RationalNumber operator ^ (const RationalNumber& B) const throw(std::invalid_argument)
{
if (!isFraction() || !B.isInteger())
{
return RationalNumber(powl(getRealNumber(), B.getRealNumber()));
}
RationalNumber S(1, 1);
RationalNumber A = *this;
long long n = B.numerator;
if (n < 0)
{
A = RationalNumber(1, 1) / A;
n = -n;
}
while (n)
{
if (n & 1)
{
S = S * A;
}
A = A * A;
n >>= 1;
}
return S;
}
RationalNumber operator * (const RationalNumber& B) const
{
if (!isFraction() || !B.isFraction())
{
return RationalNumber(getRealNumber() * B.getRealNumber());
}
return RationalNumber(numerator * B.numerator, denominator * B.denominator);
}
RationalNumber operator / (const RationalNumber& B) const throw(std::domain_error)
{
if (!isFraction() || !B.isFraction())
{
return RationalNumber(getRealNumber() / B.getRealNumber());
}
if (B.numerator == 0)
{
throw std::domain_error("Division by zero!");
}
return RationalNumber(numerator * B.denominator, denominator * B.numerator);
}
int rncCount(RationalNumberCollection *c, RationalNumber rn) {
// Wenn rn ungültig -> return 0
if (!rnIsValid(rn)) {
return 0;
}
// Länge der Collection bestimmen
int len = rncTotalUniqueCount(*(&c));
// Wenn Collection leer ist -> return 0
if (len == 0) {
return 0;
}
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// rn kürzen
rn = rnShorten(rn);
// Falls Bruch bereits vorhanden, ermittel Vorkommen des Bruchs
int i = rncSearch(*(&c), rn, 0, len-1);
if (i >= 0) {
return ptr[i][1].numerator;
}
return 0;
}
int rncSearch(RationalNumberCollection *c, RationalNumber rn, int min, int max) {
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Wenn Collection leer
if (max < min) {
return -1;
}
// Mitte der Collection ermitteln
int mid = (min + max) / 2;
// Wenn rn in der unteren Teil-Collection
if (rnLessThan(rn,ptr[mid][0])) {
return rncSearch(*(&c), rn, min, mid-1);
}
// Wenn rn in der oberen Teil-Collection
else if (rnLessThan(ptr[mid][0],rn)) {
return rncSearch(*(&c), rn, mid+1, max);
}
// rn wurde gefunden
else {
return mid;
}
}
void rncInit(RationalNumberCollection *c) {
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Allen Arrayelementen eine RationalNumber mit Zähler- und Nennerwerten von 0 eintragen,
// mit Ausnahme des Zähler-Denominators. Diese bekommen eine 1 spendiert, die für
// Rechenoperationen nötig ist.
RationalNumber rn = { 0, 0 };
RationalNumber counter = { 0, 1 };
for (int i=0; i<MAXSIZE; i++) {
ptr[i][0] = rn;
ptr[i][1] = counter;
}
// Setze totalUniqueCount auf 0
c->totalUniqueCount = 0;
// Setze totalCount auf 0
c->totalCount = 0;
// Setze sum auf 0/1
c->sum = counter;
// Setze average auf 0/1
c->average = counter;
// Setze median auf 0/1
c->median = counter;
}
RationalNumber RationalNumber::subtract (const RationalNumber &other){
int commonDenominator = Denominator * other.getDenominator();
int numerator1 = Numerator * other.getDenominator();
int numerator2 = other.getNumerator() * Denominator;
int difference = numerator1 - numerator2;
return RationalNumber (difference, commonDenominator);
}
RationalNumber RationalNumber::add(const RationalNumber &other){
int commonDenominator = Denominator * other.getDenominator();
int numerator1 = Numerator * other.getDenominator();
int numerator2 = other.getNumerator() * Denominator;
int sum = numerator1 + numerator2;
return RationalNumber (sum, commonDenominator);
}
// call by value
RationalNumber RationalNumber::operator-(const RationalNumber& other) const {
if (other.isNaN())
return RationalNumber(*this);
RationalNumber r(*this);
r -= other;
r.normalize();
return r;
}
void rncAdd(RationalNumberCollection *c, RationalNumber rn) {
// Wenn rn ungültig -> return
if (!rnIsValid(rn)) {
return;
}
// Länge der Collection ermitteln
