Add support for norm2 (#36)

Fairly straightforward as the implementation is the same as for the
1-norm.

However, we are starting to see small differences in results in some
tests. For now, the parameters were chosen to get a similar solution
with and without this library but changing them a little bit makes the
backfill test start to fail.

Part of #23

pyproject.toml

@@ -77,6 +77,7 @@ dependencies = [
   "coverage[toml]",
   "pytest",
   "pytest-insta",
+  "pytest-xdist",
 ]
 matrix-name-format = "{variable}{value}"
 

src/cvxpy_gurobi/__init__.py

@@ -99,6 +99,12 @@ class InvalidPowerError(UnsupportedExpressionError):
     msg_template = "Unsupported power: {node}, only quadratic expressions are supported"
 
 
+class InvalidNormError(UnsupportedExpressionError):
+    msg_template = (
+        "Unsupported norm: {node}, only 1-norm, 2-norm and inf-norm are supported"
+    )
+
+
 class _Timer:
     time: float
 
@@ -599,14 +605,22 @@ def visit_multiply(self, mul: multiply) -> Any:
     def visit_NegExpression(self, node: NegExpression) -> Any:
         return -self.visit(node.args[0])
 
-    def visit_norm1(self, node: cp.norm1) -> Any:
+    def _handle_norm(self, node: cp.norm1 | cp.Pnorm, p: int, name: str) -> Any:
         (x,) = node.args
         if isinstance(x, cp.Constant):
-            return np.linalg.norm(x.value.ravel(), 1)
+            return np.linalg.norm(x.value.ravel(), p)
         arg = self.translate_into_variable(x)
         varargs = [arg] if isinstance(arg, gp.Var) else arg.reshape(-1).tolist()
-        norm = gp.norm(varargs, 1)
-        return self.make_auxilliary_variable_for(norm, "norm1", lb=0)
+        norm = gp.norm(varargs, p)
+        return self.make_auxilliary_variable_for(norm, name, lb=0)
+
+    def visit_norm1(self, node: cp.norm1) -> Any:
+        return self._handle_norm(node, 1, "norm1")
+
+    def visit_Pnorm(self, node: cp.Pnorm) -> Any:
+        if node.p != 2:
+            raise InvalidNormError(node)
+        return self._handle_norm(node, 2, "norm2")
 
     def visit_power(self, node: power) -> Any:
         power = self.visit(node.p)

tests/snapshots/all__lp_genexpr_norm1_10__0.txt

@@ -1,6 +1,6 @@
 CVXPY
 Minimize
-  norm1(x) + norm1([ 1. -2.])
+  norm1(x) + norm1([ 1. -1.])
 Subject To
 Bounds
  x free
@@ -23,7 +23,7 @@ End
 ----------------------------------------
 GUROBI
 Minimize
-  0 x[0] + 0 x[1] + norm1_1 + 3 Constant
+  0 x[0] + 0 x[1] + norm1_1 + 2 Constant
 Subject To
 Bounds
  x[0] free

tests/snapshots/all__lp_genexpr_norm1_11__0.txt

@@ -1,21 +1,21 @@
 CVXPY
 Maximize
-  Sum(x @ [ 1. -2.], None, False)
+  Sum(x @ [ 1. -1.], None, False)
 Subject To
- 40: norm1(x) <= 1.0
+ 40: norm1(x) <= 1.4142135623730951
 Bounds
  x free
 End
 ----------------------------------------
 AFTER COMPILATION
 Minimize
-  - C0 + 2 C1
+  - C0 + C1
 Subject To
  R0: C0 - C2 <= 0
  R1: C1 - C3 <= 0
  R2: - C0 - C2 <= 0
  R3: - C1 - C3 <= 0
- R4: C2 + C3 <= 1
+ R4: C2 + C3 <= 1.414213562373095
 Bounds
  C0 free
  C1 free
@@ -25,9 +25,9 @@ End
 ----------------------------------------
 GUROBI
 Maximize
-  x[0] - 2 x[1]
+  x[0] - x[1]
 Subject To
- 40: norm1_1 <= 1
+ 40: norm1_1 <= 1.414213562373095
 Bounds
  x[0] free
  x[1] free

