FCSys.Utilities

General supporting functions

Information

Extends from Modelica.Icons.UtilitiesPackage (Icon for utility packages).

Package Content

Name	Description
Chemistry	Functions to support chemistry
Coordinates	Functions to handle Cartesian coordinates
Means	Package of mathematical mean functions
Polynomial	Polynomial functions
Time	Functions to check translation time
arrayBooleanEqual	Check if two Boolean vectors are equal
arrayIntegerEqual	Check if two Integer vectors are equal
arrayRealEqual	Check if two Real vectors are nearly equal
arrayStringEqual	Check if two vectors of strings are equal
assertEval	Assert function that forces Dymola to parse the message
Delta	Return the second entry of a vector minus the first (Δ)
inSign	Return the mathematical sign for the direction into a side or boundary
mod1	Modulo operator for 1-based indexing (compatible with Modelica)
plot6	Create six plots
round	Round a Real variable to the nearest integer
selectBooleans	Reduce a Boolean vector by selecting indices
selectIntegers	Reduce an Integer vector by selecting indices
Sigma	Return the sum of the first and second entries of a vector (Σ)

---

FCSys.Utilities.arrayBooleanEqual

Check if two Boolean vectors are equal

Information

Examples:
arrayIntegerEqual({1,2}, {1,2}) returns true, but arrayIntegerEqual({1,2}, {1,3}) and arrayIntegerEqual({1,2}, {1,2,3}) each return false. Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Boolean	u1[:]		First Boolean vector
Boolean	u2[:]		Second Boolean vector

Outputs

Type	Name	Description
Boolean	equal	true, if all of the entries are equal

Modelica definition

function arrayBooleanEqual 
  "Check if two Boolean vectors are equal"
  extends Modelica.Icons.Function;

  input Boolean u1[:] "First Boolean vector";
  input Boolean u2[:] "Second Boolean vector";
  output Boolean equal 
    "true, if all of the entries are equal";

algorithm 
  if size(u1, 1) <> size(u2, 1) then
    equal := false;
    return;
  end if;
  for i in 1:size(u1, 1) loop
    if u1[i] <> u2[i] then
      equal := false;
      return;
    end if;
  end for;
  equal := true;
  return;
end arrayBooleanEqual;

---

FCSys.Utilities.arrayIntegerEqual

Check if two Integer vectors are equal

Information

Examples:
arrayIntegerEqual({1,2}, {1,2}) returns true, but arrayIntegerEqual({1,2}, {1,3}) and arrayIntegerEqual({1,2}, {1,2,3}) each return false. Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Integer	u1[:]		First integer vector
Integer	u2[:]		Second integer vector

Outputs

Type	Name	Description
Boolean	equal	true, if all of the entries are equal

Modelica definition

function arrayIntegerEqual 
  "Check if two Integer vectors are equal"
  extends Modelica.Icons.Function;

  input Integer u1[:] "First integer vector";
  input Integer u2[:] "Second integer vector";
  output Boolean equal 
    "true, if all of the entries are equal";

algorithm 
  if size(u1, 1) <> size(u2, 1) then
    equal := false;
    return;
  end if;
  for i in 1:size(u1, 1) loop
    if u1[i] <> u2[i] then
      equal := false;
      return;
    end if;
  end for;
  equal := true;
  return;
end arrayIntegerEqual;

---

FCSys.Utilities.arrayRealEqual

Check if two Real vectors are nearly equal

Information

Examples:
arrayRealEqual({1,2}, {1,2}) returns true, but arrayRealEqual({1,2}, {1,2.001}) and arrayRealEqual({1,2}, {1,2,3}) each return false. Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	u1[:]		First real vector
Real	u2[:]		Second real vector
Real	epsilon	1e-7	Error tolerance

Outputs

Type	Name	Description
Boolean	equal	true, if all of the entries are equal

Modelica definition

function arrayRealEqual 
  "Check if two Real vectors are nearly equal"
  extends Modelica.Icons.Function;

  input Real u1[:] "First real vector";
  input Real u2[:] "Second real vector";
  input Real epsilon=1e-7 "Error tolerance";
  output Boolean equal 
    "true, if all of the entries are equal";

algorithm 
  if size(u1, 1) <> size(u2, 1) then
    equal := false;
    return;
  end if;
  for i in 1:size(u1, 1) loop
    if abs(u1[i] - u2[i]) > epsilon then
      equal := false;
      return;
    end if;
  end for;
  equal := true;
  return;
end arrayRealEqual;

---

FCSys.Utilities.arrayStringEqual

Check if two vectors of strings are equal

Information

Examples:
arrayStringEqual({"a","bc"}, {"a","bc"}) returns true, but arrayStringEqual({"a","bc"}, {"a","b"}) and arrayStringEqual({"a","b"}, {"a","b","c"}) each return false. Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
String	u1[:]		First string vector
String	u2[:]		Second string vector

