Unit.java
/* Copyright 2002-2023 CS GROUP
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.utils.units;
import java.io.Serializable;
import java.util.List;
import org.hipparchus.fraction.Fraction;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.Precision;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
/** Basic handling of multiplicative units.
* <p>
* This class is by no means a complete handling of units. For complete
* support, look at libraries like {@code UOM}. This class handles only
* time, length, mass and current dimensions, as well as angles (which are
* dimensionless).
* </p>
* <p>
* Instances of this class are immutable.
* </p>
* @see <a href="https://github.com/netomi/uom">UOM</a>
* @author Luc Maisonobe
* @since 11.0
*/
public class Unit implements Serializable {
/** No unit. */
public static final Unit NONE = new Unit("n/a", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO);
/** Dimensionless unit. */
public static final Unit ONE = new Unit("1", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO);
/** Percentage unit. */
public static final Unit PERCENT = new Unit("%", 1.0e-2, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO);
/** Second unit. */
public static final Unit SECOND = new Unit("s", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ONE, Fraction.ZERO, Fraction.ZERO);
/** Minute unit. */
public static final Unit MINUTE = SECOND.scale("min", 60.0);
/** Hour unit. */
public static final Unit HOUR = MINUTE.scale("h", 60);
/** Day unit. */
public static final Unit DAY = HOUR.scale("d", 24.0);
/** Julian year unit.
* @see <a href="https://www.iau.org/publications/proceedings_rules/units/">SI Units at IAU</a>
*/
public static final Unit YEAR = DAY.scale("a", 365.25);
/** Hertz unit. */
public static final Unit HERTZ = SECOND.power("Hz", Fraction.MINUS_ONE);
/** Metre unit. */
public static final Unit METRE = new Unit("m", 1.0, Fraction.ZERO, Fraction.ONE, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO);
/** Kilometre unit. */
public static final Unit KILOMETRE = METRE.scale("km", 1000.0);
/** Kilogram unit. */
public static final Unit KILOGRAM = new Unit("kg", 1.0, Fraction.ONE, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO);
/** Gram unit. */
public static final Unit GRAM = KILOGRAM.scale("g", 1.0e-3);
/** Ampere unit. */
public static final Unit AMPERE = new Unit("A", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ONE, Fraction.ZERO);
/** Radian unit. */
public static final Unit RADIAN = new Unit("rad", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ONE);
/** Degree unit. */
public static final Unit DEGREE = RADIAN.scale("°", FastMath.toRadians(1.0));
/** Arc minute unit. */
public static final Unit ARC_MINUTE = DEGREE.scale("′", 1.0 / 60.0);
/** Arc second unit. */
public static final Unit ARC_SECOND = ARC_MINUTE.scale("″", 1.0 / 60.0);
/** Revolution unit. */
public static final Unit REVOLUTION = RADIAN.scale("rev", 2.0 * FastMath.PI);
/** Newton unit. */
public static final Unit NEWTON = KILOGRAM.multiply(null, METRE).divide("N", SECOND.power(null, Fraction.TWO));
/** Pascal unit. */
public static final Unit PASCAL = NEWTON.divide("Pa", METRE.power(null, Fraction.TWO));
/** Bar unit. */
public static final Unit BAR = PASCAL.scale("bar", 100000.0);
/** Joule unit. */
public static final Unit JOULE = NEWTON.multiply("J", METRE);
/** Watt unit. */
public static final Unit WATT = JOULE.divide("W", SECOND);
/** Coulomb unit. */
public static final Unit COULOMB = SECOND.multiply("C", AMPERE);
/** Volt unit. */
public static final Unit VOLT = WATT.divide("V", AMPERE);
/** Ohm unit. */
public static final Unit OHM = VOLT.divide("Ω", AMPERE);
/** tesla unit. */
public static final Unit TESLA = VOLT.multiply(null, SECOND).divide("T", METRE.power(null, Fraction.TWO));
/** Solar Flux Unit. */
public static final Unit SOLAR_FLUX_UNIT = WATT.divide(null, METRE.power(null, Fraction.TWO).multiply(null, HERTZ)).scale("SFU", 1.0e-22);
/** Total Electron Content Unit. */
public static final Unit TOTAL_ELECTRON_CONTENT_UNIT = METRE.power(null, new Fraction(-2)).scale("TECU", 1.0e+16);
/** Earth Radii used as Bstar unit in CCSDS OMM. */
public static final Unit EARTH_RADII = new Unit("ER", 1.0, Fraction.ZERO, Fraction.ZERO, Fraction.ZERO, Fraction.ONE, Fraction.ZERO);
/** Serializable UID. */
private static final long serialVersionUID = 20210402L;
/** Name name of the unit. */
private final String name;
/** Scaling factor to SI units. */
private final double scale;
/** Mass exponent. */
private final Fraction mass;
/** Length exponent. */
private final Fraction length;
/** Time exponent. */
private final Fraction time;
/** Current exponent. */
private final Fraction current;
/** Angle exponent. */
private final Fraction angle;
/** Simple constructor.
