=[[2,1,-1],[1,3,2],[-1,2,1]], constants=[8,13,5], method="direct" Result: [x=3, y=2, z=1]
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| context | No | Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification. | |
| output_mode | No | Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details. | full |
| coefficients | Yes | Coefficient matrix A in Ax=b system (2D list, e.g., [[2,3],[1,1]]) | |
| constants | Yes | Constants vector b in Ax=b system (1D list, e.g., [8,3]) | |
| method | No | Solution method: direct=exact (square systems), least_squares=overdetermined systems | direct |
Output Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |