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17 package org.hipparchus.complex;
18
19 import java.util.ArrayList;
20 import java.util.List;
21
22 import org.hipparchus.CalculusFieldElement;
23 import org.hipparchus.Field;
24 import org.hipparchus.exception.LocalizedCoreFormats;
25 import org.hipparchus.exception.MathIllegalArgumentException;
26 import org.hipparchus.exception.NullArgumentException;
27 import org.hipparchus.util.FastMath;
28 import org.hipparchus.util.FieldSinCos;
29 import org.hipparchus.util.FieldSinhCosh;
30 import org.hipparchus.util.MathArrays;
31 import org.hipparchus.util.MathUtils;
32 import org.hipparchus.util.Precision;
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59 public class FieldComplex<T extends CalculusFieldElement<T>> implements CalculusFieldElement<FieldComplex<T>> {
60
61
62 private static final double LOG10 = 2.302585092994045684;
63
64
65 private final T imaginary;
66
67
68 private final T real;
69
70
71 private final transient boolean isNaN;
72
73
74 private final transient boolean isInfinite;
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80
81 public FieldComplex(T real) {
82 this(real, real.getField().getZero());
83 }
84
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88
89
90
91 public FieldComplex(T real, T imaginary) {
92 this.real = real;
93 this.imaginary = imaginary;
94
95 isNaN = real.isNaN() || imaginary.isNaN();
96 isInfinite = !isNaN &&
97 (real.isInfinite() || imaginary.isInfinite());
98 }
99
100
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103
104
105 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getI(final Field<T> field) {
106 return new FieldComplex<>(field.getZero(), field.getOne());
107 }
108
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112
113
114 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getMinusI(final Field<T> field) {
115 return new FieldComplex<>(field.getZero(), field.getOne().negate());
116 }
117
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121
122
123 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getNaN(final Field<T> field) {
124 return new FieldComplex<>(field.getZero().add(Double.NaN), field.getZero().add(Double.NaN));
125 }
126
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130
131
132 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getInf(final Field<T> field) {
133 return new FieldComplex<>(field.getZero().add(Double.POSITIVE_INFINITY), field.getZero().add(Double.POSITIVE_INFINITY));
134 }
135
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141 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getOne(final Field<T> field) {
142 return new FieldComplex<>(field.getOne(), field.getZero());
143 }
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148
149
150 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getMinusOne(final Field<T> field) {
151 return new FieldComplex<>(field.getOne().negate(), field.getZero());
152 }
153
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158
159 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getZero(final Field<T> field) {
160 return new FieldComplex<>(field.getZero(), field.getZero());
161 }
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166
167
168 public static <T extends CalculusFieldElement<T>> FieldComplex<T> getPi(final Field<T> field) {
169 return new FieldComplex<>(field.getZero().getPi(), field.getZero());
170 }
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179
180 @Override
181 public FieldComplex<T> abs() {
182
183 return isNaN ? getNaN(getPartsField()) : createComplex(FastMath.hypot(real, imaginary), getPartsField().getZero());
184 }
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202 @Override
203 public FieldComplex<T> add(FieldComplex<T> addend) throws NullArgumentException {
204 MathUtils.checkNotNull(addend);
205 if (isNaN || addend.isNaN) {
206 return getNaN(getPartsField());
207 }
208
209 return createComplex(real.add(addend.getRealPart()),
210 imaginary.add(addend.getImaginaryPart()));
211 }