tests/snapshots/all__lp_genexpr_norm1_13__0.txt

@@ -1,7 +1,7 @@
 CVXPY
 Minimize
-  norm1(X + -[[1.00 -2.00]
- [3.00 -4.00]])
+  norm1(X + -[[2.00 1.00]
+ [-2.00 -4.00]])
 Subject To
 Bounds
  X free
@@ -11,13 +11,13 @@ AFTER COMPILATION
 Minimize
   C0 + C1 + C2 + C3
 Subject To
- R0: - C0 + C4 <= 1
- R1: - C1 + C5 <= 3
- R2: - C2 + C6 <= -2
+ R0: - C0 + C4 <= 2
+ R1: - C1 + C5 <= -2
+ R2: - C2 + C6 <= 1
  R3: - C3 + C7 <= -4
- R4: - C0 - C4 <= -1
- R5: - C1 - C5 <= -3
- R6: - C2 - C6 <= 2
+ R4: - C0 - C4 <= -2
+ R5: - C1 - C5 <= 2
+ R6: - C2 - C6 <= -1
  R7: - C3 - C7 <= 4
 Bounds
  C0 free
@@ -34,9 +34,9 @@ GUROBI
 Minimize
   norm1_2
 Subject To
- R0: - X[0,0] + AddExpression_1[0,0] = -1
- R1: - X[0,1] + AddExpression_1[0,1] = 2
- R2: - X[1,0] + AddExpression_1[1,0] = -3
+ R0: - X[0,0] + AddExpression_1[0,0] = -2
+ R1: - X[0,1] + AddExpression_1[0,1] = -1
+ R2: - X[1,0] + AddExpression_1[1,0] = 2
  R3: - X[1,1] + AddExpression_1[1,1] = 4
 Bounds
  X[0,0] free

tests/snapshots/all__lp_genexpr_norm1_14__0.txt

@@ -1,7 +1,7 @@
 CVXPY
 Minimize
-  norm1(X) + norm1([[1.00 -2.00]
- [3.00 -4.00]])
+  norm1(X) + norm1([[2.00 1.00]
+ [-2.00 -4.00]])
 Subject To
 Bounds
  X free
@@ -32,7 +32,7 @@ End
 ----------------------------------------
 GUROBI
 Minimize
-  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + norm1_1 + 10 Constant
+  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + norm1_1 + 9 Constant
 Subject To
 Bounds
  X[0,0] free

tests/snapshots/all__lp_genexpr_norm1_15__0.txt

@@ -1,16 +1,16 @@
 CVXPY
 Maximize
-  Sum(X @ [[1.00 -2.00]
- [3.00 -4.00]], None, False)
+  Sum(X @ [[2.00 1.00]
+ [-2.00 -4.00]], None, False)
 Subject To
- 55: norm1(X) <= 1.0
+ 55: norm1(X) <= 6.0
 Bounds
  X free
 End
 ----------------------------------------
 AFTER COMPILATION
 Minimize
-  - C0 - 3 C1 + 2 C2 + 4 C3
+  - 2 C0 + 2 C1 - C2 + 4 C3
 Subject To
  R0: C0 - C4 <= 0
  R1: C1 - C5 <= 0
@@ -20,7 +20,7 @@ Subject To
  R5: - C1 - C5 <= 0
  R6: - C2 - C6 <= 0
  R7: - C3 - C7 <= 0
- R8: C4 + C5 + C6 + C7 <= 1
+ R8: C4 + C5 + C6 + C7 <= 6
 Bounds
  C0 free
  C1 free
@@ -34,9 +34,9 @@ End
 ----------------------------------------
 GUROBI
 Maximize
-  X[0,0] - 2 X[0,1] + 3 X[1,0] - 4 X[1,1]
+  2 X[0,0] + X[0,1] - 2 X[1,0] - 4 X[1,1]
 Subject To
- 55: norm1_1 <= 1
+ 55: norm1_1 <= 6
 Bounds
  X[0,0] free
  X[0,1] free

tests/snapshots/all__lp_genexpr_norm1_9__0.txt

@@ -1,6 +1,6 @@
 CVXPY
 Minimize
-  norm1(x + -[ 1. -2.])
+  norm1(x + -[ 1. -1.])
 Subject To
 Bounds
  x free
@@ -11,9 +11,9 @@ Minimize
   C0 + C1
 Subject To
  R0: - C0 + C2 <= 1
- R1: - C1 + C3 <= -2
+ R1: - C1 + C3 <= -1
  R2: - C0 - C2 <= -1
- R3: - C1 - C3 <= 2
+ R3: - C1 - C3 <= 1
 Bounds
  C0 free
  C1 free
@@ -26,7 +26,7 @@ Minimize
   norm1_2
 Subject To
  R0: - x[0] + AddExpression_1[0] = -1
- R1: - x[1] + AddExpression_1[1] = 2
+ R1: - x[1] + AddExpression_1[1] = 1
 Bounds
  x[0] free
  x[1] free