Outputs

Type	Name	Description
Boolean	equal	true, if all of the entries are equal

Modelica definition

function arrayStringEqual "Check if two vectors of strings are equal"
  extends Modelica.Icons.Function;

  input String u1[:] "First string vector";
  input String u2[:] "Second string vector";
  output Boolean equal 
    "true, if all of the entries are equal";

algorithm 
  if size(u1, 1) <> size(u2, 1) then
    equal := false;
    return;
  end if;
  for i in 1:size(u1, 1) loop
    if u1[i] <> u2[i] then
      equal := false;
      return;
    end if;
  end for;
  equal := true;
  return;
end arrayStringEqual;

---

FCSys.Utilities.assertEval

Assert function that forces Dymola to parse the message

Information

When an assert statement is false in the initial equation section of a model, Dymola 2014 gives the following error during translation:

"Error: The conditions of the following assert statements are always false:"

without parsing the message given to the assert function. This pass-through function causes the statement to be evaluated during initialization, at which point the message is evaluated.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Boolean	condition
String	message

Modelica definition

function assertEval 
  "Assert function that forces Dymola to parse the message"
  extends Modelica.Icons.Function;
  input Boolean condition;
  input String message;

algorithm 
  assert(condition, "\n" + message + "\n");
end assertEval;

---

FCSys.Utilities.Delta

Return the second entry of a vector minus the first (Δ)

Information

The translator should automatically vectorize (or "matricize") this function. For example, Delta([1,2;3,4]) returns {1,1}.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	u[2]		Vector of size two

Outputs

Type	Name	Description
Real	Delta	Second entry minus the first entry

Modelica definition

function Delta 
  "Return the second entry of a vector minus the first (Δ)"
  extends Modelica.Icons.Function;
  input Real u[2] "Vector of size two";
  output Real Delta "Second entry minus the first entry";

algorithm 
  Delta := u[2] - u[1];
end Delta;

---

FCSys.Utilities.inSign

Return the mathematical sign for the direction into a side or boundary

Information

Examples:
inSign(FCSys.BaseClasses.Side.n) returns 1 and inSign(FCSys.BaseClasses.Side.p) returns -1. Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Side	side		Side

Outputs

Type	Name	Description
Integer	sign	Sign indicating direction along the axis

Modelica definition

function inSign 
  "Return the mathematical sign for the direction into a side or boundary"
  extends Modelica.Icons.Function;
  input Side side "Side";
  output Integer sign "Sign indicating direction along the axis";

algorithm 
  sign := 3 - 2*side;
end inSign;

---

FCSys.Utilities.mod1

Modulo operator for 1-based indexing (compatible with Modelica)

Information

Examples:
mod1(4,3) returns 1. mod1(3,3) returns 3, but mod(3,3) returns 0 (where mod is the built-in modulo operator). Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Integer	num		Dividend
Integer	den		Divisor

Outputs

Type	Name	Description
Integer	index	Remainder with 1-based indexing

Modelica definition

function mod1 
  "Modulo operator for 1-based indexing (compatible with Modelica)"
  extends Modelica.Icons.Function;
  input Integer num "Dividend";
  input Integer den "Divisor";
  output Integer index "Remainder with 1-based indexing";

algorithm 
  index := mod(num - 1, den) + 1;
end mod1;

---

FCSys.Utilities.plot6

Create six plots

Information

This function calls the createPlot() function in Dymola to create a tiled array of six plots. It may not work with other tools.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
String	y1[:]	fill("", 0)	Names of the signals for the 1st plot
String	y2[:]	fill("", 0)	Names of the signals for the 2nd plot
String	y3[:]	fill("", 0)	Names of the signals for the 3rd plot
String	y4[:]	fill("", 0)	Names of the signals for the 4th plot
String	y5[:]	fill("", 0)	Names of the signals for the 5th plot
String	y6[:]	fill("", 0)	Names of the signals for the 6th plot

