APMonitor Summation with Vectors

Main.Arrays History

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  1. summation

z = m.Var() m.Equation(z==sum([sum([x[i][j] for i in range(ni)]) for j in range(nj)]))

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print('z') print(z.value)

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Arrays in Python GEKKO

Multi-dimensional arrays are defined in 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

  1. 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)])

  1. 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:)

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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
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
Changed lines 75-79 from:
     p[1] = 1
     p[2] = 1
     p[3] = 1
     p[4] = 1
     p[5] = 1
to:
     p[1:n] = 1
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     y
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   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
Changed line 84 from:
     sum = z[5]
to:
     sum = y
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(: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:)

March 06, 2017, at 01:32 PM by 45.56.3.173 -
Changed line 9 from:

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:

March 28, 2016, at 02:33 PM by 45.56.3.173 -
Changed lines 2-3 from:

(:summation, array, vector, sum, matrix, algebraic, modeling language:) (: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 :)

March 28, 2016, at 02:32 PM by 45.56.3.173 -
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(:title APMonitor Summation with Vectors:) (:summation, array, vector, sum, matrix, algebraic, modeling language:) (:description Summation of vectors and matrices in APMonitor:)

March 28, 2016, at 02:30 PM by 45.56.3.173 -
June 16, 2015, at 06:46 PM by 45.56.3.184 -
June 16, 2015, at 06:46 PM by 45.56.3.184 -
Deleted lines 0-1:

Arrays

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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:)

July 07, 2012, at 06:11 AM by 69.169.188.228 -
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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...
July 07, 2012, at 06:05 AM by 69.169.188.228 -
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   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]
June 10, 2011, at 06:12 PM by 158.35.225.240 -
Added lines 20-23:
   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]
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     sum = z[5]
to:
     sum = z[n]
November 01, 2008, at 10:46 PM by 98.199.241.177 -
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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...].

September 26, 2008, at 07:36 PM by 158.35.225.231 -
September 26, 2008, at 07:32 PM by 158.35.225.231 -
Changed lines 3-7 from:

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.

September 26, 2008, at 07:28 PM by 158.35.225.231 -
Added lines 7-59:

(: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:)

September 26, 2008, at 07:20 PM by 158.35.225.231 -
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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