View source for DMelt:Units/2 Measurements with Units

= Measurements with units =

Before we considered how to perform conversion between different units. Now we will consider
calculations with units. This part is based on the JScience project.

First, let us check the available units:

First, let us import '''International''' units and their derivatives:
<jcode lang="python">
from javax.measure.unit.SI import *
dir()
</jcode>
You will see the available units:

<jcode lang="python">
['AMPERE', 'ATTO', 'BECQUEREL', 'BIT', 'CANDELA', 'CELSIUS', 'CENTI', 
'CENTIMETER', 'CENTIMETRE', 'COULOMB', 'CUBIC_METRE', 'DECI', 'DEKA',
 'EXA', 'Editor', 'FARAD', 'FEMTO', 'GIGA', 'GRAM', 'GRAY', 'HECTO', 
 'HENRY', 'HERTZ', 'JOULE', 'KATAL', 'KELVIN', 'KILO', 'KILOGRAM', 
 'KILOMETER', 'KILOMETRE', 'LUMEN', 'LUX', 'MEGA', 'METER', 'METERS_PER_SECOND', 
 'METERS_PER_SQUARE_SECOND', 'METRE', 'METRES_PER_SECOND', 'METRES_PER_SQUARE_SECOND', 
 'METRE_PER_SECOND', 'METRE_PER_SQUARE_SECOND', 'MICRO', 'MILLI', 'MILLIMETER',
 'MILLIMETRE', 'MOLE', 'NANO', 'NEWTON', 'OHM', 'PASCAL', 'PETA', 'PICO', 
 'RADIAN', 'SECOND', 'SIEMENS', 'SIEVERT', 'SQUARE_METRE', 'STERADIAN', 'TERA', 
 'TESLA', 'VOLT', 'WATT', 'WEBER', 'YOCTO', 'YOTTA',  'ZEPTO', 'ZETTA',
</jcode>

Similarly, one can import non-international units:

<jcode lang="python">
from javax.measure.unit.NonSI import *
dir()
</jcode>

which shows

<jcode lang="python">
['ANGSTROM', 'ARE', 'ASTRONOMICAL_UNIT', 'ATMOSPHERE', 'ATOM', 
 'ATOMIC_MASS', 'BAR', 'BYTE', 'C', 'CENTIRADIAN', 'COMPUTER_POINT', 
 'CUBIC_INCH', 'CURIE', 'ClassPath', 'DAY', 'DAY_SIDEREAL', 'DECIBEL', 
 'DEGREE_ANGLE', 'DYNE', 'E', 'ELECTRON_MASS', 'ELECTRON_VOLT', 'ERG', 
 'FAHRENHEIT', 'FARADAY', 'FOOT', 'FOOT_SURVEY_US', 'FRANKLIN', 'G',
 'GALLON_DRY_US', 'GALLON_LIQUID_US', 'GALLON_UK', 'GAUSS', 'GILBERT', 
 'GRADE', 'HECTARE', 'HORSEPOWER', 'HOUR', 'INCH', 'INCH_OF_MERCURY',
 'KILOGRAM_FORCE', 'KILOMETERS_PER_HOUR', 'KILOMETRES_PER_HOUR', 'KNOT', 
 'LAMBERT', 'LIGHT_YEAR', 'LITER', 'LITRE', 'MACH', 'MAXWELL', 'METRIC_TON',
 'MILE', 'MILES_PER_HOUR', 'MILLIMETER_OF_MERCURY', 'MINUTE', 'MINUTE_ANGLE',
 'MONTH', 'NAUTICAL_MILE', 'OCTET', 'OUNCE', 'OUNCE_LIQUID_UK', 'OUNCE_LIQUID_US', 
 'PARSEC', 'PERCENT', 'PIXEL', 'POINT', 'POISE', 'POUND', 'POUND_FORCE', 'RAD', 
 'RANKINE', 'REM', 'REVOLUTION', 'ROENTGEN', 'RUTHERFORD', 'SECOND_ANGLE', 'SPHERE',
 'STOKE', 'TON_UK', 'TON_US', 'UserMacrosDir', 'WEEK', 'YARD', 'YEAR', 
 'YEAR_CALENDAR', 'YEAR_SIDEREAL',
</jcode>

Let is define the mass in pounds:

<jcode lang="python">
>> from  org.jscience.physics.amount import *
>> from javax.measure.unit.NonSI import *
>>>from javax.measure.unit.SI import *
>> m0=Amount.valueOf(100, POUND)    # define mass in pounds
>> m1=Amount.valueOf(100, KILOGRAM) # in kg
>> print m0, m1
Output: 100 lb  100 kg
</jcode>


= Arithmetics with measures using units =

You can do the standard math with measures using different units.