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219
220
221 public FieldComplex<T> add(T addend) {
222 if (isNaN || addend.isNaN()) {
223 return getNaN(getPartsField());
224 }
225
226 return createComplex(real.add(addend), imaginary);
227 }
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237 @Override
238 public FieldComplex<T> add(double addend) {
239 if (isNaN || Double.isNaN(addend)) {
240 return getNaN(getPartsField());
241 }
242
243 return createComplex(real.add(addend), imaginary);
244 }
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260 public FieldComplex<T> conjugate() {
261 if (isNaN) {
262 return getNaN(getPartsField());
263 }
264
265 return createComplex(real, imaginary.negate());
266 }
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310 @Override
311 public FieldComplex<T> divide(FieldComplex<T> divisor)
312 throws NullArgumentException {
313 MathUtils.checkNotNull(divisor);
314 if (isNaN || divisor.isNaN) {
315 return getNaN(getPartsField());
316 }
317
318 final T c = divisor.getRealPart();
319 final T d = divisor.getImaginaryPart();
320 if (c.isZero() && d.isZero()) {
321 return getNaN(getPartsField());
322 }
323
324 if (divisor.isInfinite() && !isInfinite()) {
325 return getZero(getPartsField());
326 }
327
328 if (FastMath.abs(c).getReal() < FastMath.abs(d).getReal()) {
329 T q = c.divide(d);
330 T invDen = c.multiply(q).add(d).reciprocal();
331 return createComplex(real.multiply(q).add(imaginary).multiply(invDen),
332 imaginary.multiply(q).subtract(real).multiply(invDen));
333 } else {
334 T q = d.divide(c);
335 T invDen = d.multiply(q).add(c).reciprocal();
336 return createComplex(imaginary.multiply(q).add(real).multiply(invDen),
337 imaginary.subtract(real.multiply(q)).multiply(invDen));
338 }
339 }
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349 public FieldComplex<T> divide(T divisor) {
350 if (isNaN || divisor.isNaN()) {
351 return getNaN(getPartsField());
352 }
353 if (divisor.isZero()) {
354 return getNaN(getPartsField());
355 }
356 if (divisor.isInfinite()) {
357 return !isInfinite() ? getZero(getPartsField()) : getNaN(getPartsField());
358 }
359 return createComplex(real.divide(divisor), imaginary.divide(divisor));
360 }
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370 @Override
371 public FieldComplex<T> divide(double divisor) {
372 if (isNaN || Double.isNaN(divisor)) {
373 return getNaN(getPartsField());
374 }
375 if (divisor == 0.0) {
376 return getNaN(getPartsField());
377 }
378 if (Double.isInfinite(divisor)) {
379 return !isInfinite() ? getZero(getPartsField()) : getNaN(getPartsField());
380 }
381 return createComplex(real.divide(divisor), imaginary.divide(divisor));
382 }
383
384
385 @Override
386 public FieldComplex<T> reciprocal() {
387 if (isNaN) {
388 return getNaN(getPartsField());
389 }
390
391 if (real.isZero() && imaginary.isZero()) {
392 return getInf(getPartsField());
393 }
394
395 if (isInfinite) {
396 return getZero(getPartsField());
397 }
398
399 if (FastMath.abs(real).getReal() < FastMath.abs(imaginary).getReal()) {
400 T q = real.divide(imaginary);
401 T scale = real.multiply(q).add(imaginary).reciprocal();
402 return createComplex(scale.multiply(q), scale.negate());
403 } else {
404 T q = imaginary.divide(real);
405 T scale = imaginary.multiply(q).add(real).reciprocal();
406 return createComplex(scale, scale.negate().multiply(q));
407 }
408 }
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434 @Override
435 public boolean equals(Object other) {
436 if (this == other) {
437 return true;
438 }
439 if (other instanceof FieldComplex){
440 @SuppressWarnings("unchecked")
441 FieldComplex<T> c = (FieldComplex<T>) other;
442 if (c.isNaN) {
443 return isNaN;
444 } else {
445 return real.equals(c.real) && imaginary.equals(c.imaginary);
446 }
447 }
448 return false;
449 }
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468 public static <T extends CalculusFieldElement<T>>boolean equals(FieldComplex<T> x, FieldComplex<T> y, int maxUlps) {
469 return Precision.equals(x.real.getReal(), y.real.getReal(), maxUlps) &&