Modelica definition

function plot6 "Create six plots"
  extends Modelica.Icons.Function;
  input String y1[:]=fill("", 0) 
    "Names of the signals for the 1st plot";
  input String y2[:]=fill("", 0) 
    "Names of the signals for the 2nd plot";
  input String y3[:]=fill("", 0) 
    "Names of the signals for the 3rd plot";
  input String y4[:]=fill("", 0) 
    "Names of the signals for the 4th plot";
  input String y5[:]=fill("", 0) 
    "Names of the signals for the 5th plot";
  input String y6[:]=fill("", 0) 
    "Names of the signals for the 6th plot";

algorithm 
  createPlot(
    id=1,
    position={0,0,440,650},
    y=y1,
    erase=false,
    grid=true,
    online=true,
    legendLocation=5,
    legendHorizontal=false,
    leftTitleType=1,
    bottomTitleType=1);
  createPlot(
    id=1,
    position={0,0,440,325},
    y=y2,
    erase=false,
    grid=true,
    online=true,
    legendLocation=5,
    legendHorizontal=false,
    subPlot=2,
    leftTitleType=1,
    bottomTitleType=1);
  createPlot(
    id=2,
    position={450,0,440,650},
    y=y3,
    erase=false,
    grid=true,
    legendLocation=5,
    legendHorizontal=false,
    online=true,
    leftTitleType=1,
    bottomTitleType=1);
  createPlot(
    id=2,
    position={450,0,440,325},
    y=y4,
    erase=false,
    grid=true,
    legendLocation=5,
    legendHorizontal=false,
    online=true,
    subPlot=2,
    leftTitleType=1,
    bottomTitleType=1);
  createPlot(
    id=3,
    position={900,0,440,650},
    y=y5,
    erase=false,
    grid=true,
    legendLocation=5,
    legendHorizontal=false,
    online=true,
    leftTitleType=1,
    bottomTitleType=1);
  createPlot(
    id=3,
    position={900,0,440,325},
    y=y6,
    erase=false,
    grid=true,
    legendLocation=5,
    legendHorizontal=false,
    online=true,
    subPlot=2,
    leftTitleType=1,
    bottomTitleType=1);
end plot6;

---

FCSys.Utilities.round

Round a Real variable to the nearest integer

Information

Example:
round(1.6) returns 2 as an Integer.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	u		Real variable

Outputs

Type	Name	Description
Integer	y	Nearest integer

Modelica definition

function round 
  "Round a Real variable to the nearest integer"
  extends Modelica.Icons.Function;
  input Real u "Real variable";
  output Integer y "Nearest integer";

algorithm 
  y := integer(u + 0.5);
end round;

---

FCSys.Utilities.selectBooleans

Reduce a Boolean vector by selecting indices

Information

This function is useful where it is necessary to select entries from a vector that is not an explicit variable.

Example:
selectBooleans({true, false, true}, {1,3}) returns {true, true}. An alternative to this function is to assign a variable to the full vector (full = {true, false, true}) and extract from that variable (full[{1,3}]). However, this is not valid in Modelica: {true, false, true}[{1,3}].

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Boolean	full[:]		Original vector
Integer	indices[:]		Selected indices

Outputs

Type	Name	Description
Boolean	reduced[size(indices, 1)]	Reduced vector

Modelica definition

function selectBooleans 
  "Reduce a Boolean vector by selecting indices"
  extends Modelica.Icons.Function;
  input Boolean full[:] "Original vector";
  input Integer indices[:](each min=1) "Selected indices";
  output Boolean reduced[size(indices, 1)] "Reduced vector";

algorithm 
  reduced := {full[i] for i in indices};
end selectBooleans;

---

FCSys.Utilities.selectIntegers

Reduce an Integer vector by selecting indices

Information

This function is useful where it is necessary to select entries from a vector that is not an explicit variable.

Example:
selectBooleans({3, 2, 1}, {1,3}) returns {3, 1}. An alternative to this function is to assign a variable to the full vector (full = {3, 2, 1}) and extract from that variable (full[{1,3}]). However, this is not valid in Modelica: {3, 2, 1}[{1,3}].

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Integer	full[:]		Original vector
Integer	indices[:]		Selected indices

Outputs

Type	Name	Description
Integer	reduced[size(indices, 1)]	Reduced vector

Modelica definition

function selectIntegers 
  "Reduce an Integer vector by selecting indices"
  extends Modelica.Icons.Function;
  input Integer full[:] "Original vector";
  input Integer indices[:](each min=1) "Selected indices";
  output Integer reduced[size(indices, 1)] "Reduced vector";

algorithm 
  reduced := {full[i] for i in indices};
end selectIntegers;

---

FCSys.Utilities.Sigma

Return the sum of the first and second entries of a vector (Σ)

Information

The translator should automatically vectorize (or "matricize") this function. For example, Sigma([1,2;3,4]) returns {3,7}. In contrast, sum([1,2;3,4]) returns 10.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	u[2]		Vector of size two

Outputs

Type	Name	Description
Real	Sigma	Sum of the first and second entries

Modelica definition

function Sigma 
  "Return the sum of the first and second entries of a vector (Σ)"
  extends Modelica.Icons.Function;

  input Real u[2] "Vector of size two";
  output Real Sigma "Sum of the first and second entries";

algorithm 
  Sigma := u[1] + u[2];
end Sigma;