Fix MB01XX test signatures (43 failing tests in PR #258)

# Fix MB01XX Test Signatures

## Problem Summary
PR #258 has **43 failing tests** due to function signature mismatches. Tests were generated with incorrect LLM prompt and are missing required parameters.

**Root Cause:**
- Tests call MB01XX functions with wrong argument count/types
- Missing workspace arrays (dwork_obj)
- Mode parameters correctly use integers (0/1) per design
- Reference documentation created: `MB01XX_SIGNATURE_REFERENCE.md`

**Example Issue:**
```python
# Python wrapper expects (11 args):
mb01ld(uplo, trans, m, n, k, alpha, beta, r_obj, a_obj, x_obj, dwork_obj)

# Test incorrectly calls (8 args):
mb01ld(0, 0, n, k, alpha, beta, B, A)  # Missing: m, r_obj, x_obj, dwork_obj
```

## Key Findings

1. **3 functions have NO Python wrappers:** MB01KD, MB01MD, MB01ND
2. **7 non-existent functions in tests:** mb01kx, mb01lx, mb01mx, mb01nx, mb01ox, mb01px, mb01qx
3. **Mode parameters use integers:** UPLO=0/1, TRANS=0/1 (not strings - this is intentional design)
4. **Workspace arrays required** for most functions (exceptions: MB01SD, MB01SS, MB01XD, MB01XY)
5. **11 functions exist in wrapper but not tested:** mb01oc, mb01oe, mb01oh, mb01oo, mb01os, mb01ot, mb01rb, mb01rh, mb01rt, mb01rw, mb01ry

**Reference Document:** `MB01XX_SIGNATURE_REFERENCE.md` contains complete signature analysis

---

## Multi-Phase Fix Plan

### Phase 1: Audit and Cleanup (Foundation)
**Goal:** Remove invalid tests, document scope

**Tasks:**
- [ ] Remove tests for 7 non-existent functions (mb01kx, mb01lx, mb01mx, mb01nx, mb01ox, mb01px, mb01qx)
- [ ] Skip tests for 3 unwrapped functions (MB01KD, MB01MD, MB01ND) with `@pytest.mark.skip("No Python wrapper")`
- [ ] Create test inventory and group by function family

**Deliverable:** Clean test file with ~33 valid tests

---

### Phase 2: Fix Simple Functions (No Workspace)
**Goal:** Fix 4 functions without workspace requirements

**Functions:**
- [ ] **MB01SD** - Row/column scaling: `mb01sd(jobs, m, n, a_obj, r_obj, c_obj)` → `a_obj`
- [ ] **MB01SS** - Symmetric scaling: `mb01ss(jobs, uplo, n, a_obj, d_obj)` → `a_obj`
- [ ] **MB01XD** - Matrix inversion: `mb01xd(uplo, n, a_obj)` → `(a_obj, info)`
- [ ] **MB01XY** - Matrix inversion (variant): `mb01xy(uplo, n, a_obj)` → `(a_obj, info)`

**Test Data:** Extract from `SLICOT-Reference/doc/MB01{SD,SS,XD,XY}.html`

**Deliverable:** 4+ passing tests

---

### Phase 3: Fix Scaling/Normalization Functions
**Goal:** Fix matrix scaling utilities

**Functions:**
- [ ] **MB01PD** - Safe range scaling: 9 parameters including block structure (nbl, nrows_obj)
- [ ] **MB01QD** - Scale by CTO/CFROM: 10 parameters

**Challenges:** Block structure parameters, matrix type codes

**Deliverable:** 2+ passing tests

---

### Phase 4: Fix Symmetric/Skew-symmetric Transformations
**Goal:** Fix similarity transformation functions

**Functions:**
- [ ] **MB01LD** - Skew-symmetric similarity (workspace: required)
- [ ] **MB01RD** - Symmetric similarity (workspace: M*N)
- [ ] **MB01RU** - Symmetric similarity simplified (workspace: M*N)
- [ ] **MB01RX** - Symmetric matrix operation (no workspace)

**Test Strategy:**
```python
# Allocate workspace
dwork = np.zeros(m*n, dtype=np.float64, order='F')
r_obj, x_obj, info = slicutlet.mb01rd(uplo, trans, m, n, alpha, beta, r_obj, a_obj, x_obj, dwork)
```

**Deliverable:** 4+ passing tests

---

### Phase 5: Fix Hessenberg Operations
**Goal:** Fix Hessenberg matrix multiplication/transformation

**Functions:**
- [ ] **MB01OD** - Combined Hessenberg+triangular (workspace: N*N)
- [ ] **MB01TD** - Quasi-triangular product (workspace: N-1)
- [ ] **MB01UD** - Hessenberg multiply (no workspace)
- [ ] **MB01UW** - Hessenberg with workspace
- [ ] **MB01UX** - Triangular-Hessenberg (real)
- [ ] **MB01UY** - Triangular-Hessenberg (variant)

**Test Strategy:** Create Hessenberg matrices (upper triangular + one subdiagonal)

**Deliverable:** 6+ passing tests

---

### Phase 6: Fix Special Operations
**Goal:** Fix specialized functions

**Functions:**
- [ ] **MB01VD** - Kronecker-like product (returns dimensions: `c_obj, mc, nc, info`)
- [ ] **MB01WD** - Lyapunov-like operation (DICO: 0=Continuous, 1=Discrete)
- [ ] **MB01YD** - Symmetric rank-k-l update
- [ ] **MB01ZD** - Triangular-Hessenberg solve (DIAG: 0=Non-unit, 1=Unit)