In this small example we defined two masses in different units and then divided by 3, multiplied by 5
and added another mass in kilograms. When we print it, we convert the answer to kilograms.

<jcode lang="python">
from  org.jscience.physics.amount import Amount
from javax.measure.unit.NonSI import *
from javax.measure.unit.SI import *
m0=Amount.valueOf(100, POUND)    # define mass in pounds
m1=Amount.valueOf(100, KILOGRAM) # in kg
m= m0.divide(2).times(5).plus(m1)

from java.lang.System import * # we use Java system output in UTF-8
out.println( m.to(KILOGRAM))
</jcode>

The answer in kg is:

<jcode lang="python">
(213.39809249999996 ± 2.8E-14) kg
</jcode>

The last "± 2.8E-14" does nor mean much since we defined the values without errors.
We can do now manipulation assuming that each value has measurement uncertainty  ("error").

<jcode lang="python">
from  org.jscience.physics.amount import Amount
from javax.measure.unit.NonSI import *
from javax.measure.unit.SI import *
m0=Amount.valueOf(100, 5, POUND)    # define mass with error in pounds 100 +- 5
m1=Amount.valueOf(100, 2, KILOGRAM) # in kg with error, 100 +-2 kg
m= m0.divide(2).times(5).plus(m1)
from java.lang.System import *
out.println( m.toString());
</jcode>

Now the output has a meaningful error:

<jcode lang="python">
(4.7E2 ± 17.) lb
</jcode>

Look at the class API for the "Amount" objects here: <javadoc>org.jscience.physics.amount.Amount</javadoc>
or in the summary <javadoc>org.jscience.physics.amount.package-summary</javadoc>.

Let's build a small example. Let's calculate the speed of a free falling object:

<jcode lang="python">
from org.jscience.physics.amount import Amount
from org.jscience.physics.amount import Constants
from javax.measure.unit.SI import *
 
TIME=Amount.valueOf(100,SECOND)
v=TIME.times(Constants.g) # t*gravitation constant
print  v 
</jcode>




Which will show the output:
<jcode lang="python">
(980.6649999999997 ± 1.7E-13) m/s
</jcode>

Note that "Constants.g" is the gravitational constant which is 
<jcode lang="python">
(9.8066499999999976 ± 8.9E-16) m/s²
</jcode>
<ifauth !@member>
<jnote> important>
You are not full member and  have a limited access to this section.
One can unlock this part  after  becoming [[https://datamelt.org/members/selock| a full member</javadoc>. 
</jnote>
</ifauth>
<ifauth @member,@admin,@editor>

More details can be found here. The API is in Java:
* <javadoc>org/jscience/physics/amount/package-summary.html| Physics Amount package</javadoc>.
* <javadoc>org/jscience/physics/model/package-summary.html| Physics model package</javadoc>
* <javadoc>org/jscience/mathematics/function/package-summary.html| Math function package</javadoc>
* <javadoc>org/jscience/mathematics/number/package-summary.html| Math number package</javadoc>
* <javadoc>org/jscience/mathematics/vector/package-summary.html| Math vector package</javadoc>
</ifauth>

== Values with units using VisAd ==

The Java package <javadoc>visad/package-summary|VisAd</javadoc> contains powerful classes <javadoc>visad.Real</javadoc> and <javadoc>visad.Data</javadoc> to perform calculations with units and errors. 

If your quantities are physical and have associated Units, then you might prefer to create a VisAD MathType that explicitly defines the metadata characteristics of your quantities. A MathType is used to define the kind of mathematical object that the Data object approximates. Every Data object in VisAD must have a MathType. In the previous examples, a default MathType with the name "Generic" was implicitly used for our Real objects.

In the simplest form for dealing with Units, the constructor for a MathType which defines Real values is:

<jcode>
RealType(String name, Unit u, Set s)
</jcode>

which allows you to assign a unique name to this MathType, a Unit for this, and define a default Set. In practice, the Set is seldom used and should just be passed as null in most cases. Here is an example using Java codding:

<jcode lang="java">
import visad.*;
Real t1,t2,sum;
RealType k = new RealType("kelvin",SI.kelvin,null);
t2 = new Real(k,273.);
t1 = new Real(k,255.);
sum = (Real) t1.add(t2);
System.out.println("sum = "+sum+" "+sum.getUnit());
</jcode>

When you run this example, you get: sum = 528.0 K
In this example, we use an SI Unit (ampere, candela, kelvin, kilogram, meter, second, mole, radian, steradian). Note that we constructed two variables with the same MathType, that is the same name, Unit, and Set.

This example shows how to define values with errors
and how to perform mathematical transformation while propagating errors (independently) using Jython/Python:
 
<ifauth>
<jcode lang="python">
dmelt 47090181.py
</jcode>
</ifauth>

[[Category:Measurements]]
[[Category:Units]]