470 Precision.equals(x.imaginary.getReal(), y.imaginary.getReal(), maxUlps);
471 }
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482 public static <T extends CalculusFieldElement<T>>boolean equals(FieldComplex<T> x, FieldComplex<T> y) {
483 return equals(x, y, 1);
484 }
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501 public static <T extends CalculusFieldElement<T>>boolean equals(FieldComplex<T> x, FieldComplex<T> y,
502 double eps) {
503 return Precision.equals(x.real.getReal(), y.real.getReal(), eps) &&
504 Precision.equals(x.imaginary.getReal(), y.imaginary.getReal(), eps);
505 }
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522 public static <T extends CalculusFieldElement<T>>boolean equalsWithRelativeTolerance(FieldComplex<T> x,
523 FieldComplex<T> y,
524 double eps) {
525 return Precision.equalsWithRelativeTolerance(x.real.getReal(), y.real.getReal(), eps) &&
526 Precision.equalsWithRelativeTolerance(x.imaginary.getReal(), y.imaginary.getReal(), eps);
527 }
528
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531
532
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535
536 @Override
537 public int hashCode() {
538 if (isNaN) {
539 return 7;
540 }
541 return 37 * (17 * imaginary.hashCode() + real.hashCode());
542 }
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549
550 @Override
551 public boolean isZero() {
552 return real.isZero() && imaginary.isZero();
553 }
554
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560 public T getImaginary() {
561 return imaginary;
562 }
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568
569 public T getImaginaryPart() {
570 return imaginary;
571 }
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578 @Override
579 public double getReal() {
580 return real.getReal();
581 }
582
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588 public T getRealPart() {
589 return real;
590 }
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599 @Override
600 public boolean isNaN() {
601 return isNaN;
602 }
603
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607 public boolean isReal() {
608 return imaginary.isZero();
609 }
610
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614 public boolean isMathematicalInteger() {
615 return isReal() && Precision.isMathematicalInteger(real.getReal());
616 }
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627 @Override
628 public boolean isInfinite() {
629 return isInfinite;
630 }
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654 @Override
655 public FieldComplex<T> multiply(FieldComplex<T> factor)
656 throws NullArgumentException {
657 MathUtils.checkNotNull(factor);
658 if (isNaN || factor.isNaN) {
659 return getNaN(getPartsField());
660 }
661 if (real.isInfinite() ||
662 imaginary.isInfinite() ||
663 factor.real.isInfinite() ||
664 factor.imaginary.isInfinite()) {
665
666 return getInf(getPartsField());
667 }
668 return createComplex(real.linearCombination(real, factor.real, imaginary.negate(), factor.imaginary),
669 real.linearCombination(real, factor.imaginary, imaginary, factor.real));
670 }
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680 @Override
681 public FieldComplex<T> multiply(final int factor) {
682 if (isNaN) {
683 return getNaN(getPartsField());
684 }
685 if (real.isInfinite() || imaginary.isInfinite()) {
686 return getInf(getPartsField());
687 }
688 return createComplex(real.multiply(factor), imaginary.multiply(factor));
689 }
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699 @Override
700 public FieldComplex<T> multiply(double factor) {
701 if (isNaN || Double.isNaN(factor)) {
702 return getNaN(getPartsField());
703 }
704 if (real.isInfinite() ||
705 imaginary.isInfinite() ||
706 Double.isInfinite(factor)) {
707
708 return getInf(getPartsField());
709 }
710 return createComplex(real.multiply(factor), imaginary.multiply(factor));
711 }
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719
720
721 public FieldComplex<T> multiply(T factor) {
722 if (isNaN || factor.isNaN()) {