* @param name name of the unit
* @param scale scaling factor to SI units
* @param mass mass exponent
* @param length length exponent
* @param time time exponent
* @param current current exponent
* @param angle angle exponent
*/
public Unit(final String name, final double scale,
final Fraction mass, final Fraction length,
final Fraction time, final Fraction current,
final Fraction angle) {
this.name = name;
this.scale = scale;
this.mass = mass;
this.length = length;
this.time = time;
this.current = current;
this.angle = angle;
}
/** Get the name of the unit.
* @return name of the unit
*/
public String getName() {
return name;
}
/** Get the scaling factor to SI units.
* @return scaling factor to SI units
*/
public double getScale() {
return scale;
}
/** Get the mass exponent.
* @return mass exponent
*/
public Fraction getMass() {
return mass;
}
/** Get the length exponent.
* @return length exponent
*/
public Fraction getLength() {
return length;
}
/** Get the time exponent.
* @return time exponent
*/
public Fraction getTime() {
return time;
}
/** Get the current exponent.
* @return current exponent
*/
public Fraction getCurrent() {
return current;
}
/** Get the angle exponent.
* @return angle exponent
*/
public Fraction getAngle() {
return angle;
}
/** Check if a unit has the same dimension as another unit.
* @param other other unit to check against
* @return true if unit has the same dimension as the other unit
*/
public boolean sameDimension(final Unit other) {
return time.equals(other.time) && length.equals(other.length) &&
mass.equals(other.mass) && current.equals(other.current) &&
angle.equals(other.angle);
}
/** Create the SI unit with same dimension.
* @return a new unit, with same dimension as instance and scaling factor set to 1.0
*/
public Unit sameDimensionSI() {
final StringBuilder builder = new StringBuilder();
append(builder, KILOGRAM.name, mass);
append(builder, METRE.name, length);
append(builder, SECOND.name, time);
append(builder, AMPERE.name, current);
append(builder, RADIAN.name, angle);
if (builder.length() == 0) {
builder.append('1');
}
return new Unit(builder.toString(), 1.0, mass, length, time, current, angle);
}
/** Ensure some units are compatible with reference units.
* @param description description of the units list (for error message generation)
* @param reference reference units
* @param units units to check
* @param allowScaleDifferences if true, unit with same dimension but different
* scale (like {@link #KILOMETRE} versus {@link #METRE}) are allowed, otherwise they will trigger an exception
* @exception OrekitException if units are not compatible (number of elements, dimensions or scaling)
*/
public static void ensureCompatible(final String description, final List<Unit> reference,
final boolean allowScaleDifferences, final List<Unit> units) {
if (units.size() != reference.size()) {
throw new OrekitException(OrekitMessages.WRONG_NB_COMPONENTS,
description, reference.size(), units.size());
}
for (int i = 0; i < reference.size(); ++i) {
if (!reference.get(i).sameDimension(units.get(i))) {
throw new OrekitException(OrekitMessages.INCOMPATIBLE_UNITS,
reference.get(i).getName(),
units.get(i).getName());
}
if (!(allowScaleDifferences ||
Precision.equals(reference.get(i).getScale(), units.get(i).getScale(), 1))) {
throw new OrekitException(OrekitMessages.INCOMPATIBLE_UNITS,
reference.get(i).getName(),
units.get(i).getName());
}
}
}
/** Append a dimension contribution to a unit name.
* @param builder builder for unit name
* @param dim name of the dimension
* @param exp exponent of the dimension
*/
private void append(final StringBuilder builder, final String dim, final Fraction exp) {
if (!exp.isZero()) {
if (builder.length() > 0) {
builder.append('.');
}
builder.append(dim);
if (exp.getDenominator() == 1) {
if (exp.getNumerator() != 1) {
builder.append(Integer.toString(exp.getNumerator()).
replace('-', '⁻').
replace('0', '⁰').
replace('1', '¹').
replace('2', '²').
replace('3', '³').
replace('4', '⁴').
replace('5', '⁵').
replace('6', '⁶').
replace('7', '⁷').
replace('8', '⁸').
replace('9', '⁹'));
}
} else {
builder.
append("^(").
append(exp.getNumerator()).
append('/').
append(exp.getDenominator()).
append(')');
}
}
}
/** Create an alias for a unit.