**Deliverable:** 4+ passing tests

---

### Phase 7: Fix Complex Function
**Goal:** Fix the only complex MB01XX function

**Function:**
- [ ] **MB01UZ** - Complex triangular-Hessenberg
  - `alpha`: Python complex type (`1.0 + 0.5j`)
  - Arrays: `dtype=np.complex128`
  - Workspace: `zwork = np.zeros(..., dtype=np.complex128)`

**Deliverable:** 1+ passing test

---

### Phase 8: Validation and PR Update
**Goal:** Ensure all tests pass, update PR

**Tasks:**
- [ ] Run full test suite: `pytest python/tests/test_mb01xx.py -v`
- [ ] Verify test count: ~33 passing (43 - 7 nonexistent - 3 unwrapped)
- [ ] Add coverage for 11 missing wrapped functions (optional)
- [ ] Commit: `REFACTOR: Fix MB01XX test signatures (Phases 1-8)`
- [ ] Push to `fix/mb01xx-test-signatures` branch
- [ ] Update PR #258 description

**Deliverable:** Clean PR with all valid tests passing

---

## Mode Parameter Design (CRITICAL)

**From `CLAUDE.md` Translation Conventions:**

Mode parameters (CHARACTER*1 in Fortran) → **`const i32` in C** (deliberate design):
- Avoid string handling in C
- Use integer values: 0, 1, 2
- Python tests pass integers, not strings

**Mapping:**
- **UPLO:** 0=Upper, 1=Lower
- **TRANS:** 0=NoTranspose, 1=Transpose, 2=ConjugateTranspose
- **SIDE:** 0=Left, 1=Right
- **DIAG:** 0=Non-unit, 1=Unit
- **JOBS:** Function-specific
- **TYPE:** 0=General, 1=Lower, 2=Upper, 3=Hessenberg, 4/5/6=Band
- **SCUN:** 0=Scale, 1=Unscale
- **DICO:** 0=Continuous, 1=Discrete

**Example Flow:**
```
Python Test: uplo=0 → Wrapper: int uplo → C: const i32 uplo → BLAS: "U" (ternary)
```

C code converts to strings only when calling BLAS/LAPACK:
```c
SLC_DSYR2K((uplo ? "L" : "U"), (trans ? "T" : "N"), ...);
```

---

## Test Data Approach

For each function:
1. Read `SLICOT-Reference/doc/MBXXXX.html` "Example" section
2. Find Fortran READ statements to understand data format
3. Extract "Program Data" (column-major Fortran convention)
4. Extract "Program Results" for expected outputs
5. Write Python test with `assert_allclose(result, expected, rtol=1e-14)`

**Workspace Sizing Patterns:**
- `M*N` for general transformations
- `N*N` for square matrix operations
- `N-1` for quasi-triangular
- Check HTML "Arguments" section for LDWORK requirements

---

## Open Questions

1. Should we add tests for 11 unwrapped functions in extension_mb.c?
2. Should we create wrappers for MB01KD, MB01MD, MB01ND?
3. Test tolerance: rtol=1e-14 or looser (1e-10)?
4. Execute sequentially (one PR) or in parallel (multiple PRs per phase)?

---

## References

- **Signature Reference:** `MB01XX_SIGNATURE_REFERENCE.md`
- **SLICOT Docs:** `SLICOT-Reference/doc/MB*.html`
- **Python Wrappers:** `python/extensions/extension_mb.c`
- **C Implementations:** `src/MB/mb*.c`
- **Current PR:** #258
- **Fix Branch:** `fix/mb01xx-test-signatures`

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Fix MB01XX test signatures (43 failing tests in PR #258) #264

Fix MB01XX Test Signatures

Problem Summary

Key Findings

Multi-Phase Fix Plan

Phase 1: Audit and Cleanup (Foundation)

Phase 2: Fix Simple Functions (No Workspace)

Phase 3: Fix Scaling/Normalization Functions

Phase 4: Fix Symmetric/Skew-symmetric Transformations

Phase 5: Fix Hessenberg Operations

Phase 6: Fix Special Operations

Phase 7: Fix Complex Function

Phase 8: Validation and PR Update

Mode Parameter Design (CRITICAL)

Test Data Approach

Open Questions

References

Metadata

Assignees

Labels

Projects

Milestone

Relationships

Development

Fix MB01XX test signatures (43 failing tests in PR #258) #264

Description

Fix MB01XX Test Signatures

Problem Summary

Key Findings

Multi-Phase Fix Plan

Phase 1: Audit and Cleanup (Foundation)

Phase 2: Fix Simple Functions (No Workspace)

Phase 3: Fix Scaling/Normalization Functions

Phase 4: Fix Symmetric/Skew-symmetric Transformations

Phase 5: Fix Hessenberg Operations

Phase 6: Fix Special Operations

Phase 7: Fix Complex Function

Phase 8: Validation and PR Update

Mode Parameter Design (CRITICAL)

Test Data Approach

Open Questions

References

Metadata

Metadata

Assignees

Labels

Projects

Milestone

Relationships

Development

Issue actions