Fix #548: [Model] CosineProductIntegration

docs/paper/reductions.typ

@@ -85,6 +85,7 @@
   "Satisfiability": [SAT],
   "KSatisfiability": [$k$-SAT],
   "CircuitSAT": [CircuitSAT],
+  "CosineProductIntegration": [Cosine Product Integration],
   "Factoring": [Factoring],
   "KingsSubgraph": [King's Subgraph MIS],
   "TriangularSubgraph": [Triangular Subgraph MIS],
@@ -1911,6 +1912,17 @@ NP-completeness was established by Garey, Johnson, and Stockmeyer @gareyJohnsonS
   *Example.* Let $A = {3, 7, 1, 8, 2, 4}$ ($n = 6$) and target $B = 11$. Selecting $A' = {3, 8}$ gives sum $3 + 8 = 11 = B$. Another solution: $A' = {7, 4}$ with sum $7 + 4 = 11 = B$.
 ]
 
+#problem-def("CosineProductIntegration")[
+  Given integers $a_1, dots, a_n$, determine whether
+  $
+    integral_0^(2 pi) product_(i=1)^n cos(a_i theta) dif theta != 0.
+  $
+][
+  Cosine Product Integration appears as problem A7 AN14 in Garey and Johnson @garey1979. Expanding each cosine as $(e^(i a_i theta) + e^(-i a_i theta)) / 2$ shows that the integral equals $(2 pi / 2^n)$ times the number of sign vectors $epsilon in {-1, 1}^n$ with $sum_i epsilon_i a_i = 0$. Therefore the integral is nonzero exactly when there exists a balanced signed sum. Equivalently, after replacing each coefficient by its absolute value, the YES instances are precisely those whose multiset can be partitioned into two equal-sum parts. Garey and Johnson note the resulting decision problem remains solvable in pseudo-polynomial time @garey1979, and the same equivalence inherits the $O^*(2^(n slash 2))$ meet-in-the-middle exact algorithm used for Partition and Subset Sum @horowitz1974.
+
+  *Example.* For coefficients $(2, 3, 5)$ we have the balanced sign assignment $+2 + 3 - 5 = 0$, so the integral equals $(2 pi / 2^3) times 2 = pi / 2$ and the answer is YES. For coefficients $(1, 2, 6)$ the total absolute sum is $9$, which is odd, so no balanced sign assignment exists and the integral is zero; hence the answer is NO.
+]
+
 #{
   let x = load-model-example("ShortestCommonSupersequence")
   let alpha-size = x.instance.alphabet_size

docs/src/cli.md

@@ -296,6 +296,7 @@ pred create UndirectedTwoCommodityIntegralFlow --graph 0-2,1-2,2-3 --capacities
 pred create LengthBoundedDisjointPaths --graph 0-1,1-6,0-2,2-3,3-6,0-4,4-5,5-6 --source 0 --sink 6 --num-paths-required 2 --bound 3 -o lbdp.json
 pred create Factoring --target 15 --bits-m 4 --bits-n 4 -o factoring.json
 pred create Factoring --target 21 --bits-m 3 --bits-n 3 -o factoring2.json
+pred create CosineProductIntegration --coefficients 2,3,5 -o cpi.json
 pred create X3C --universe 9 --sets "0,1,2;0,2,4;3,4,5;3,5,7;6,7,8;1,4,6;2,5,8" -o x3c.json
 pred create MinimumTardinessSequencing --n 5 --deadlines 5,5,5,3,3 --precedence-pairs "0>3,1>3,1>4,2>4" -o mts.json
 ```
@@ -447,6 +448,14 @@ Solution: [1, 0, 0, 1]
 Evaluation: Valid(2)
 ```
 
+Some models do not yet have an ILP reduction path. For example, `CosineProductIntegration`
+currently needs brute force:
+
+```bash
+pred create CosineProductIntegration --coefficients 2,3,5 -o cpi.json
+pred solve cpi.json --solver brute-force
+```
+
 Solve a reduction bundle (from `pred reduce`):
 
 ```bash
@@ -483,7 +492,7 @@ If the shell argument is omitted, `pred completions` auto-detects your current s
 
 ## JSON Output
 
-All commands support `-o` to write JSON to a file and `--json` to print JSON to stdout:
+Successful data-producing commands support `-o` to write JSON to a file and `--json` to print JSON to stdout:
 
