selen 0.15.5

Constraint Satisfaction Problem (CSP) solver
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
/// Temporary performance test for LP solver
/// Tests a 100x100 problem to measure solve time and memory usage

use selen::lpsolver::{LpProblem, LpConfig};
use selen::lpsolver::simplex_primal::PrimalSimplex;

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_large_lp_problem_100x100() {
    // Problem size
    let n_vars = 100;      // 100 variables
    let n_constraints = 100; // 100 constraints
    
    println!("\n=== LP Solver Performance Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    
    // Create a feasible LP problem
    // Maximize: sum of all variables (c = [1, 1, ..., 1])
    let c: Vec<f64> = vec![1.0; n_vars];
    
    // Constraints: Each constraint sums a subset of variables <= some bound
    // Make it structured so it's feasible and not trivial
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // Add constraints of the form: x_i + x_{i+1} + ... + x_{i+9} <= 50
    // This creates overlapping constraints
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..10 {
            let idx = (i + j) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(50.0);
    }
    
    // Variable bounds: 0 <= x_i <= 10
    let lower = vec![0.0; n_vars];
    let upper = vec![10.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    // Create solver with default config (no limits)
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    // Time the solve
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    // Check result
    assert!(result.is_ok(), "Solver should succeed: {:?}", result);
    let solution = result.unwrap();
    
    println!("\n=== Results ===");
    println!("Status: {:?}", solution.status);
    println!("Objective value: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3} seconds ({:.1} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    
    // Calculate some statistics
    let sum_x: f64 = solution.x.iter().sum();
    let max_x = solution.x.iter().fold(f64::NEG_INFINITY, |a, &b| a.max(b));
    let min_x = solution.x.iter().fold(f64::INFINITY, |a, &b| a.min(b));
    
    println!("Sum of variables: {:.6}", sum_x);
    println!("Max variable value: {:.6}", max_x);
    println!("Min variable value: {:.6}", min_x);
    
    // Verify constraints are satisfied
    println!("\nVerifying constraints...");
    let mut max_violation = 0.0_f64;
    for i in 0..n_constraints {
        let lhs: f64 = problem.a[i].iter()
            .zip(solution.x.iter())
            .map(|(a_ij, x_j)| a_ij * x_j)
            .sum();
        let violation = (lhs - problem.b[i]).max(0.0);
        max_violation = max_violation.max(violation);
    }
    println!("Max constraint violation: {:.2e}", max_violation);
    assert!(max_violation < 1e-6, "Constraints should be satisfied");
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("\n=== Performance Summary ===");
    println!("✓ Problem solved successfully");
    println!("✓ Time: {:.3}s", elapsed.as_secs_f64());
    println!("✓ Estimated memory: ~{:.2} MB (constraint matrix: {:.2} MB, basis: {:.2} MB)", 
             estimated_total_mb, constraint_matrix_mb, basis_matrices_mb);
    println!("✓ Iterations: {}", solution.iterations);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_very_large_lp_problem_200x200() {
    // Even larger problem to stress test
    let n_vars = 200;
    let n_constraints = 200;
    
    println!("\n=== LP Solver Large Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        // Sparse constraints - only 5% non-zero
        for j in 0..10 {
            let idx = (i * 7 + j * 13) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(30.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![5.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed");
    let solution = result.unwrap();
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("\n=== Results (200x200) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_dense_problem_50x50() {
    // Smaller but dense problem
    let n_vars = 50;
    let n_constraints = 50;
    
    println!("\n=== LP Solver Dense Problem Test ===");
    println!("Problem size: {} variables, {} constraints (DENSE)", n_vars, n_constraints);
    
    let c: Vec<f64> = (0..n_vars).map(|i| (i + 1) as f64).collect();
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // Dense constraints - all variables in each constraint
    for i in 0..n_constraints {
        let row: Vec<f64> = (0..n_vars)
            .map(|j| ((i * j + 1) % 10) as f64 / 10.0)
            .collect();
        a.push(row);
        b.push(100.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![20.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed");
    let solution = result.unwrap();
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("\n=== Results (50x50 Dense) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_very_large_problem_500x500() {
    // Very large problem
    let n_vars = 500;
    let n_constraints = 500;
    
    println!("\n=== LP Solver Very Large Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // Sparse constraints - only ~2% non-zero
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..10 {
            let idx = (i * 11 + j * 17) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(25.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![5.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed");
    let solution = result.unwrap();
    
    println!("\n=== Results (500x500) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Memory: {:.2} MB", estimated_total_mb);
    
