package org.djunits.unit;
   
   import java.io.Serializable;
   import java.util.Arrays;
   import java.util.LinkedHashSet;
   import java.util.Set;
   
   import org.djunits.Throw;
   import org.djunits.unit.quantity.Quantities;
  import org.djunits.unit.quantity.Quantity;
  import org.djunits.unit.scale.IdentityScale;
  import org.djunits.unit.scale.LinearScale;
  import org.djunits.unit.scale.OffsetLinearScale;
  import org.djunits.unit.scale.Scale;
  import org.djunits.unit.si.SIDimensions;
  import org.djunits.unit.si.SIPrefix;
  import org.djunits.unit.si.SIPrefixes;
  import org.djunits.unit.unitsystem.UnitSystem;
  import org.djunits.unit.util.UnitRuntimeException;
  
  /**
   * All units are internally <i>stored</i> relative to a standard unit with conversion factor. This means that e.g., a meter is
   * stored with conversion factor 1.0, whereas kilometer is stored with a conversion factor 1000.0. This means that if we want to
   * express a length meter in kilometers, we have to <i>divide</i> by the conversion factor.
   * <p>
   * Copyright (c) 2019-2020 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
   * BSD-style license. See <a href="https://djunits.org/docs/license.html">DJUNITS License</a>
   * </p>
   * @author <a href="https://www.tudelft.nl/averbraeck" target="_blank">Alexander Verbraeck</a>
   * @param <U> the unit to reference the actual unit in return values
   */
  public class Unit<U extends Unit<U>> implements Serializable, Cloneable
  {
      /** */
      private static final long serialVersionUID = 20190818L;
  
      /** The id of the unit; has to be unique within the unit name. Used for, e.g., localization and retrieval. */
      private String id;
  
      /** The abbreviations in the default locale. All abbreviations an be used in the valueOf() and of() methods. */
      private Set<String> abbreviations;
  
      /** The default display abbreviation in the default locale for printing. Included in the abbreviations list. */
      private String defaultDisplayAbbreviation;
  
      /** The default textual abbreviation in the default locale for data entry. Included in the abbreviations list. */
      private String defaultTextualAbbreviation;
  
      /** The long name of the unit in the default locale. */
      private String name;
  
      /** The scale to use to convert between this unit and the standard (e.g., SI, BASE) unit. */
      private Scale scale;
  
      /** The unit system, e.g. SI or Imperial. */
      private UnitSystem unitSystem;
  
      /** Has the unit been automatically generated or not. */
      private boolean generated;
  
      /** Does the unit have the standard SI signature? */
      private boolean baseSIUnit;
  
      /**
       * The corresponding unit base that contains all registered units for the unit as well as SI dimension information. The base
       * unit of a unit base is null.
       */
      private Quantity<U> quantity;
  
      // TODO create a static that loads all unit classes in the registry
  
      /**
       * Initialize a blank unit that can be built through reflection with several 'setter' methods followed by calling the
       * build(...) method.
       */
      protected Unit()
      {
          //
      }
  
      /**
       * Build the unit, using the information of the provided builder class. First check rigorously if all necessary fields in
       * the builder have been set, and whether they are consistent and valid. The behavior is as follows: the defaultAbbreviation
       * and defaultTextualAbbreviation are added to the abbreviations set, if they are not yet already there. When the
       * defaultAbbreviation is set and the defaultTextualAbbreviation is not set, the defaultTextualAbbreviation gets the value
       * of defaultAbbreviation. The reverse also holds: When the defaultTextualAbbreviation is set and the defaultAbbreviation is
       * not set, the defaultAbbreviation gets the value of defaultTextualAbbreviation. When neither the
       * defaultTextualAbbreviation, nor the defaultAbbreviation are set, both get the value of the unitId provided in the
       * builder.
       * @param builder Builder&lt;U&gt;; Builder&lt;U&gt; the object that contains the information about the construction of the
       *            class
       * @return U; the constructed unit
       * @throws UnitRuntimeException when not all fields have been set
       */
      @SuppressWarnings("unchecked")
      public U build(final Builder<U> builder) throws UnitRuntimeException
      {
          // Check the validity
          String cName = getClass().getSimpleName();
         Throw.whenNull(builder.getId(), "Constructing unit %s: id cannot be null", cName);
         Throw.when(builder.getId().length() == 0, UnitRuntimeException.class, "Constructing unit %s: id.length cannot be 0",
                 cName);
         String unitId = builder.getId();
         Throw.whenNull(builder.getQuantity(), "Constructing unit %s.%s: baseUnit cannot be null", cName, unitId);
         Throw.whenNull(builder.getName(), "Constructing unit %s.%s: name cannot be null", cName, unitId);
         Throw.when(builder.getName().length() == 0, UnitRuntimeException.class,
                 "Constructing unit %s.%s: name.length cannot be 0", cName, unitId);
         Throw.whenNull(builder.getScale(), "Constructing unit %s.%s: scale cannot be null", cName, unitId);
         Throw.whenNull(builder.getUnitSystem(), "Constructing unit %s.%s: unitSystem cannot be null", cName, unitId);
 
         // set the key fields
         this.id = unitId;
         this.name = builder.getName();
         this.quantity = builder.getQuantity();
         this.unitSystem = builder.getUnitSystem();
         this.scale = builder.getScale();
         this.generated = builder.isGenerated();
         this.baseSIUnit = this.scale.isBaseSIScale();
 
         // Set and check the abbreviations
         if (builder.getDefaultDisplayAbbreviation() == null)
         {
             if (builder.getDefaultTextualAbbreviation() == null)
             {
                 this.defaultDisplayAbbreviation = unitId;
             }
             else
             {
                 this.defaultDisplayAbbreviation = builder.getDefaultTextualAbbreviation();
             }
         }
         else
         {
             this.defaultDisplayAbbreviation = builder.getDefaultDisplayAbbreviation();
         }
         if (builder.getDefaultTextualAbbreviation() == null)
         {
             this.defaultTextualAbbreviation = this.defaultDisplayAbbreviation;
         }
         else
         {
             this.defaultTextualAbbreviation = builder.getDefaultTextualAbbreviation();
         }
         this.abbreviations = new LinkedHashSet<>();
         this.abbreviations.add(this.defaultDisplayAbbreviation);
         this.abbreviations.add(this.defaultTextualAbbreviation);
         this.abbreviations.addAll(builder.getAdditionalAbbreviations());
 
         // See what SI prefixes have to be registered. If not specified: NONE.
         SIPrefixes siPrefixes = builder.getSiPrefixes() == null ? SIPrefixes.NONE : builder.getSiPrefixes();
 
         // Register the unit, possibly including all SI prefixes
         this.quantity.registerUnit((U) this, siPrefixes, builder.getSiPrefixPowerFactor());
         return (U) this;
     }
 
     /**
      * Create a scaled version of this unit with the same unit system but another SI prefix and scale.
      * @param siPrefix SIPrefix; the prefix for which to scale the unit
      * @param siPrefixPower double; the power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters.
      * @param automaticallyGenerated boolean; indicate whether the unit has been automatically generated
      * @return U; a scaled instance of this unit
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveSI(final SIPrefix siPrefix, final double siPrefixPower, final boolean automaticallyGenerated)
     {
         Throw.whenNull(siPrefix, "siPrefix cannot be null");
         try
         {
             U clone = clone();
 
             // Get values: combine all prefixes with all names / abbreviations
             String cloneId = siPrefix.getDefaultTextualPrefix() + clone.getId();
             String cloneName = clone.getName();
             if (cloneName.startsWith("square "))
             {
                 cloneName = "square " + siPrefix.getPrefixName() + cloneName.substring(6);
             }
             else if (clone.getName().startsWith("cubic "))
             {
                 cloneName = "cubic " + siPrefix.getPrefixName() + cloneName.substring(5);
             }
             else
             {
                 cloneName = siPrefix.getPrefixName() + cloneName;
             }
             Set<String> cloneAbbreviations = new LinkedHashSet<>();
             for (String abbreviation : clone.getAbbreviations())
             {
                 cloneAbbreviations.add(siPrefix.getDefaultTextualPrefix() + abbreviation);
             }
             String cloneDefaultAbbreviation = siPrefix.getDefaultDisplayPrefix() + clone.getDefaultDisplayAbbreviation();
             String cloneDefaultTextualAbbreviation = siPrefix.getDefaultTextualPrefix() + clone.getDefaultTextualAbbreviation();
 
             // Make a builder and set values
             Builder<U> builder = makeBuilder();
             builder.setId(cloneId);
             builder.setName(cloneName);
             builder.setQuantity(this.quantity);
             builder.setSiPrefixes(SIPrefixes.NONE, 1.0);
             builder.setDefaultDisplayAbbreviation(cloneDefaultAbbreviation);
             builder.setDefaultTextualAbbreviation(cloneDefaultTextualAbbreviation);
             builder.setAdditionalAbbreviations(cloneAbbreviations.toArray(new String[cloneAbbreviations.size()]));
             if (getScale() instanceof OffsetLinearScale)
             {
                 builder.setScale(new OffsetLinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit(),
                         0.0));
             }
             else
             {
                 builder.setScale(new LinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit()));
             }
             builder.setUnitSystem(this.unitSystem); // SI_BASE stays SI_BASE with prefix
             builder.setGenerated(automaticallyGenerated);
 
             return clone.build(builder);
         }
         catch (CloneNotSupportedException exception)
         {
             throw new UnitRuntimeException(exception);
         }
     }
 
     /**
      * Create a scaled version of this unit with the same unit system but another SI prefix and scale. This method is used for a
      * unit that is explicitly scaled with an SI prefix.
      * @param siPrefix SIPrefix; the prefix for which to scale the unit
      * @param siPrefixPower double; the power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters.
      * @return a scaled instance of this unit
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveSI(final SIPrefix siPrefix, final double siPrefixPower)
     {
         return deriveSI(siPrefix, siPrefixPower, false);
     }
 
     /**
      * Create a scaled version of this unit with the same unit system but another SI prefix and scale, where the "k" and "kilo"
      * abbreviations at the start will be replaced by the new information from the SIPrefix.
      * @param siPrefix SIPrefix; the prefix for which to scale the unit
      * @param siPrefixPower double; the power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters.
      * @param automaticallyGenerated boolean; indicate whether the unit has been automatically generated
      * @return U; a scaled instance of this unit
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveSIKilo(final SIPrefix siPrefix, final double siPrefixPower, final boolean automaticallyGenerated)
     {
         Throw.whenNull(siPrefix, "siPrefix cannot be null");
         Throw.when(!this.id.startsWith("k"), UnitRuntimeException.class, "deriving from a kilo-unit: id should start with 'k'");
         Throw.when(!this.defaultTextualAbbreviation.startsWith("k"), UnitRuntimeException.class,
                 "deriving from a kilo-unit: defaultTextualAbbreviation should start with 'k'");
         Throw.when(!this.defaultDisplayAbbreviation.startsWith("k"), UnitRuntimeException.class,
                 "deriving from a kilo-unit: defaultDisplayAbbreviation should start with 'k'");
         Throw.when(!this.name.startsWith("kilo"), UnitRuntimeException.class,
                 "deriving from a kilo-unit: name should start with 'kilo'");
         for (String abbreviation : getAbbreviations())
         {
             Throw.when(!abbreviation.startsWith("k"), UnitRuntimeException.class,
                     "deriving from a kilo-unit: each abbreviation should start with 'k'");
         }
 
         try
         {
             U clone = clone();
 
             // get values: combine all prefixes with all names / abbreviations
             String cloneId = siPrefix.getDefaultTextualPrefix() + clone.getId().substring(1);
             String cloneName = siPrefix.getPrefixName() + clone.getName().substring(4);
             Set<String> cloneAbbreviations = new LinkedHashSet<>();
             for (String abbreviation : clone.getAbbreviations())
             {
                 cloneAbbreviations.add(siPrefix.getDefaultTextualPrefix() + abbreviation.substring(1));
             }
             String cloneDefaultAbbreviation =
                     siPrefix.getDefaultDisplayPrefix() + clone.getDefaultDisplayAbbreviation().substring(1);
             String cloneDefaultTextualAbbreviation =
                     siPrefix.getDefaultTextualPrefix() + clone.getDefaultTextualAbbreviation().substring(1);
 
             // make a builder and set values
             Builder<U> builder = makeBuilder();
             builder.setId(cloneId);
             builder.setName(cloneName);
             builder.setQuantity(this.quantity);
             builder.setSiPrefixes(SIPrefixes.NONE, 1.0);
             builder.setDefaultDisplayAbbreviation(cloneDefaultAbbreviation);
             builder.setDefaultTextualAbbreviation(cloneDefaultTextualAbbreviation);
             builder.setAdditionalAbbreviations(cloneAbbreviations.toArray(new String[cloneAbbreviations.size()]));
             if (getScale() instanceof OffsetLinearScale)
             {
                 builder.setScale(new OffsetLinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit(),
                         0.0));
             }
             else
             {
                 builder.setScale(new LinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit()));
             }
 
             builder.setUnitSystem(this.unitSystem);
             builder.setGenerated(automaticallyGenerated);
 
             return clone.build(builder);
         }
         catch (CloneNotSupportedException exception)
         {
             throw new UnitRuntimeException(exception);
         }
     }
 
     /**
      * Create a scaled version of this unit with the same unit system but another SI prefix and scale. The "per" units scale in
      * the opposite direction as the normally scaled units. It will yield units like "/ms", "/mus", "/ns", etc.
      * @param siPrefix SIPrefix; the prefix for which to scale the unit
      * @param siPrefixPower double; the power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters.
      * @param automaticallyGenerated boolean; indicate whether the unit has been automatically generated
      * @return U; a scaled instance of this unit
      * @throws UnitRuntimeException when cloning fails
      */
     public U derivePerSI(final SIPrefix siPrefix, final double siPrefixPower, final boolean automaticallyGenerated)
     {
         Throw.whenNull(siPrefix, "siPrefix cannot be null");
         try
         {
             U clone = clone();
 
             // Get values: combine all prefixes with all names / abbreviations
             String cloneId = siPrefix.getDefaultTextualPrefix() + clone.getId().replace("1/", "").replace("/", "").trim();
             String cloneName =
                     siPrefix.getPrefixName() + clone.getName().replace("per", "").replace("1/", "").replace("/", "").trim();
             Set<String> cloneAbbreviations = new LinkedHashSet<>();
             for (String abbreviation : clone.getAbbreviations())
             {
                 cloneAbbreviations
                         .add(siPrefix.getDefaultTextualPrefix() + abbreviation.replace("1/", "").replace("/", "").trim());
                 cloneAbbreviations
                         .add("1" + siPrefix.getDefaultTextualPrefix() + abbreviation.replace("1/", "").replace("/", "").trim());
             }
             String cloneDefaultAbbreviation = siPrefix.getDefaultDisplayPrefix()
                     + clone.getDefaultDisplayAbbreviation().replace("1/", "").replace("/", "").trim();
             String cloneDefaultTextualAbbreviation = siPrefix.getDefaultTextualPrefix()
                     + clone.getDefaultTextualAbbreviation().replace("1/", "").replace("/", "").trim();
 
             // Make a builder and set values
             Builder<U> builder = makeBuilder();
             builder.setId(cloneId);
             builder.setName(cloneName);
             builder.setQuantity(this.quantity);
             builder.setSiPrefixes(SIPrefixes.NONE, 1.0);
             builder.setDefaultDisplayAbbreviation(cloneDefaultAbbreviation);
             builder.setDefaultTextualAbbreviation(cloneDefaultTextualAbbreviation);
             builder.setAdditionalAbbreviations(cloneAbbreviations.toArray(new String[cloneAbbreviations.size()]));
             if (getScale() instanceof OffsetLinearScale)
             {
                 builder.setScale(new OffsetLinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit(),
                         0.0));
             }
             else
             {
                 builder.setScale(new LinearScale(
                         (siPrefixPower == 1.0 ? siPrefix.getFactor() : Math.pow(siPrefix.getFactor(), siPrefixPower))
                                 * ((LinearScale) getScale()).getConversionFactorToStandardUnit()));
             }
             builder.setUnitSystem(this.unitSystem); // SI_BASE stays SI_BASE with prefix
             builder.setGenerated(automaticallyGenerated);
 
             return clone.build(builder);
         }
         catch (CloneNotSupportedException exception)
         {
             throw new UnitRuntimeException(exception);
         }
     }
 
     /**
      * Create a linearly scaled version of this unit. The scale field will be filled with the correct scaleFactor. Note that the
      * unit that is used for derivation can already have a scaleFactor.
      * @param scaleFactor double; the linear scale factor of the unit
      * @param derivedId String; the new id of the derived unit
      * @param derivedName String; the new name of the derived unit
      * @param derivedUnitSystem UnitSystem; the unit system of the derived unit
      * @param derivedDefaultDisplayAbbreviation String; the default abbreviation to use in e.g, the toString() method. Can be
      *            null.
      * @param derivedDefaultTextualAbbreviation String; the default textual abbreviation to use in, e.g, typing. Can be null.
      * @param derivedAbbreviations String...; the other valid abbreviations for the unit, e.g. {"h", "hr", "hour"}. Can be left
      *            out.
      * @return U; a linearly scaled instance of this unit with new id, abbreviation, name, and unit system
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveLinear(final double scaleFactor, final String derivedId, final String derivedName,
             final UnitSystem derivedUnitSystem, final String derivedDefaultDisplayAbbreviation,
             final String derivedDefaultTextualAbbreviation, final String... derivedAbbreviations)
     {
         String cName = getClass().getSimpleName();
         Throw.whenNull(derivedId, "deriving unit from %s.%s; derivedId cannot be null", cName, this.id);
         Throw.whenNull(derivedName, "deriving unit from %s.%s; derivedName cannot be null", cName, this.id);
         Throw.whenNull(derivedUnitSystem, "deriving unit from %s.%s; derivedUnitSystem cannot be null", cName, this.id);
         if (!getScale().getClass().equals(LinearScale.class) && !getScale().getClass().equals(IdentityScale.class))
         {
             throw new UnitRuntimeException("Cannot derive from unit " + cName + "." + getId() + " with scale "
                     + getScale().getClass().getSimpleName() + ". Scale should be Linear");
         }
 
         try
         {
             U clone = clone();
 
             // make a builder and set values
             Builder<U> builder = makeBuilder();
             builder.setId(derivedId);
             builder.setName(derivedName);
             builder.setQuantity(this.quantity);
             builder.setSiPrefixes(SIPrefixes.NONE, 1.0);
             builder.setScale(new LinearScaleg/djunits/unit/scale/LinearScale.html#LinearScale">LinearScale(scaleFactor * ((LinearScale) getScale()).getConversionFactorToStandardUnit()));
             builder.setUnitSystem(derivedUnitSystem);
             builder.setDefaultDisplayAbbreviation(derivedDefaultDisplayAbbreviation);
             builder.setDefaultTextualAbbreviation(derivedDefaultTextualAbbreviation);
             if (derivedAbbreviations != null)
             {
                 builder.setAdditionalAbbreviations(derivedAbbreviations);
             }
 
             return clone.build(builder);
         }
         catch (CloneNotSupportedException exception)
         {
             throw new UnitRuntimeException(exception);
         }
     }
 
     /**
      * Create a linearly scaled version of this unit. The scale field will be filled with the correct scaleFactor. Note that the
      * unit that is used for derivation can already have a scaleFactor.
      * @param scaleFactor double; the linear scale factor of the unit
      * @param derivedId String; the new id of the derived unit
      * @param derivedName String; the new name of the derived unit
      * @param derivedUnitSystem UnitSystem; the unit system of the derived unit
      * @return U; a linearly scaled instance of this unit with new id, abbreviation, name, and unit system
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveLinear(final double scaleFactor, final String derivedId, final String derivedName,
             final UnitSystem derivedUnitSystem)
     {
         return deriveLinear(scaleFactor, derivedId, derivedName, derivedUnitSystem, null, null);
     }
 
     /**
      * Create a linearly scaled version of this unit. The unitSystem will be copied. The scale field will be filled with the
      * correct scaleFactor. Note that the unit that is used for derivation can already have a scaleFactor.
      * @param scaleFactor double; the linear scale factor of the unit
      * @param derivedId String; the new id of the derived unit
      * @param derivedName String; the new name of the derived unit
      * @return U; a linearly scaled instance of this unit with new id, abbreviation, name, and unit system
      * @throws UnitRuntimeException when cloning fails
      */
     public U deriveLinear(final double scaleFactor, final String derivedId, final String derivedName)
     {
         return deriveLinear(scaleFactor, derivedId, derivedName, getUnitSystem());
     }
 
     /**
      * Create a Builder. Override at subclasses to create extended builder.
      * @return an instance of a builder.
      */
     public Builder<U> makeBuilder()
     {
         return new Builder<U>();
     }
 
     /**
      * Create or lookup a unit based on given SI dimensions. E.g., a unit with dimensions 1/s^2 or kg.m/s^2.
      * @param siDimensions SIDimensions; the vector with the dimensionality of the unit
      * @return SIUnit; an SIUnit object with the right dimensions
      */
     @SuppressWarnings("unchecked")
     public static SIUnit lookupOrCreateUnitWithSIDimensions(final SIDimensions siDimensions)
     {
         Throw.whenNull(siDimensions, "siDimensions cannot be null");
 
         Quantity<SIUnit> quantity = null;
         SIUnit unit = null;
 
         Set<Quantity<?>> baseUnitSet = Quantities.INSTANCE.getQuantities(siDimensions);
         for (Quantity<?> bu : baseUnitSet)
         {
             if (bu.getStandardUnit().getClass().equals(Unit.class))
             {
                 quantity = (Quantity<SIUnit>) bu;
             }
         }
 
         if (quantity == null)
         {
             quantity = new Quantity<SIUnit>(siDimensions.toString(), siDimensions);
             Builder<SIUnit> builder = new Builder<>();
             builder.setId(siDimensions.toString(true, true));
             builder.setName(siDimensions.toString(true, true));
             builder.setQuantity(quantity);
             builder.setScale(IdentityScale.SCALE);
             builder.setGenerated(true);
             builder.setUnitSystem(UnitSystem.SI_DERIVED);
             builder.setSiPrefixes(SIPrefixes.NONE, 1.0);
             unit = new SIUnit();
             unit.build(builder); // it will be registered at the BaseUnit
         }
         else
         {
             unit = quantity.getStandardUnit();
         }
 
         return unit;
     }
 
     /**
      * Retrieve the unit id.
      * @return String; the unit id
      */
     public String getId()
     {
         return this.id;
     }
 
     /**
      * Retrieve a safe copy of the unit abbreviations.
      * @return Set&lt;String&gt;; the unit abbreviations
      */
     public Set<String> getAbbreviations()
     {
         return new LinkedHashSet<>(this.abbreviations);
     }
 
     /**
      * Retrieve the default abbreviation.
      * @return String; the default abbreviation
      */
     public String getDefaultDisplayAbbreviation()
     {
         return this.defaultDisplayAbbreviation;
     }
 
     /**
      * Retrieve the default textual abbreviation.
      * @return String; the default textual abbreviation
      */
     public String getDefaultTextualAbbreviation()
     {
         return this.defaultTextualAbbreviation;
     }
 
     /**
      * Retrieve the name of this unit.
      * @return String; the name of this unit
      */
     public String getName()
     {
         return this.name;
     }
 
     /**
      * Retrieve the scale of this unit.
      * @return Scale; the scale of this unit
      */
     public Scale getScale()
     {
         return this.scale;
     }
 
     /**
      * Retrieve the unit system of this unit.
      * @return unitSystem the unit system of this unit
      */
     public UnitSystem getUnitSystem()
     {
         return this.unitSystem;
     }
 
     /**
      * Retrieve the unit base of this unit.
      * @return BaseUnit&lt;U&gt;; the unit base of this unit. if this unit is itself a unit base; the returned value is
      *         <code>null</code>
      */
     public Quantity<U> getQuantity()
     {
         return this.quantity;
     }
 
     /**
      * Indicate whether is unit was automatically generated.
      * @return boolean; true if this unit has been automatically generate; false if it was not automatically generated
      */
     public boolean isGenerated()
     {
         return this.generated;
     }
 
     /**
      * Indicate whether this unit has the standard SI signature.
      * @return boolean; true if this unit has the standard SI signature; false if this unit does not have the standard SI
      *         signature
      */
     public boolean isBaseSIUnit()
     {
         return this.baseSIUnit;
     }
 
     /**
      * Retrieve the standard unit (SI Unit) belonging to this unit.
      * @return U; the standard unit (SI unit) belonging to this unit
      */
     public U getStandardUnit()
     {
         return getQuantity().getStandardUnit();
     }
 
     /** {@inheritDoc} */
     @SuppressWarnings("unchecked")
     @Override
     public U clone() throws CloneNotSupportedException
     {
         return (U) super.clone();
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         result = prime * result + ((this.abbreviations == null) ? 0 : this.abbreviations.hashCode());
         result = prime * result + ((this.quantity == null) ? 0 : this.quantity.hashCode());
         result = prime * result + ((this.defaultDisplayAbbreviation == null) ? 0 : this.defaultDisplayAbbreviation.hashCode());
         result = prime * result + ((this.defaultTextualAbbreviation == null) ? 0 : this.defaultTextualAbbreviation.hashCode());
         result = prime * result + (this.generated ? 1231 : 1237);
         result = prime * result + ((this.id == null) ? 0 : this.id.hashCode());
         result = prime * result + ((this.name == null) ? 0 : this.name.hashCode());
         result = prime * result + ((this.scale == null) ? 0 : this.scale.hashCode());
         result = prime * result + ((this.unitSystem == null) ? 0 : this.unitSystem.hashCode());
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings("checkstyle:needbraces")
     public boolean equals(final Object obj)
     {
         if (this == obj)
             return true;
         if (obj == null)
             return false;
         if (getClass() != obj.getClass())
             return false;
         Unit<?> other = (Unit<?>) obj;
         if (this.abbreviations == null)
         {
             if (other.abbreviations != null)
                 return false;
         }
         else if (!this.abbreviations.equals(other.abbreviations))
             return false;
         if (this.quantity == null)
         {
             if (other.quantity != null)
                 return false;
         }
         else if (!this.quantity.equals(other.quantity))
             return false;
         if (this.defaultDisplayAbbreviation == null)
         {
             if (other.defaultDisplayAbbreviation != null)
                 return false;
         }
         else if (!this.defaultDisplayAbbreviation.equals(other.defaultDisplayAbbreviation))
             return false;
         if (this.defaultTextualAbbreviation == null)
         {
             if (other.defaultTextualAbbreviation != null)
                 return false;
         }
         else if (!this.defaultTextualAbbreviation.equals(other.defaultTextualAbbreviation))
             return false;
         if (this.generated != other.generated)
             return false;
         if (this.id == null)
         {
             if (other.id != null)
                 return false;
         }
         else if (!this.id.equals(other.id))
             return false;
         if (this.name == null)
         {
             if (other.name != null)
                 return false;
         }
         else if (!this.name.equals(other.name))
             return false;
         if (this.scale == null)
         {
             if (other.scale != null)
                 return false;
         }
         else if (!this.scale.equals(other.scale))
             return false;
         if (this.unitSystem == null)
         {
             if (other.unitSystem != null)
                 return false;
         }
         else if (!this.unitSystem.equals(other.unitSystem))
             return false;
         return true;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         return this.defaultDisplayAbbreviation;
     }
 
     /**
      * The class that contains the information to build a unit.
      * <p>
      * Copyright (c) 2019-2020 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved.
      * <br>
      * BSD-style license. See <a href="https://djunits.org/docs/license.html">DJUNITS License</a>.
      * <p>
      * @author <a href="https://www.tudelft.nl/averbraeck" target="_blank">Alexander Verbraeck</a>
      * @param <U> the unit for which the builder contains the information.
      */
     public static class Builder<U extends Unit<U>> implements Serializable
     {
         /** ... */
         private static final long serialVersionUID = 20191018L;
 
         /** The id of the unit; has to be unique within the unit name. Used for, e.g., localization and retrieval. */
         private String id;
 
         /** The abbreviations in the default locale. All abbreviations an be used in the valueOf() and of() methods. */
         private Set<String> additionalAbbreviations = new LinkedHashSet<>();
 
         /** The default abbreviation in the default locale for printing. Included in the abbreviations list. */
         private String defaultDisplayAbbreviation;
 
         /** The default textual abbreviation in the default locale for data entry. Included in the abbreviations list. */
         private String defaultTextualAbbreviation;
 
         /** The full name of the unit in the default locale. */
         private String name;
 
         /** The scale to use to convert between this unit and the standard (e.g., SI, BASE) unit. */
         private Scale scale;
 
         /** The unit system, e.g. SI or Imperial. */
         private UnitSystem unitSystem;
 
         /** Whether or not the unit supports SI prefixes from "yotta" (y) to "yocto" (Y). */
         private SIPrefixes siPrefixes;
 
         /** The power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters. */
         private double siPrefixPower = 1.0;
 
         /** Whether the unit has been automatically generated or not. */
         private boolean generated = false;
 
         /**
          * The corresponding unit base that contains all registered units for the unit as well as SI dimension information. The
          * unit base should never be null.
          */
         private Quantity<U> quantity;
 
         /**
          * Empty constructor. Content is generated through chaining: new
          * Unit.Builder&lt;TypeUnit&gt;().setId("id").setName("name");
          */
         public Builder()
         {
             // Empty constructor. Content is generated through (chaining of) method calls
         }
 
         /**
          * Return whether SI prefixes, ranging from yotta (y) to yocto (Y), will be generated.
          * @return siPrefixes, NONE (e.g., for inch), ALL (e.g., for meter) or KILO (e.g., for kilometer)
          */
         public SIPrefixes getSiPrefixes()
         {
             return this.siPrefixes;
         }
 
         /**
          * Return the power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters.
          * @return siPrefixPower double; power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters
          */
         public double getSiPrefixPowerFactor()
         {
             return this.siPrefixPower;
         }
 
         /**
          * Set whether SI prefixes, ranging from yotta (y) to yocto (Y), are allowed. If not set; this property defaults to
          * <code>false</code>.
          * @param newSiPrefixes SIPrefixes; SIPrefixes set siPrefixes, NONE (e.g., for inch), ALL (e.g., for meter) or KILO
          *            (e.g., for kilometer)
          * @param power double; power factor of the SI prefixes, e.g. 2.0 for square meters and 3.0 for cubic meters
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setSiPrefixes(final SIPrefixes newSiPrefixes, final double power)
         {
             this.siPrefixes = newSiPrefixes;
             this.siPrefixPower = power;
             return this;
         }
 
         /**
          * Retrieve the id of the unit that this builder builds.
          * @return String; the id of the unit that this builder builds
          */
         public String getId()
         {
             return this.id;
         }
 
         /**
          * Set the id of the unit that this builder builds.
          * @param newId String; set the id of the unit that this builder builds (must be set; the default is <code>null</code>
          *            which is invalid)
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setId(final String newId)
         {
             this.id = newId;
             return this;
         }
 
         /**
          * Retrieve the additional abbreviations.
          * @return Set&lt;String&gt;; the additional abbreviations
          */
         public Set<String> getAdditionalAbbreviations()
         {
             return this.additionalAbbreviations;
         }
 