tests/snapshots/all__lp_genexpr_norm2_0__0.txt

@@ -12,23 +12,19 @@ Minimize
 Subject To
  R0: - x_0 + soc_t_0 = 0
  R1: - x_1 + soc_x_1 = 0
- R2: - x_2 + soc_x_2 = 0
- qc0: [ - soc_t_0 ^2 + soc_x_1 ^2 + soc_x_2 ^2 ] <= 0
+ qc0: [ - soc_t_0 ^2 + soc_x_1 ^2 ] <= 0
 Bounds
  x_0 free
  x_1 free
- x_2 free
  soc_x_1 free
- soc_x_2 free
 End
 ----------------------------------------
 GUROBI
 Minimize
-  0 x[0] + 0 x[1] + norm2_1
+  0 x + norm2_1
 Subject To
 Bounds
- x[0] free
- x[1] free
+ x free
 General Constraints
- GC0: norm2_1 = NORM ( 2 ) ( x[0] , x[1] )
+ GC0: norm2_1 = NORM ( 2 ) ( x )
 End

tests/snapshots/all__lp_genexpr_norm2_10__0.txt

@@ -0,0 +1,35 @@
+CVXPY
+Minimize
+  Pnorm(x, 2) + Pnorm([ 1. -1.], 2)
+Subject To
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  x_0
+Subject To
+ R0: - x_0 + soc_t_0 = 0
+ R1: - x_1 + soc_x_1 = 0
+ R2: - x_2 + soc_x_2 = 0
+ qc0: [ - soc_t_0 ^2 + soc_x_1 ^2 + soc_x_2 ^2 ] <= 0
+Bounds
+ x_0 free
+ x_1 free
+ x_2 free
+ soc_x_1 free
+ soc_x_2 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 x[0] + 0 x[1] + norm2_1 + 1.414213562373095 Constant
+Subject To
+Bounds
+ x[0] free
+ x[1] free
+ Constant = 1
+General Constraints
+ GC0: norm2_1 = NORM ( 2 ) ( x[0] , x[1] )
+End

tests/snapshots/all__lp_genexpr_norm2_11__0.txt

@@ -0,0 +1,37 @@
+CVXPY
+Maximize
+  Sum(x @ [ 1. -1.], None, False)
+Subject To
+ 40: Pnorm(x, 2) <= 1.4142135623730951
+Bounds
+ x free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  - x_0 + x_1
+Subject To
+ R0: x_2 <= 1.414213562373095
+ R1: - x_2 + soc_t_1 = 0
+ R2: - x_0 + soc_x_2 = 0
+ R3: - x_1 + soc_x_3 = 0
+ qc0: [ - soc_t_1 ^2 + soc_x_2 ^2 + soc_x_3 ^2 ] <= 0
+Bounds
+ x_0 free
+ x_1 free
+ x_2 free
+ soc_x_2 free
+ soc_x_3 free
+End
+----------------------------------------
+GUROBI
+Maximize
+  x[0] - x[1]
+Subject To
+ 40: norm2_1 <= 1.414213562373095
+Bounds
+ x[0] free
+ x[1] free
+General Constraints
+ GC0: norm2_1 = NORM ( 2 ) ( x[0] , x[1] )
+End

tests/snapshots/all__lp_genexpr_norm2_12__0.txt

@@ -0,0 +1,43 @@
+CVXPY
+Minimize
+  Pnorm(X, 2)
+Subject To
+Bounds
+ X free
+End
+----------------------------------------
+AFTER COMPILATION
+Minimize
+  x_0
+Subject To
+ R0: - x_0 + soc_t_0 = 0
+ R1: - x_1 + soc_x_1 = 0
+ R2: - x_2 + soc_x_2 = 0
+ R3: - x_3 + soc_x_3 = 0
+ R4: - x_4 + soc_x_4 = 0
+ qc0: [ - soc_t_0 ^2 + soc_x_1 ^2 + soc_x_2 ^2 + soc_x_3 ^2 + soc_x_4 ^2 ]
+   <= 0
+Bounds
+ x_0 free
+ x_1 free
+ x_2 free
+ x_3 free
+ x_4 free
+ soc_x_1 free
+ soc_x_2 free
+ soc_x_3 free
+ soc_x_4 free
+End
+----------------------------------------
+GUROBI
+Minimize
+  0 X[0,0] + 0 X[0,1] + 0 X[1,0] + 0 X[1,1] + norm2_1
+Subject To
+Bounds
+ X[0,0] free
+ X[0,1] free
+ X[1,0] free
+ X[1,1] free
+General Constraints
+ GC0: norm2_1 = NORM ( 2 ) ( X[0,0] , X[0,1] , X[1,0] , X[1,1] )
+End