    // Performance summary
    let time_per_var = elapsed.as_secs_f64() / n_vars as f64;
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    println!("\n=== Performance Metrics ===");
    println!("Time per variable: {:.6}s ({:.3} ms)", time_per_var, time_per_var * 1000.0);
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_dense_500x500_50_percent() {
    // Test 500x500 with 50% density to compare with sparse version
    let n_vars = 500;
    let n_constraints = 500;
    
    println!("\n=== LP Solver 500x500 DENSE (50%) Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    println!("Density: ~50% (250 non-zeros per constraint)");
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // 50% density - 250 non-zero entries per constraint
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..250 {
            let idx = (i * 3 + j * 2) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(125.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![1.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed: {:?}", result.err());
    let solution = result.unwrap();
    
    println!("\n=== Results (500x500 DENSE 50%) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Memory: {:.2} MB", estimated_total_mb);
    
    let time_per_var = elapsed.as_secs_f64() / n_vars as f64;
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    println!("\n=== Performance Metrics ===");
    println!("Time per variable: {:.6}s ({:.3} ms)", time_per_var, time_per_var * 1000.0);
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
    
    // Compare with sparse version
    println!("\n=== Density Impact ===");
    println!("Sparse 500x500 (~2% density): ~100 seconds");
    println!("Dense 500x500 (50% density): {:.1} seconds", elapsed.as_secs_f64());
    let slowdown = elapsed.as_secs_f64() / 100.0;
    println!("Density slowdown factor: {:.1}x", slowdown);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_dense_500x500_10_percent() {
    // Test 500x500 with 10% density
    let n_vars = 500;
    let n_constraints = 500;
    
    println!("\n=== LP Solver 500x500 MEDIUM DENSE (10%) Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    println!("Density: ~10% (50 non-zeros per constraint)");
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // 10% density - 50 non-zero entries per constraint
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..50 {
            let idx = (i * 7 + j * 11) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(25.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![1.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed: {:?}", result.err());
    let solution = result.unwrap();
    
    println!("\n=== Results (500x500 10% DENSE) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Memory: {:.2} MB", estimated_total_mb);
    
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_large_problem_300x300() {
    // Large problem - sweet spot test
    let n_vars = 300;
    let n_constraints = 300;
    
    println!("\n=== LP Solver Large Problem Test (300x300) ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // Sparse constraints
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..10 {
            let idx = (i * 7 + j * 11) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(30.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![5.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed");
    let solution = result.unwrap();
    
    println!("\n=== Results (300x300) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Memory: {:.2} MB", estimated_total_mb);
    
    let time_per_var = elapsed.as_secs_f64() / n_vars as f64;
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    println!("\n=== Performance Metrics ===");
    println!("Time per variable: {:.6}s ({:.3} ms)", time_per_var, time_per_var * 1000.0);
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_very_dense_500x500_80_percent() {
    // Dense problem - 500x500 with 80% density
    let n_vars = 500;
    let n_constraints = 500;
    
    println!("\n=== LP Solver 500x500 VERY DENSE (80%) Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    println!("Density: ~80% (400 non-zeros per constraint)");
    println!("Expected: Fast convergence due to high density");
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // 80% density - 400 non-zero entries per constraint
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..400 {
            let idx = (i + j) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(200.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![1.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    let config = LpConfig::unlimited();
    let mut solver = PrimalSimplex::new(config);
    
    let result = solver.solve(&problem);
    
    assert!(result.is_ok(), "Solver should succeed: {:?}", result.err());
    let solution = result.unwrap();
    