* @param newName name of the new unit
* @return a new unit representing same unit as the instance but with a different name
*/
public Unit alias(final String newName) {
return new Unit(newName, scale, mass, length, time, current, angle);
}
/** Scale a unit.
* @param newName name of the new unit
* @param factor scaling factor
* @return a new unit representing scale times the instance
*/
public Unit scale(final String newName, final double factor) {
return new Unit(newName, factor * scale, mass, length, time, current, angle);
}
/** Create power of unit.
* @param newName name of the new unit
* @param exponent exponent to apply
* @return a new unit representing the power of the instance
*/
public Unit power(final String newName, final Fraction exponent) {
final int num = exponent.getNumerator();
final int den = exponent.getDenominator();
double s = (num == 1) ? scale : FastMath.pow(scale, num);
if (den > 1) {
if (den == 2) {
s = FastMath.sqrt(s);
} else if (den == 3) {
s = FastMath.cbrt(s);
} else {
s = FastMath.pow(s, 1.0 / den);
}
}
return new Unit(newName, s,
mass.multiply(exponent), length.multiply(exponent),
time.multiply(exponent), current.multiply(current),
angle.multiply(exponent));
}
/** Create root of unit.
* @param newName name of the new unit
* @return a new unit representing the square root of the instance
*/
public Unit sqrt(final String newName) {
return new Unit(newName, FastMath.sqrt(scale),
mass.divide(2), length.divide(2),
time.divide(2), current.divide(2),
angle.divide(2));
}
/** Create product of units.
* @param newName name of the new unit
* @param other unit to multiply with
* @return a new unit representing the this times the other unit
*/
public Unit multiply(final String newName, final Unit other) {
return new Unit(newName, scale * other.scale,
mass.add(other.mass), length.add(other.length),
time.add(other.time), current.add(other.current),
angle.add(other.angle));
}
/** Create quotient of units.
* @param newName name of the new unit
* @param other unit to divide with
* @return a new unit representing the this divided by the other unit
*/
public Unit divide(final String newName, final Unit other) {
return new Unit(newName, scale / other.scale,
mass.subtract(other.mass), length.subtract(other.length),
time.subtract(other.time), current.subtract(other.current),
angle.subtract(other.angle));
}
/** Convert a value to SI units.
* @param value value instance unit
* @return value in SI units
*/
public double toSI(final double value) {
return value * scale;
}
/** Convert a value to SI units.
* @param value value instance unit
* @return value in SI units
*/
public double toSI(final Double value) {
return value == null ? Double.NaN : value.doubleValue() * scale;
}
/** Convert a value from SI units.
* @param value value SI unit
* @return value in instance units
*/
public double fromSI(final double value) {
return value / scale;
}
/** Convert a value from SI units.
* @param value value SI unit
* @return value in instance units
*/
public double fromSI(final Double value) {
return value == null ? Double.NaN : value.doubleValue() / scale;
}
/** Parse a unit.
* <p>
* The grammar for unit specification allows chains units multiplication and
* division, as well as putting powers on units.
* </p>
* <p>The symbols used for units are the SI units with some extensions.
* </p>
* <dl>
* <dt>year</dt>
* <dd>the accepted non-SI unit for Julian year is "a" but we also accept "yr"</dd>
* <dt>day</dt>
* <dd>the accepted non-SI unit for day is "d" but we also accept "day"</dd>
* <dt>dimensionless</dt>
* <dd>both "1" and "#" (U+0023, NUMBER SIGN) are accepted</dd>
* <dt>mass</dt>
* <dd>"g" is the standard symbol, despite the unit is "kg" (it is the only
* unit that has a prefix in its name, so all multiples must be based on "g")</dd>
* <dt>degrees</dt>
* <dd>the base symbol for degrees is "°" (U+00B0, DEGREE SIGN), but we also accept
* "◦" (U+25E6, WHITE BULLET) and "deg"</dd>
* <dt>arcminute</dt>
* <dd>The base symbol for arcminute is "′" (U+2032, PRIME) but we also accept "'" (U+0027, APOSTROPHE)</dd>
* <dt>arcsecond</dt>
* <dd>The base symbol for arcsecond is "″" (U+2033, DOUBLE PRIME) but we also accept
* "''" (two occurrences of U+0027, APOSTROPHE), "\"" (U+0022, QUOTATION MARK) and "as"</dd>
* </dl>
* <p>
* All the SI prefix (from "y", yocto, to "Y", Yotta) are accepted, as well
* as integer prefixes. The standard symbol for micro 10⁻⁶ is "µ" (U+00B5, MICRO SIGN),
* but we also accept "μ" (U+03BC, GREEK SMALL LETTER MU). Beware that some combinations
* are forbidden, for example "Pa" is Pascal, not peta-years, and "as" is arcsecond for
* this parser, not atto-seconds, because many people in the space field use mas for
* milliarcseconds and µas for microarcseconds. Beware that prefixes are case-sensitive!