 ```bash
 pred list -o problems.json       # save to file
@@ -493,6 +502,8 @@ pred path MIS QUBO --json
 pred solve problem.json --json
 ```
 
+Errors are still reported as plain text on stderr, even when `--json` is set.
+
 This is useful for scripting and piping:
 
 ```bash

problemreductions-cli/src/cli.rs

@@ -17,10 +17,12 @@ Piping (use - to read from stdin):
   pred create MIS --graph 0-1,1-2 | pred evaluate - --config 1,0,1
   pred create MIS --graph 0-1,1-2 | pred reduce - --to QUBO
 
-JSON output (any command):
+JSON output (successful commands):
   pred list --json                 # JSON to stdout
   pred show MIS --json | jq '.'   # pipe to jq
 
+Errors are reported on stderr as text, even when `--json` is set.
+
 Use `pred <command> --help` for detailed usage of each command.
 Use `pred list` to see all available problem types.
 
@@ -229,6 +231,7 @@ Flags by problem type:
   LengthBoundedDisjointPaths      --graph, --source, --sink, --num-paths-required, --bound
   Factoring                       --target, --m, --n
   BinPacking                      --sizes, --capacity
+  CosineProductIntegration        --coefficients
   SubsetSum                       --sizes, --target
   PaintShop                       --sequence
   MaximumSetPacking               --sets [--weights]
@@ -274,7 +277,8 @@ Examples:
   pred create FVS --arcs \"0>1,1>2,2>0\" --weights 1,1,1
   pred create UndirectedTwoCommodityIntegralFlow --graph 0-2,1-2,2-3 --capacities 1,1,2 --source-1 0 --sink-1 3 --source-2 1 --sink-2 3 --requirement-1 1 --requirement-2 1
   pred create X3C --universe 9 --sets \"0,1,2;0,2,4;3,4,5;3,5,7;6,7,8;1,4,6;2,5,8\"
-  pred create SetBasis --universe 4 --sets \"0,1;1,2;0,2;0,1,2\" --k 3")]
+  pred create SetBasis --universe 4 --sets \"0,1;1,2;0,2;0,1,2\" --k 3
+  pred create CosineProductIntegration --coefficients 2,3,5")]
 pub struct CreateArgs {
     /// Problem type (e.g., MIS, QUBO, SAT). Omit when using --example.
     #[arg(value_parser = crate::problem_name::ProblemNameParser)]
@@ -375,6 +379,9 @@ pub struct CreateArgs {
     /// Item sizes for BinPacking (comma-separated, e.g., "3,3,2,2")
     #[arg(long)]
     pub sizes: Option<String>,
+    /// Integer cosine frequencies for CosineProductIntegration (comma-separated, e.g., "2,3,5")
+    #[arg(long)]
+    pub coefficients: Option<String>,
     /// Bin capacity for BinPacking
     #[arg(long)]
     pub capacity: Option<String>,

problemreductions-cli/src/commands/create.rs

@@ -13,8 +13,9 @@ use problemreductions::models::graph::{
     SteinerTree,
 };
 use problemreductions::models::misc::{
-    BinPacking, FlowShopScheduling, LongestCommonSubsequence, MinimumTardinessSequencing,
-    PaintShop, SequencingWithinIntervals, ShortestCommonSupersequence, SubsetSum,
+    BinPacking, CosineProductIntegration, FlowShopScheduling, LongestCommonSubsequence,
+    MinimumTardinessSequencing, PaintShop, SequencingWithinIntervals, ShortestCommonSupersequence,
+    SubsetSum,
 };
 use problemreductions::prelude::*;
 use problemreductions::registry::collect_schemas;
@@ -55,6 +56,7 @@ fn all_data_flags_empty(args: &CreateArgs) -> bool {
         && args.requirement_1.is_none()
         && args.requirement_2.is_none()
         && args.sizes.is_none()
+        && args.coefficients.is_none()
         && args.capacity.is_none()
         && args.sequence.is_none()
         && args.sets.is_none()
@@ -233,7 +235,6 @@ fn type_format_hint(type_name: &str, graph_type: Option<&str>) -> &'static str {
         "Vec<Vec<usize>>" => "semicolon-separated groups: \"0,1;2,3\"",
         "usize" => "integer",
         "u64" => "integer",
-        "Vec<u64>" => "comma-separated integers: 0,0,5",
         "i64" => "integer",
         "BigUint" => "nonnegative decimal integer",
         "Vec<BigUint>" => "comma-separated nonnegative decimal integers: 3,7,1,8",
@@ -280,6 +281,7 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str {
         "PartitionIntoTriangles" => "--graph 0-1,1-2,0-2",
         "Factoring" => "--target 15 --m 4 --n 4",
         "SequencingWithinIntervals" => "--release-times 0,0,5 --deadlines 11,11,6 --lengths 3,1,1",
+        "CosineProductIntegration" => "--coefficients 2,3,5",
         "SteinerTree" => "--graph 0-1,1-2,1-3,3-4 --edge-weights 2,2,1,1 --terminals 0,2,4",
         "OptimalLinearArrangement" => "--graph 0-1,1-2,2-3 --bound 5",
         "DirectedTwoCommodityIntegralFlow" => {
@@ -954,6 +956,21 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
             )
         }
 
