(!****************************************************************
CP example problems
===================
file linctr.mos
```````````````
Posting and propagating linear constraints.
(c) 2008 Artelys S.A. and Fair Isaac Corporation
Creation: 2005, rev. Mar. 2013
*****************************************************************!)
model "Linear constraints"
uses "kalis"
declarations
N = 3
R = 1..N
x: array(R) of cpvar
c1: cpctr
end-declarations
forall(i in R) do
0 <= x(i); x(i) <= 50
setname(x(i), "x"+i)
end-do
! Automated post+propagation
x(1) >= x(3) + 5
writeln(x(1), " ", x(3))
! Named constraint (explicit post)
c1:= x(3) >= x(2) + 10
if cp_post(c1) then
writeln("With constraint c1: ", x)
else exit(1)
end-if
! Stop automated propagation
setparam("kalis_auto_propagate", false)
! Automated post w/o propagation
x(2) >= 10
writeln("new bound for x2: ", x)
if cp_propagate then
writeln("after propagation: ", x)
end-if
! Minimize the value of x(1)
if cp_minimize(x(1)) then
write("Solution: ")
forall(i in R) write(getsol(x(i)), " ")
writeln
end-if
end-model
|
(!******************************************************
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
*******************************************************!)
model "Scalar_Product"
uses "kalis"
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)
if (result1 <> result2 or result1 <> 3) then
writeln("TEST FAILED : failed for one-dimensionnal array")
writeln("result1=", result1, ", result2=", result2)
exit(1)
end-if
! Case 2
result1 := sum(i in RM, j in R2) (getsol(x2(i, j)) * B(i, j))
result2 := getsol(Sp2)
if (result1 <> result2 or result1 <> 3) then
writeln("TEST FAILED: failed for multi-dimensional array")
writeln("result1=", result1, ", result2=", result2)
exit(1)
end-if
! Case 3
tol := 1e-4
result1 := sum(i in R) (getsol(x3(i)) * C(i))
result2 := getsol(Sp3)
if (abs(result1 - result2) > tol or abs(result1 - 3) > tol) then
writeln("TEST FAILED: failed for cpfloatvar array")
writeln("result1=", result1, ", result2=", result2)
exit(1)
end-if
!**** Validate commutativity of dot operator ****
if (getsol(dot(A, x)) <> 3) then
writeln("TEST FAILED: failed for commutation 1: dot(ar, acpvar)")
exit(1)
end-if
if (getsol(dot(B, x2)) <> 3) then
writeln("TEST FAILED: failed for commutation 2: dot(ar, acpvar)")
exit(1)
end-if
if (abs(getsol(dot(C, x3)) - 3) > tol) then
writeln("TEST FAILED: failed for commutation 3: dot(ar, acpfloatvar)")
exit(1)
end-if
!**** Validate dot operator with array of integer ****
if (getsol(dot(x, AInt)) <> 3) then
writeln("TEST FAILED: failed integer version 1: dot(acpvar, ai)")
exit(1)
end-if
if (getsol(dot(x2, BInt)) <> 3) then
writeln("TEST FAILED: failed for integer version 2: dot(acpvar, ai)")
exit(1)
end-if
if (abs(getsol(dot(x3, CInt)) - 3) > tol) then
writeln("TEST FAILED: failed for integer version 3: dot(acpfloatvar, ai)")
exit(1)
end-if
if (getsol(dot(AInt, x)) <> 3) then
writeln("TEST FAILED: failed for commutation 4: dot(ai, acpvar)")
exit(1)
end-if
if (getsol(dot(BInt, x2)) <> 3) then
writeln("TEST FAILED: failed for commutation 5: dot(ai, acpvar)")
exit(1)
end-if
if (abs(getsol(dot(CInt, x3)) - 3) > tol) then
writeln("TEST FAILED: failed for commutation 6: dot(ai, acpfloatvar)")
exit(1)
end-if
writeln("TEST PASSED")
end-model
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