APMonitor Summation with Vectors
Main.Arrays History
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Added lines 174-177:
# summation
z = m.Var()
m.Equation(z==sum([sum([x[i][j] for i in range(ni)]) for j in range(nj)]))
z = m.Var()
m.Equation(z==sum([sum([x[i][j] for i in range(ni)]) for j in range(nj)]))
Added lines 184-185:
print('z')
print(z.value)
print(z.value)
Added lines 150-180:
!!!! Arrays in Python GEKKO
Multi-dimensional arrays are defined in [[https://gekko.readthedocs.io/en/latest/model_methods.html|Python GEKKO]] with the m.Array() function or with list comprehensions.
(:source lang=python:)
from gekko import GEKKO
m = GEKKO()
ni = 3 # number of rows
nj = 2 # number of columns
# best method: use m.Array function
x = m.Array(m.Var,(ni,nj))
m.Equations([x[i][j]==i*j+1 for i in range(ni) for j in range(nj)])
# another way: list comprehensions
y = [[m.Var() for j in range(nj)] for i in range(ni)]
for i in range(ni):
for j in range(nj):
m.Equation(x[i][j]**2==y[i][j])
m.solve()
print('x:')
print(x)
print('y=x**2:')
print(y)
(:sourceend:)
Added lines 118-119:
An additional example is a matrix summation where there are two indices of the parameter matrix ''p''.
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!!! Example
to:
!!! Examples
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! Summation with arrays
to:
! Method #1: Summation with arrays
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! Summation without arrays
Model array
Model array
to:
! Method #2: Summation with the sum object
Objects
z = sum(5)
End Objects
Connections
p[1:n] = z.x[1:n]
y = z.y
End Connections
Model
Constants
n = 5
End Constants
Objects
z = sum(5)
End Objects
Connections
p[1:n] = z.x[1:n]
y = z.y
End Connections
Model
Constants
n = 5
End Constants
Changed lines 75-79 from:
p[1] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5
to:
p[1:n] = 1
Added line 79:
y
Deleted lines 82-89:
z[1] = p[1]
z[2] = z[1] + p[2]
z[3] = z[2] + p[3]
z[4] = z[3] + p[4]
z[5] = z[4] + p[5]
End Intermediates
Changed line 84 from:
sum = z[5]
to:
sum = y
Added lines 88-119:
(:cellnr:)
! Method #3: Summation without arrays
Model array
Parameters
p[1] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2] = z[1] + p[2]
z[3] = z[2] + p[3]
z[4] = z[3] + p[4]
z[5] = z[4] + p[5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:tableend:)
(:table border=1 width=100% align=left bgcolor=#EEEEEE cellspacing=0:)
! Method #3: Summation without arrays
Model array
Parameters
p[1] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2] = z[1] + p[2]
z[3] = z[2] + p[3]
z[4] = z[3] + p[4]
z[5] = z[4] + p[5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:tableend:)
(:table border=1 width=100% align=left bgcolor=#EEEEEE cellspacing=0:)
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Arrays with more than one dimension are allowed. The array indices are separated by commas as in ''var[i,j,k...]'' or ''var[i][j][k]''. For operations on matrices, the precedence of operations is determined by the number of colons separating the vector indices. Matrix elements with fewer colon separators are executed first. For example, a set of 24 intermediate variables posed as:
to:
Arrays with more than one dimension are allowed. The array indices are separated by brackets as ''var[i][j][k]''. For operations on matrices, the precedence of operations is determined by the number of colons separating the vector indices. Matrix elements with fewer colon separators are executed first. For example, a set of 24 intermediate variables posed as:
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(:summation, array, vector, sum, matrix, algebraic, modeling language:)
(:description Summation of vectors and matrices in APMonitor:)
(:description Summation of vectors and matrices in APMonitor:)
to:
(:keywords summation, array, vector, sum, matrix, algebraic, modeling language:)
(:description Summation of vectors and matrices in APMonitor :)
(:description Summation of vectors and matrices in APMonitor :)
Added lines 1-4:
(:title APMonitor Summation with Vectors:)
(:summation, array, vector, sum, matrix, algebraic, modeling language:)
(:description Summation of vectors and matrices in APMonitor:)
(:summation, array, vector, sum, matrix, algebraic, modeling language:)
(:description Summation of vectors and matrices in APMonitor:)
Deleted lines 0-1:
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(:table border=1 width=50% align=left bgcolor=#EEEEEE cellspacing=0:)
to:
(:table border=1 width=100% align=left bgcolor=#EEEEEE cellspacing=0:)
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Arrays with more than one dimension are allowed. The array indices are separated by commas as in ''var[i,j,k...]''.
to:
Arrays with more than one dimension are allowed. The array indices are separated by commas as in ''var[i,j,k...]'' or ''var[i][j][k]''. For operations on matrices, the precedence of operations is determined by the number of colons separating the vector indices. Matrix elements with fewer colon separators are executed first. For example, a set of 24 intermediate variables posed as:
* x[1:2][1::3][1:::4] = 1
results in the following set of equations:
* x[1][1][1] = 1
* x[2][1][1] = 1
* x[1][2][1] = 1
* x[2][2][1] = 1
* x[1][3][1] = 1
* x[2][3][1] = 1
* x[1][1][2] = 1
* etc...