+        // CosineProductIntegration
+        "CosineProductIntegration" => {
+            let coefficients_str = args.coefficients.as_deref().ok_or_else(|| {
+                anyhow::anyhow!(
+                    "CosineProductIntegration requires --coefficients\n\n\
+                     Usage: pred create CosineProductIntegration --coefficients 2,3,5"
+                )
+            })?;
+            let coefficients: Vec<i64> = util::parse_comma_list(coefficients_str)?;
+            (
+                ser(CosineProductIntegration::new(coefficients))?,
+                resolved_variant.clone(),
+            )
+        }
+
         // PaintShop
         "PaintShop" => {
             let seq_str = args.sequence.as_deref().ok_or_else(|| {

problemreductions-cli/tests/cli_tests.rs

@@ -4068,6 +4068,86 @@ fn test_create_factoring_missing_bits() {
     );
 }
 
+// ---- CosineProductIntegration create tests ----
+
+#[test]
+fn test_create_cosine_product_integration() {
+    let output = pred()
+        .args([
+            "create",
+            "CosineProductIntegration",
+            "--coefficients",
+            "2,3,5",
+        ])
+        .output()
+        .unwrap();
+    assert!(
+        output.status.success(),
+        "stderr: {}",
+        String::from_utf8_lossy(&output.stderr)
+    );
+    let stdout = String::from_utf8(output.stdout).unwrap();
+    let json: serde_json::Value = serde_json::from_str(&stdout).unwrap();
+    assert_eq!(json["type"], "CosineProductIntegration");
+    assert_eq!(json["data"]["coefficients"], serde_json::json!([2, 3, 5]));
+}
+
+#[test]
+fn test_create_cosine_product_integration_no_flags_shows_help() {
+    let output = pred()
+        .args(["create", "CosineProductIntegration"])
+        .output()
+        .unwrap();
+    assert!(
+        !output.status.success(),
+        "should exit non-zero when showing help without data flags"
+    );
+    let stderr = String::from_utf8_lossy(&output.stderr);
+    assert!(
+        stderr.contains("--coefficients"),
+        "expected '--coefficients' in help output, got: {stderr}"
+    );
+    assert!(
+        stderr.contains("pred create CosineProductIntegration --coefficients 2,3,5"),
+        "expected cosine-product example in help output, got: {stderr}"
+    );
+}
+
+#[test]
+fn test_create_cosine_product_integration_missing_coefficients() {
+    let output = pred()
+        .args(["create", "CosineProductIntegration", "--target", "15"])
+        .output()
+        .unwrap();
+    assert!(!output.status.success());
+    let stderr = String::from_utf8_lossy(&output.stderr);
+    assert!(
+        stderr.contains("CosineProductIntegration requires --coefficients"),
+        "expected missing-coefficients error, got: {stderr}"
+    );
+    assert!(
+        stderr.contains("pred create CosineProductIntegration --coefficients 2,3,5"),
+        "expected usage example in error output, got: {stderr}"
+    );
+}
+
+#[test]
+fn test_create_model_example_cosine_product_integration() {
+    let output = pred()
+        .args(["create", "--example", "CosineProductIntegration"])
+        .output()
+        .unwrap();
+    assert!(
+        output.status.success(),
+        "stderr: {}",
+        String::from_utf8_lossy(&output.stderr)
+    );
+    let stdout = String::from_utf8(output.stdout).unwrap();
+    let json: serde_json::Value = serde_json::from_str(&stdout).unwrap();
+    assert_eq!(json["type"], "CosineProductIntegration");
+    assert_eq!(json["data"]["coefficients"], serde_json::json!([2, 3, 5]));
+}
+
 // ---- Timeout tests (H3) ----
 
 #[test]