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Defining, posting and propagating linear constraints Description
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scalar_product.mos (!****************************************************** CP example problems =================== file scalar_product.mos ``````````````````````` Using the scalar/dot product operator for the efficient creation of `cplinexpr` expressions of the form: A_1 * x_1 + A_2 * x_2 + ... + A_n * x_n specified as: dot(x, A) with `x` an array of cpvar or cpfloatvar, and `A` an array of real or integer in place of using this less efficient form: sum(i in 1..n) (x(i) * A(i)) Copyright(C) 2019 Artelys S.A. and Fair Isaac Corporation Creation: 2019, rev. Apr. 2022 *******************************************************!) model "Scalar_Product" uses "kalis" options keepassert setparam("KALIS_VERBOSE_LEVEL", 1) declarations n: integer ! Specify the test size end-declarations n := 10 if isodd(n) then n += 1 end-if !**** Case 1: Defining a linear constraint over cpvar **** declarations R=1..n x: array(R) of cpvar A: array(R) of real AIntVersion: array(R) of integer Sp : cplinexp end-declarations ! Initialization forall(i in R) do setname(x(i), "x" +i) -100 <= x(i); x(i) <= 100 A(i) := i AInt(i) := i end-do ! Constraint definition Sp := dot(x, A) ! Same expression as: Sp := sum(i in R) (x(i) * A(i)) Sp = 3 ! Posting the constraint !**** Case 2: Working with 2-dimensional arrays **** m := n div 2 declarations RM=1..m R2=1..2 x2: array(RM, R2) of cpvar B: array(RM, R2) of real BInt: array(RM, R2) of integer sp2 : cplinexp end-declarations ! Initialization forall(i in RM, j in R2) do setname(x2(i,j), "x" + i + "_" + j) -100 <= x2(i,j); x2(i,j) <= 100 B(i,j) := i + j BInt(i,j) := i + j end-do ! Constraint definition Sp2 := dot(x2, B) Sp2 = 3 !**** Case 3: Defining a linear constraint with cpfloatvar **** writeln("Sub test 3") declarations x3: array(R) of cpfloatvar C: array(R) of real CInt: array(R) of integer Sp3 : cplinexp end-declarations ! Initialization forall(i in R) do setname(x3(i), "y_" + i) -100 <= x3(i); x3(i) <= 100 C(i) := i CInt(i) := i end-do ! Constraint definition Sp3 := dot(x3, C) Sp3 = 3 !**** Solve the problem **** res := cp_minimise(x2(1, 1)) writeln("Problem solved: ", res) writeln("Sp=", Sp.sol, " Sp2=", Sp2.sol, " Sp3=", Sp3.sol) writeln(array(i in R) x(i).sol) writeln(array(i in RM,j in R2) x2(i,j).sol) writeln(array(i in R) x3(i).sol) !**** Validate the results **** ! Case 1 result1 := sum(i in R) (getsol(x(i)) * A(i)) result2 := getsol(Sp) assert(result1 = result2 and result1 = 3, "TEST FAILED : failed for one-dimensional array\n"+ "result1="+ result1+ ", result2="+ result2, 1) ! Case 2 result1 := sum(i in RM, j in R2) (getsol(x2(i, j)) * B(i, j)) result2 := getsol(Sp2) assert(result1 = result2 and result1 = 3, "TEST FAILED: failed for multi-dimensional array\n"+ "result1="+ result1+ ", result2="+ result2, 1) ! Case 3 tol := 1e-4 result1 := sum(i in R) (getsol(x3(i)) * C(i)) result2 := getsol(Sp3) assert(abs(result1 - result2) <= tol and abs(result1 - 3) <= tol, "TEST FAILED: failed for cpfloatvar array\n"+ "result1="+ result1+ ", result2="+ result2, 1) !**** Validate commutativity of dot operator **** assert(getsol(dot(A, x)) = 3, "TEST FAILED: failed for commutation 1: dot(ar, acpvar)",1) assert(getsol(dot(B, x2)) = 3, "TEST FAILED: failed for commutation 2: dot(ar, acpvar)",1) assert(abs(getsol(dot(C, x3)) - 3) <= tol, "TEST FAILED: failed for commutation 3: dot(ar, acpfloatvar)",1) !**** Validate dot operator with array of integer **** assert(getsol(dot(x, AInt)) = 3, "TEST FAILED: failed integer version 1: dot(acpvar, ai)",1) assert(getsol(dot(x2, BInt)) = 3, "TEST FAILED: failed for integer version 2: dot(acpvar, ai)",1) assert(abs(getsol(dot(x3, CInt)) - 3) <= tol, "TEST FAILED: failed for integer version 3: dot(acpfloatvar, ai)",1) assert(getsol(dot(AInt, x)) = 3, "TEST FAILED: failed for commutation 4: dot(ai, acpvar)",1) assert(getsol(dot(BInt, x2)) = 3, "TEST FAILED: failed for commutation 5: dot(ai, acpvar)",1) assert(abs(getsol(dot(CInt, x3)) - 3) <= tol, "TEST FAILED: failed for commutation 6: dot(ai, acpfloatvar)",1) writeln("TEST PASSED") end-model | |||||||||||||
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