* x[1:2][1::3][1:::4] = 1
results in the following set of equations:
* x[1][1][1] = 1
* x[2][1][1] = 1
* x[1][2][1] = 1
* x[2][2][1] = 1
* x[1][3][1] = 1
* x[2][3][1] = 1
* x[1][1][2] = 1
* etc...
Added lines 68-94:
End Equations
End Model
(:cellnr:)
! Matrix Summation
Model
Parameters
p[1:10][1::5] = 1
End Parameters
Variables
x
End Variables
Intermediates
! sum the rows
n[0][1:5] = 0
n[1:10][1::5] = n[0:9][1::5] + p[1:10][1::5]
! sum the columns that are summation of rows
m[0] = 0
m[1:5] = m[0:4] + n[10][1:5]
End Intermediates
Equations
! solution = 50
x = m[5]
End Model
(:cellnr:)
! Matrix Summation
Model
Parameters
p[1:10][1::5] = 1
End Parameters
Variables
x
End Variables
Intermediates
! sum the rows
n[0][1:5] = 0
n[1:10][1::5] = n[0:9][1::5] + p[1:10][1::5]
! sum the columns that are summation of rows
m[0] = 0
m[1:5] = m[0:4] + n[10][1:5]
End Intermediates
Equations
! solution = 50
x = m[5]
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Constants
n = 5
End Constants
n = 5
End Constants
Changed line 25 from:
p[1:5] = 1
to:
p[1:n] = 1
Changed line 34 from:
z[2:5] = z[1:4] + p[2:5]
to:
z[2:n] = z[1:n-1] + p[2:n]
Changed line 38 from:
sum = z[5]
to:
sum = z[n]
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!!! Higher dimensional arrays
Arrays with more than one dimension are allowed. The array indices are separated by commas as in ''var[i,j,k...]''.
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Variable or object arrays are defined by square brackets with a range of integers and separated by a colon. Arrays may be used to define multiple equations or operations on one line. Any line with an array is processed sequentially from the lowest to the highest index.
to:
Variable or object arrays are defined by square brackets with a range of integers and separated by a colon as ''variable[index 1:index 2]''. Arrays may be used to define multiple equations or connections on one line. Any line with an array is processed sequentially from the lowest to the highest index. The model parser creates and processes the arrays as if they were written sequential in non-array form as shown in the example.
!!! Array Index Consistency
When processing the arrays, the parser checks for array size consistency. An error with an appropriate message is returned if the vector indeces are of different dimension.
!!! Array Index Consistency
When processing the arrays, the parser checks for array size consistency. An error with an appropriate message is returned if the vector indeces are of different dimension.
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(:table border=1 width=50% align=left bgcolor=#EEEEEE cellspacing=0:)
(:cellnr:)
! Summation with arrays
Model array
Parameters
p[1:5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2:5] = z[1:4] + p[2:5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:cellnr:)
! Summation without arrays
Model array
Parameters
p[1] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2] = z[1] + p[2]
z[3] = z[2] + p[3]
z[4] = z[3] + p[4]
z[5] = z[4] + p[5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:tableend:)
(:cellnr:)
! Summation with arrays
Model array
Parameters
p[1:5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2:5] = z[1:4] + p[2:5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:cellnr:)
! Summation without arrays
Model array
Parameters
p[1] = 1
p[2] = 1
p[3] = 1
p[4] = 1
p[5] = 1
End Parameters
Variables
sum
End Variables
Intermediates
z[1] = p[1]
z[2] = z[1] + p[2]
z[3] = z[2] + p[3]
z[4] = z[3] + p[4]
z[5] = z[4] + p[5]
End Intermediates
Equations
sum = z[5]
End Equations
End Model
(:tableend:)
Added lines 1-6:
!! Arrays
Variable or object arrays are defined by square brackets with a range of integers and separated by a colon. Arrays may be used to define multiple equations or operations on one line. Any line with an array is processed sequentially from the lowest to the highest index.
!!! Example
Variable or object arrays are defined by square brackets with a range of integers and separated by a colon. Arrays may be used to define multiple equations or operations on one line. Any line with an array is processed sequentially from the lowest to the highest index.
!!! Example