723 return getNaN(getPartsField());
724 }
725 if (real.isInfinite() ||
726 imaginary.isInfinite() ||
727 factor.isInfinite()) {
728
729 return getInf(getPartsField());
730 }
731 return createComplex(real.multiply(factor), imaginary.multiply(factor));
732 }
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737
738 public FieldComplex<T> multiplyPlusI() {
739 return createComplex(imaginary.negate(), real);
740 }
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746 public FieldComplex<T> multiplyMinusI() {
747 return createComplex(imaginary, real.negate());
748 }
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757 @Override
758 public FieldComplex<T> negate() {
759 if (isNaN) {
760 return getNaN(getPartsField());
761 }
762
763 return createComplex(real.negate(), imaginary.negate());
764 }
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782 @Override
783 public FieldComplex<T> subtract(FieldComplex<T> subtrahend)
784 throws NullArgumentException {
785 MathUtils.checkNotNull(subtrahend);
786 if (isNaN || subtrahend.isNaN) {
787 return getNaN(getPartsField());
788 }
789
790 return createComplex(real.subtract(subtrahend.getRealPart()),
791 imaginary.subtract(subtrahend.getImaginaryPart()));
792 }
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802 @Override
803 public FieldComplex<T> subtract(double subtrahend) {
804 if (isNaN || Double.isNaN(subtrahend)) {
805 return getNaN(getPartsField());
806 }
807 return createComplex(real.subtract(subtrahend), imaginary);
808 }
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817
818 public FieldComplex<T> subtract(T subtrahend) {
819 if (isNaN || subtrahend.isNaN()) {
820 return getNaN(getPartsField());
821 }
822 return createComplex(real.subtract(subtrahend), imaginary);
823 }
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838 @Override
839 public FieldComplex<T> acos() {
840 if (isNaN) {
841 return getNaN(getPartsField());
842 }
843
844 return this.add(this.sqrt1z().multiplyPlusI()).log().multiplyMinusI();
845 }
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860 @Override
861 public FieldComplex<T> asin() {
862 if (isNaN) {
863 return getNaN(getPartsField());
864 }
865
866 return sqrt1z().add(this.multiplyPlusI()).log().multiplyMinusI();
867 }
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882 @Override
883 public FieldComplex<T> atan() {
884 if (isNaN) {
885 return getNaN(getPartsField());
886 }
887
888 final T one = getPartsField().getOne();
889 if (real.isZero()) {
890
891
892 if (imaginary.multiply(imaginary).subtract(one).isZero()) {
893 return getNaN(getPartsField());
894 }
895
896
897 final T zero = getPartsField().getZero();
898 final FieldComplex<T> tmp = createComplex(one.add(imaginary).divide(one.subtract(imaginary)), zero).
899 log().multiplyPlusI().multiply(0.5);
900 return createComplex(FastMath.copySign(tmp.real, real), tmp.imaginary);
901
902 } else {
903
904 final FieldComplex<T> n = createComplex(one.add(imaginary), real.negate());
905 final FieldComplex<T> d = createComplex(one.subtract(imaginary), real);
906 return n.divide(d).log().multiplyPlusI().multiply(0.5);
907 }
908
909 }
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939 @Override
940 public FieldComplex<T> cos() {
941 if (isNaN) {
942 return getNaN(getPartsField());
943 }
944
945 final FieldSinCos<T> scr = FastMath.sinCos(real);
946 final FieldSinhCosh<T> schi = FastMath.sinhCosh(imaginary);
947 return createComplex(scr.cos().multiply(schi.cosh()), scr.sin().negate().multiply(schi.sinh()));
948 }
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980 @Override
981 public FieldComplex<T> cosh() {
982 if (isNaN) {
983 return getNaN(getPartsField());
984 }
985
986 final FieldSinhCosh<T> schr = FastMath.sinhCosh(real);
987 final FieldSinCos<T> sci = FastMath.sinCos(imaginary);
988 return createComplex(schr.cosh().multiply(sci.cos()), schr.sinh().multiply(sci.sin()));
989 }
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1022 @Override
1023 public FieldComplex<T> exp() {
1024 if (isNaN) {
1025 return getNaN(getPartsField());