* Integer prefixes can be used to specify units like "30s", but only once at the beginning
* of the specification (i.e. "2rev/d²" is accepted, but "rev/(2d)²" is refused). Conforming
* with SI brochure "The International System of Units" (9th edition, 2019), each SI
* prefix is part of the unit and precedes the unit symbol without a separator
* (i.e. MHz is seen as one identifier).
* </p>
* <dl>
* <dt>multiplication</dt>
* <dd>can specified with either "*" (U+002A, ASTERISK), "×" (U+00D7, MULTIPLICATION SIGN),
* "." (U+002E, FULL STOP) or "·" (U+00B7, MIDDLE DOT) as the operator</dd>
* <dt>division</dt>
* <dd>can be specified with either "/" (U+002F, SOLIDUS) or "⁄" (U+2044, FRACTION SLASH)
* as the operator</dd>
* <dt>powers</dt>
* <dd>can be specified either by
* <ul>
* <li>prefixing with the unicode "√" (U+221A, SQUARE ROOT) character</li>
* <li>postfixing with "**", "^" or implicitly using unicode superscripts</li>
* </ul>
* </dd>
* </dl>
* <p>
* Exponents can be specified in different ways:
* <ul>
* <li>as an integer, as in "m^-2" or "m⁻²"</li>
* <li>directly as unicode characters for the few fractions that unicode supports, as in "Ω^⅞"</li>
* <li>as the special decimal value 0.5 which is used by CCSDS, as in "km**0.5"</li>
* <li>as a pair of parentheses surrounding two integers separated by a solidus or fraction slash,
* as in "Pa^(11/12)"</li>
* </ul>
* For integer exponents, the digits must be ASCII digits from the Basic Latin block from
* unicode if explicit exponent marker "**" or "^" is used, or using unicode superscript
* digits if implicit exponentiation (i.e. no markers at all) is used. Unicode superscripts
* are not allowed for fractional exponents because unicode does not provide a superscript solidus.
* Negative exponents can be used too.
* <p>
* These rules mean all the following (silly) examples are parsed properly:
* MHz, km/√d, kg.m.s⁻¹, µas^⅖/(h**(2)×m)³, km/√(kg.s), km**0.5, 2rev/d²
* </p>
* @param unitSpecification unit specification to parse
* @return parsed unit
*/
public static Unit parse(final String unitSpecification) {
// parse the specification
final List<PowerTerm> terms = Parser.buildTermsList(unitSpecification);
if (terms == null) {
// special handling of "n/a"
return Unit.NONE;
}
// build compound unit
Unit unit = Unit.ONE;
for (final PowerTerm term : terms) {
try {
Unit u = PrefixedUnit.valueOf(term.getBase().toString());
if (!Fraction.ONE.equals(term.getExponent())) {
u = u.power(null, term.getExponent());
}
u = u.scale(null, term.getScale());
unit = unit.multiply(null, u);
} catch (IllegalArgumentException iae) {
throw new OrekitException(OrekitMessages.UNKNOWN_UNIT, term.getBase());
}
}
// give final name to unit
return unit.alias(unitSpecification);
}
/** Check if the instance represents the same unit as another instance.
* <p>
* The name is not considered so aliases are considered equal.
* </p>
* @param unit other unit
* @return true if the instance and the other unit refer to the same unit
*/
public boolean equals(final Object unit) {
if (unit == this) {
// first fast check
return true;
}
if (unit instanceof Unit) {
final Unit u = (Unit) unit;
return Precision.equals(scale, u.scale, 1) &&
mass.equals(u.mass) && length.equals(u.length) && time.equals(u.time) &&
current.equals(u.current) && angle.equals(u.angle);
}
return false;
}
/** Get a hashcode for this unit.
* @return hashcode
*/
public int hashCode() {
return 0x67e7 ^
(Double.hashCode(scale) << 12) ^
(mass.hashCode() << 10) ^
(length.hashCode() << 8) ^
(time.hashCode() << 6) ^
(current.hashCode() << 4) ^
(angle.hashCode() << 2);
}
/** {@inheritDoc} */
@Override
public String toString() {
return getName();
}
}