int len = rncTotalUniqueCount(*(&c));
// rn kürzen
rn = rnShorten(rn);
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Falls Bruch bereits vorhanden
int i = rncSearch(*(&c), rn, 0, len-1);
if (i >= 0) {
// Erhöhe Counter des Bruchs
ptr[i][1].numerator++;
// Erhöhe totalCount der Collection
c->totalCount++;
// Erhöhe sum der Collection
c->sum = rnShorten(rnAdd(c->sum,rn));
// Berechne average der Collection
rncCalcAverage(*(&c));
return;
}
// Falls nocht nicht alle Elemente des Arrays belegt sind
if (len < MAXSIZE) {
// Trage den Bruch ein und erhöhe den Counter des Bruchs
ptr[len][0] = rn;
ptr[len][1].numerator++;
// Erhöhe totalUniqueCount der Collection
c->totalUniqueCount++;
// Erhöhe totalCount der Collection
c->totalCount++;
// Erhöhe sum der Collection
c->sum = rnShorten(rnAdd(c->sum,rn));
// Berechne average der Collection
rncCalcAverage(*(&c));
}
// Collection sortieren wenn Länge der Collection > 0
if (len > 0) {
rncSort(*(&c), len+1);
}
// Berechne median der Collection
rncCalcMedian(*(&c));
}
// call by value
RationalNumber RationalNumber::operator+(const RationalNumber& other) const {
if (other.isNaN())
return RationalNumber(*this);
/*
RationalNumber result(nomi() * other.deno() + other.nomi() * deno(),
deno() * other.deno());
return result;
*/
RationalNumber r(*this);
r += other;
r.normalize();
return r;
}
void rncRemove(RationalNumberCollection *c, RationalNumber rn) {
// Wenn rn ungültig -> return
if (!rnIsValid(rn)) {
return;
}
// Länge der Collection ermitteln
int len = rncTotalUniqueCount(*(&c));
// Wenn Collection leer -> return
if (len == 0) {
return;
}
// rn kürzen
rn = rnShorten(rn);
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Falls Bruch bereits vorhanden
int i = rncSearch(*(&c), rn, 0, len-1);
if (i >= 0) {
// Veringere Counter des Bruchs
ptr[i][1].numerator--;
// Veringere totalCount der Collection
c->totalCount--;
// Verringere sum der Collection
c->sum = rnShorten(rnSubtract(c->sum,rn));
// Wenn Counter anschließend == 0, entferne Bruch aus Collection
if (ptr[i][1].numerator == 0) {
ptr[i][0].numerator = 0;
ptr[i][0].denominator = 0;
// Verringere totalUniqueCount der Collection
c->totalUniqueCount--;
// Collection sortieren wenn Bruch nicht letzter Bruch in der Collection war
if (len > 1) {
rncSort(*(&c), len);
}
// Berechne median der Collection
rncCalcMedian(*(&c));
}
// Berechne average der Collection
rncCalcAverage(*(&c));
}
}
V3R SymmetryOperation::getReducedVector(const Kernel::IntMatrix &matrix,
const V3R &vector) const {
Kernel::IntMatrix translationMatrix(3, 3, false);
for (size_t i = 0; i < order(); ++i) {
Kernel::IntMatrix tempMatrix(3, 3, true);
for (size_t j = 0; j < i; ++j) {
tempMatrix *= matrix;
}
translationMatrix += tempMatrix;
}
return (translationMatrix * vector) *
RationalNumber(1, static_cast<int>(order()));
}
void rncCalcMedian(RationalNumberCollection *c) {
// Länge der Collection bestimmen
int len = rncTotalUniqueCount(*(&c));
// Wenn Collection leer
if (len == 0) {
RationalNumber result = { 0, 1 };
c->median = result;
}
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Wenn Länge der Collection == 1
if (len == 1) {
c->median = ptr[0][0];
}
// Wenn Länge der Collection == 2
if (len == 2) {
RationalNumber r = { 2, 1 };
c->median = rnShorten(rnDivide(rnAdd(ptr[0][0], ptr[1][0]), r));
}
// Wenn Länge der Collection gerade
if (len%2 == 0) {
RationalNumber r = { 2, 1 };
int lowerMedian = (len / 2) - 1;
int upperMedian = len / 2;
c->median = rnShorten(rnDivide(rnAdd(ptr[lowerMedian][0], ptr[upperMedian][0]), r));
}
// Wenn Länge der Collection ungerade
else {
int median = len / 2;
c->median = ptr[median][0];
}
}
/// Determines the symbol from the translation vector using a map.