1026 }
1027
1028 final T expReal = FastMath.exp(real);
1029 final FieldSinCos<T> sc = FastMath.sinCos(imaginary);
1030 return createComplex(expReal.multiply(sc.cos()), expReal.multiply(sc.sin()));
1031 }
1032
1033
1034 @Override
1035 public FieldComplex<T> expm1() {
1036 if (isNaN) {
1037 return getNaN(getPartsField());
1038 }
1039
1040 final T expm1Real = FastMath.expm1(real);
1041 final FieldSinCos<T> sc = FastMath.sinCos(imaginary);
1042 return createComplex(expm1Real.multiply(sc.cos()), expm1Real.multiply(sc.sin()));
1043 }
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1079 @Override
1080 public FieldComplex<T> log() {
1081 if (isNaN) {
1082 return getNaN(getPartsField());
1083 }
1084
1085 return createComplex(FastMath.log(FastMath.hypot(real, imaginary)),
1086 FastMath.atan2(imaginary, real));
1087 }
1088
1089
1090 @Override
1091 public FieldComplex<T> log1p() {
1092 return add(1.0).log();
1093 }
1094
1095
1096 @Override
1097 public FieldComplex<T> log10() {
1098 return log().divide(LOG10);
1099 }
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1116 @Override
1117 public FieldComplex<T> pow(FieldComplex<T> x)
1118 throws NullArgumentException {
1119
1120 MathUtils.checkNotNull(x);
1121
1122 if (x.imaginary.isZero()) {
1123 final int nx = (int) FastMath.rint(x.real.getReal());
1124 if (x.real.getReal() == nx) {
1125
1126 return pow(nx);
1127 } else if (this.imaginary.isZero()) {
1128
1129 final T realPow = FastMath.pow(this.real, x.real);
1130 if (realPow.isFinite()) {
1131 return createComplex(realPow, getPartsField().getZero());
1132 }
1133 }
1134 }
1135
1136
1137 return this.log().multiply(x).exp();
1138
1139 }
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1155
1156 public FieldComplex<T> pow(T x) {
1157
1158 final int nx = (int) FastMath.rint(x.getReal());
1159 if (x.getReal() == nx) {
1160
1161 return pow(nx);
1162 } else if (this.imaginary.isZero()) {
1163
1164 final T realPow = FastMath.pow(this.real, x);
1165 if (realPow.isFinite()) {
1166 return createComplex(realPow, getPartsField().getZero());
1167 }
1168 }
1169
1170
1171 return this.log().multiply(x).exp();
1172
1173 }
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1189 @Override
1190 public FieldComplex<T> pow(double x) {
1191
1192 final int nx = (int) FastMath.rint(x);
1193 if (x == nx) {
1194
1195 return pow(nx);
1196 } else if (this.imaginary.isZero()) {
1197
1198 final T realPow = FastMath.pow(this.real, x);
1199 if (realPow.isFinite()) {
1200 return createComplex(realPow, getPartsField().getZero());
1201 }
1202 }
1203
1204
1205 return this.log().multiply(x).exp();
1206
1207 }
1208
1209
1210 @Override
1211 public FieldComplex<T> pow(final int n) {
1212
1213 FieldComplex<T> result = getField().getOne();
1214 final boolean invert;
1215 int p = n;
1216 if (p < 0) {
1217 invert = true;
1218 p = -p;
1219 } else {
1220 invert = false;
1221 }
1222
1223
1224 FieldComplex<T> square = this;
1225 while (p > 0) {
1226 if ((p & 0x1) > 0) {
1227 result = result.multiply(square);
1228 }
1229 square = square.multiply(square);
1230 p = p >> 1;
1231 }
1232
1233 return invert ? result.reciprocal() : result;
1234
1235 }
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268 @Override
1269 public FieldComplex<T> sin() {
1270 if (isNaN) {
1271 return getNaN(getPartsField());
1272 }
1273
1274 final FieldSinCos<T> scr = FastMath.sinCos(real);
1275 final FieldSinhCosh<T> schi = FastMath.sinhCosh(imaginary);
1276 return createComplex(scr.sin().multiply(schi.cosh()), scr.cos().multiply(schi.sinh()));
1277
1278 }
1279
1280
1281
1282 @Override
1283 public FieldSinCos<FieldComplex<T>> sinCos() {
1284 if (isNaN) {
1285 return new FieldSinCos<>(getNaN(getPartsField()), getNaN(getPartsField()));
1286 }
1287
1288 final FieldSinCos<T> scr = FastMath.sinCos(real);
1289 final FieldSinhCosh<T> schi = FastMath.sinhCosh(imaginary);
1290 return new FieldSinCos<>(createComplex(scr.sin().multiply(schi.cosh()), scr.cos().multiply(schi.sinh())),
1291 createComplex(scr.cos().multiply(schi.cosh()), scr.sin().negate().multiply(schi.sinh())));