         /**
          * Set the additional abbreviations.
          * @param newAdditionalAbbreviations String...; the additional abbreviations
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setAdditionalAbbreviations(final String... newAdditionalAbbreviations)
         {
             this.additionalAbbreviations = new LinkedHashSet<>(Arrays.asList(newAdditionalAbbreviations)); // safe copy
             return this;
         }
 
         /**
          * Retrieve the default display abbreviation.
          * @return String; the default display abbreviation
          */
         public String getDefaultDisplayAbbreviation()
         {
             return this.defaultDisplayAbbreviation;
         }
 
         /**
          * Set the default display abbreviation.
          * @param newDefaultDisplayAbbreviation String; the default display abbreviation
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setDefaultDisplayAbbreviation(final String newDefaultDisplayAbbreviation)
         {
             this.defaultDisplayAbbreviation = newDefaultDisplayAbbreviation;
             return this;
         }
 
         /**
          * Retrieve the default textual abbreviation.
          * @return String; the default textual abbreviation
          */
         public String getDefaultTextualAbbreviation()
         {
             return this.defaultTextualAbbreviation;
         }
 
         /**
          * Set the default textual abbreviation.
          * @param newDefaultTextualAbbreviation String; the default textual abbreviation
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setDefaultTextualAbbreviation(final String newDefaultTextualAbbreviation)
         {
             this.defaultTextualAbbreviation = newDefaultTextualAbbreviation;
             return this;
         }
 
         /**
          * Return the name.
          * @return String; the name
          */
         public String getName()
         {
             return this.name;
         }
 
         /**
          * Set the name.
          * @param newName String; the name
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setName(final String newName)
         {
             this.name = newName;
             return this;
         }
 
         /**
          * Retrieve the scale.
          * @return Scale; the scale
          */
         public Scale getScale()
         {
             return this.scale;
         }
 
         /**
          * Set the scale.
          * @param newScale Scale; set the scale
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setScale(final Scale newScale)
         {
             this.scale = newScale;
             return this;
         }
 
         /**
          * Retrieve the unit system.
          * @return unitSystem UnitSystem; the unit system
          */
         public UnitSystem getUnitSystem()
         {
             return this.unitSystem;
         }
 
         /**
          * Set the unit system.
          * @param newUnitSystem UnitSystem; the unit system
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setUnitSystem(final UnitSystem newUnitSystem)
         {
             this.unitSystem = newUnitSystem;
             return this;
         }
 
         /**
          * Retrieve the generated flag.
          * @return generated Boolean; the generated flag
          */
         public boolean isGenerated()
         {
             return this.generated;
         }
 
         /**
          * Set the generated flag. Defaults to false. Should be set for units that are automatically generated.
          * @param newGenerated boolean; the value for the generated flag
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setGenerated(final boolean newGenerated)
         {
             this.generated = newGenerated;
             return this;
         }
 
         /**
          * Retrieve the unit base.
          * @return baseUnit BaseUnit&lt;U&gt;; the unit base
          */
         public Quantity<U> getQuantity()
         {
             return this.quantity;
         }
 
         /**
          * Set the unit base. Can never be null and has to be filled.
          * @param newQuantity Quantity&lt;U&gt;; the unit base
          * @return Builder; this builder instance that is being constructed (for method call chaining)
          */
         public Builder<U> setQuantity(final Quantity<U> newQuantity)
         {
             this.quantity = newQuantity;
             return this;
         }
 
         /** {@inheritDoc} */
         @Override
         public String toString()
         {
             return "Builder [id=" + this.id + ", name=" + this.name + ", scale=" + this.scale + "]";
         }
 
     }
 
     /**
      * Find or create a unit for the given SI dimensions.
      * @param unitString String; the textual representation of the unit
      * @return SIUnit; the unit
      * @throws IllegalArgumentException when the unit cannot be parsed or is incorrect
      * @throws NullPointerException when the unitString argument is null
      */
     public static SIUnit getUnit(final String unitString)
     {
         Throw.whenNull(unitString, "Error parsing SIVector: unitString is null");
         Throw.when(unitString.length() == 0, IllegalArgumentException.class, "Error parsing SIVector: empty unitString");
         try
         {
             SIUnit unit = Unit.lookupOrCreateUnitWithSIDimensions(SIDimensions.of(unitString));
             if (unit != null)
             {
                 return unit;
             }
         }
         catch (Exception exception)
         {
             throw new IllegalArgumentException("Error parsing SIUnit from " + unitString, exception);
         }
         throw new IllegalArgumentException("Error parsing SIVector with unit " + unitString);
     }
 
 }