std::string SymmetryElementMirrorGenerator::determineSymbol(
const SymmetryOperation &operation) const {
V3R rawTranslation = determineTranslation(operation);
V3R translation;
for (size_t i = 0; i < 3; ++i) {
translation[i] = rawTranslation[i] > RationalNumber(1, 2)
? rawTranslation[i] - 1
: rawTranslation[i];
}
std::string symbol = g_glideSymbolMap[translation.getPositiveVector()];
/* Some space groups have "unconventional glides" for which there is no
* proper symbol, so the general symbol "g" is used for these cases.
* Examples can be found in No. 227 (Fd-3m).
*/
if (symbol == "") {
return "g";
}
return symbol;
}
void rncCalcAverage(RationalNumberCollection *c) {
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Alle Brüche in der Collection zählen und sie summieren
int i = 0;
RationalNumber count = { 0, 1 };
RationalNumber result = { 0, 1 };
while(ptr[i][1].numerator > 0) {
result = rnAdd(result, rnMultiply(ptr[i][0], ptr[i][1]));
count.numerator += ptr[i][1].numerator;
i++;
}
// Wenn keine Brüche gespeichert
if (count.numerator == 0) {
count.numerator = 1;
}
// Gekürzte RationalNumber zurückgeben
c->average = rnShorten(rnDivide(result, count));
}
//return the quotient of this and a
RationalNumber RationalNumber::operator/(RationalNumber a)
{
return RationalNumber(numerator * a.denominator, denominator * a.numerator);
}
//returns the difference of this and a
RationalNumber RationalNumber::operator-(RationalNumber a)
{
int num = numerator * a.denominator - a.numerator * denominator;
int denom = a.denominator * denominator;
return RationalNumber(num, denom);
}
//definition for overload method operator /
RationalNumber RationalNumber::operator/(RationalNumber rn)
{
return RationalNumber(numerator*rn.denominator, denominator*rn.numerator);
}
RationalNumber RationalNumber:: reciprocal(){
return RationalNumber(Denominator, Numerator);
}
RationalNumber RationalNumber::multiply(const RationalNumber &other){
int numer = Numerator * other.getNumerator();
int denom = Denominator * other.getDenominator();
return RationalNumber (numer, denom);
}
void rncSort(RationalNumberCollection *c, int len) {
// Temporäre Collection erstellen
RationalNumberCollection temp;
rncInit(&temp);
// Zeiger auf Collection
RationalNumber (*ptr)[2] = c->rn;
// Zeiger auf temporäre Collection
RationalNumber (*tempptr)[2] = temp.rn;
// Variablen zum Speichern von Indexpositionen
int tempIndex = 0;
int minIndex = 0;
// Solange sich Brüche in der Collection c befinden
while (minIndex != -1) {
minIndex = -1;
// Suche kleinsten Bruch aus der Collection c
int minCount;
for (int i=0; i<len; i++) {
if (ptr[i][1].numerator == 0) {
continue;
}
if (minIndex == -1 || rnLessThan(ptr[i][0],ptr[minIndex][0])) {
minIndex = i;
minCount = ptr[i][1].numerator;
}
}
// Wenn kleinsten Bruch gefunden
if (minIndex != -1) {
// Übertrage den gefunden kleinsten Bruch und dessen Vorkommen in die Collection temp
tempptr[tempIndex][0] = ptr[minIndex][0];
tempptr[tempIndex][1].numerator = minCount;
// Erhöhe den totalUniqueCount der Collection temp
temp.totalUniqueCount++;
// Entferne den gefunden kleinsten Bruch und dessen Vorkommen aus der Collection c
ptr[minIndex][0].numerator = 0;
ptr[minIndex][0].denominator = 0;
ptr[minIndex][1].numerator = 0;
// Zeige auf den nächsten Index der Collection temp
tempIndex++;
}
}
// Übertrage alle Brüche und ihre Vorkommen der Collection temp in die Collection c
int tempLen = rncTotalUniqueCount(&temp);
for (int j=0; j<tempLen; j++) {
ptr[j][0] = tempptr[j][0];
ptr[j][1].numerator = tempptr[j][1].numerator;
}
}