    println!("\n=== Results (500x500 DENSE 80%) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    
    // Use statistics from the LP solver!
    println!("\n=== Statistics from LP Solver ===");
    println!("Solve time: {:.3}s ({:.0} ms)", 
             solution.stats.solve_time_ms / 1000.0, 
             solution.stats.solve_time_ms);
    println!("Peak memory: {:.2} MB", solution.stats.peak_memory_mb);
    println!("Phase 1 time: {:.3}s ({} iterations)", 
             solution.stats.phase1_time_ms / 1000.0, 
             solution.stats.phase1_iterations);
    println!("Phase 2 time: {:.3}s ({} iterations)", 
             solution.stats.phase2_time_ms / 1000.0, 
             solution.stats.phase2_iterations);
    println!("Factorizations: {}", solution.stats.factorizations);
    
    let time_per_iter = solution.stats.solve_time_ms / solution.iterations as f64;
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    
    println!("\n=== Performance Metrics ===");
    println!("Time per iteration: {:.2} ms", time_per_iter);
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
    
    println!("\n=== Comparison ===");
    println!("500x500 @ 50% density: 35s, 250 iterations");
    println!("500x500 @ 80% density: {:.1}s, {} iterations", 
             solution.stats.solve_time_ms / 1000.0, solution.iterations);
}

#[test]
#[ignore] // Run with: cargo test --release --ignored
fn test_extreme_large_problem_1000x1000() {
    // Extremely large problem
    let n_vars = 1000;
    let n_constraints = 1000;
    
    println!("\n=== LP Solver EXTREME Large Problem Test ===");
    println!("Problem size: {} variables, {} constraints", n_vars, n_constraints);
    println!("⚠ This test may take 10+ minutes!");
    
    let c: Vec<f64> = vec![1.0; n_vars];
    
    let mut a = Vec::new();
    let mut b = Vec::new();
    
    // Very sparse constraints - only ~1% non-zero
    for i in 0..n_constraints {
        let mut row = vec![0.0; n_vars];
        for j in 0..10 {
            let idx = (i * 13 + j * 19) % n_vars;
            row[idx] = 1.0;
        }
        a.push(row);
        b.push(20.0);
    }
    
    let lower = vec![0.0; n_vars];
    let upper = vec![4.0; n_vars];
    
    let problem = LpProblem::new(n_vars, n_constraints, c, a, b, lower, upper);
    
    // Add a timeout to avoid hanging tests
    let config = LpConfig::unlimited().with_timeout_ms(600_000); // 10 minute timeout
    let mut solver = PrimalSimplex::new(config);
    
    // Estimate memory usage from problem dimensions
    let constraint_matrix_mb = (n_vars * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let basis_matrices_mb = (2 * n_constraints * n_constraints * 8) as f64 / (1024.0 * 1024.0);
    let estimated_total_mb = constraint_matrix_mb + basis_matrices_mb;
    
    println!("Estimated memory: {:.2} MB", estimated_total_mb);
    
    let start = std::time::Instant::now();
    let result = solver.solve(&problem);
    let elapsed = start.elapsed();
    
    assert!(result.is_ok(), "Solver should succeed");
    let solution = result.unwrap();
    
    println!("\n=== Results (1000x1000) ===");
    println!("Status: {:?}", solution.status);
    println!("Objective: {:.6}", solution.objective);
    println!("Iterations: {}", solution.iterations);
    println!("Solve time: {:.3}s ({} ms)", 
             elapsed.as_secs_f64(), 
             elapsed.as_millis());
    println!("Memory: {:.2} MB", estimated_total_mb);
    
    // Performance summary
    let time_per_var = elapsed.as_secs_f64() / n_vars as f64;
    let iter_per_constraint = solution.iterations as f64 / n_constraints as f64;
    println!("\n=== Performance Metrics ===");
    println!("Time per variable: {:.6}s ({:.3} ms)", time_per_var, time_per_var * 1000.0);
    println!("Iterations per constraint: {:.2}", iter_per_constraint);
    
    if elapsed.as_secs() > 60 {
        println!("\n⚠ WARNING: Solve time exceeded 1 minute - this is approaching practical limits");
    } else if elapsed.as_secs() > 30 {
        println!("\n⚠ NOTE: Solve time > 30s - consider sparse matrix implementation for this size");
    }
}