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Bounds from a parameter

A capacity per generator, an energy limit per battery, a flow limit per line: bounds usually come from data and differ by member. lower= and upper= accept a number, applied to every column, or a Param, giving each member its own value.

import numpy as np
from nimopt import Model, Param, Set

G = Set("G", np.array(["g0", "g1"]))
cap = Param.from_dense("cap", (G,), np.array([5.0, 7.0]))

m = Model("schedule")
m.var("x", (G,), upper=cap)

lower, upper = m.column_bounds()
print(lower)
print(upper)
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Output
[0. 0.]
[5. 7.]

Broadcasting a narrower parameter​

A parameter indexed over fewer dimensions than the variable is broadcast over the rest. A capacity per unit bounds every period of that unit.

import numpy as np
from nimopt import Model, Param, Set

G = Set("G", np.array(["g0", "g1"]))
T = Set("T", np.array(["t0", "t1", "t2"]))
cap = Param.from_dense("cap", (G,), np.array([5.0, 7.0]))

m = Model("schedule")
m.var("x", (G, T), upper=cap)

print(m.column_bounds()[1])
Run this example
Output
[5. 5. 5. 7. 7. 7.]

Six columns. The three periods of each unit take the capacity of that unit.

A bound has a value at every column​

A bound with no value at some member of the variable raises ValueError, and the message gives the member. A dense parameter covers its product by construction. A long-form parameter can omit a member.

import numpy as np
from nimopt import Model, Param, Set

S = Set("S", np.array(["a", "b", "c"]))
cap = Param.from_long("cap", (S,), {"S": np.array(["a", "c"])}, np.array([1.0, 3.0]))

m = Model("bounds")
m.var("x", (S,), upper=cap)

m.column_bounds()
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Raises ValueError
ValueError: the upper bound 'cap' has no value at member ('b',) of variable 'x'; give the bound a value at every member of the variable

The check runs when the bound vectors are built. column_bounds(), assemble() and solve() all build them.

A bound over a dimension the variable lacks​

A parameter indexed over a dimension the variable is not declared on raises ValueError. A bound is per column, and a dimension the variable does not have selects no column.

import numpy as np
from nimopt import Model, Param, Set

G = Set("G", np.array(["g0", "g1"]))
W = Set("W", np.array(["w0", "w1"]))
cap = Param.from_dense("cap", (W,), np.array([5.0, 7.0]))

m = Model("schedule")
m.var("x", (G,), upper=cap)
Run this example
Raises ValueError
ValueError: variable 'x' is declared over ('G',) and is not over ['W']; its upper bound 'cap' is declared over ('W',)