1292 }
1293
1294
1295 @Override
1296 public FieldComplex<T> atan2(FieldComplex<T> x) {
1297
1298
1299 final FieldComplex<T> r = x.multiply(x).add(multiply(this)).sqrt();
1300
1301 if (x.real.getReal() >= 0) {
1302
1303 return divide(r.add(x)).atan().multiply(2);
1304 } else {
1305
1306 return divide(r.subtract(x)).atan().multiply(-2).add(x.real.getPi());
1307 }
1308 }
1309
1310
1311
1312
1313
1314
1315 @Override
1316 public FieldComplex<T> acosh() {
1317 final FieldComplex<T> sqrtPlus = add(1).sqrt();
1318 final FieldComplex<T> sqrtMinus = subtract(1).sqrt();
1319 return add(sqrtPlus.multiply(sqrtMinus)).log();
1320 }
1321
1322
1323
1324
1325
1326
1327 @Override
1328 public FieldComplex<T> asinh() {
1329 return add(multiply(this).add(1.0).sqrt()).log();
1330 }
1331
1332
1333
1334
1335
1336
1337 @Override
1338 public FieldComplex<T> atanh() {
1339 final FieldComplex<T> logPlus = add(1).log();
1340 final FieldComplex<T> logMinus = createComplex(getPartsField().getOne().subtract(real), imaginary.negate()).log();
1341 return logPlus.subtract(logMinus).multiply(0.5);
1342 }
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374 @Override
1375 public FieldComplex<T> sinh() {
1376 if (isNaN) {
1377 return getNaN(getPartsField());
1378 }
1379
1380 final FieldSinhCosh<T> schr = FastMath.sinhCosh(real);
1381 final FieldSinCos<T> sci = FastMath.sinCos(imaginary);
1382 return createComplex(schr.sinh().multiply(sci.cos()), schr.cosh().multiply(sci.sin()));
1383 }
1384
1385
1386
1387 @Override
1388 public FieldSinhCosh<FieldComplex<T>> sinhCosh() {
1389 if (isNaN) {
1390 return new FieldSinhCosh<>(getNaN(getPartsField()), getNaN(getPartsField()));
1391 }
1392
1393 final FieldSinhCosh<T> schr = FastMath.sinhCosh(real);
1394 final FieldSinCos<T> sci = FastMath.sinCos(imaginary);
1395 return new FieldSinhCosh<>(createComplex(schr.sinh().multiply(sci.cos()), schr.cosh().multiply(sci.sin())),
1396 createComplex(schr.cosh().multiply(sci.cos()), schr.sinh().multiply(sci.sin())));
1397 }
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435 @Override
1436 public FieldComplex<T> sqrt() {
1437 if (isNaN) {
1438 return getNaN(getPartsField());
1439 }
1440
1441 if (isZero()) {
1442 return getZero(getPartsField());
1443 }
1444
1445 T t = FastMath.sqrt((FastMath.abs(real).add(FastMath.hypot(real, imaginary))).multiply(0.5));
1446 if (real.getReal() >= 0.0) {
1447 return createComplex(t, imaginary.divide(t.multiply(2)));
1448 } else {
1449 return createComplex(FastMath.abs(imaginary).divide(t.multiply(2)),
1450 FastMath.copySign(t, imaginary));
1451 }
1452 }
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470 public FieldComplex<T> sqrt1z() {
1471 final FieldComplex<T> t2 = this.multiply(this);
1472 return createComplex(getPartsField().getOne().subtract(t2.real), t2.imaginary.negate()).sqrt();
1473 }
1474
1475
1476
1477
1478
1479
1480 @Override
1481 public FieldComplex<T> cbrt() {
1482 final T magnitude = FastMath.cbrt(abs().getRealPart());
1483 final FieldSinCos<T> sc = FastMath.sinCos(getArgument().divide(3));
1484 return createComplex(magnitude.multiply(sc.cos()), magnitude.multiply(sc.sin()));
1485 }
1486
1487
1488
1489
1490
1491
1492 @Override
1493 public FieldComplex<T> rootN(int n) {
1494 final T magnitude = FastMath.pow(abs().getRealPart(), 1.0 / n);
1495 final FieldSinCos<T> sc = FastMath.sinCos(getArgument().divide(n));
1496 return createComplex(magnitude.multiply(sc.cos()), magnitude.multiply(sc.sin()));
1497 }
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530 @Override
1531 public FieldComplex<T> tan() {
1532 if (isNaN || real.isInfinite()) {
1533 return getNaN(getPartsField());
1534 }
1535 if (imaginary.getReal() > 20.0) {
1536 return getI(getPartsField());
1537 }
1538 if (imaginary.getReal() < -20.0) {
1539 return getMinusI(getPartsField());
1540 }
1541
1542 final FieldSinCos<T> sc2r = FastMath.sinCos(real.multiply(2));
1543 T imaginary2 = imaginary.multiply(2);
1544 T d = sc2r.cos().add(FastMath.cosh(imaginary2));
1545
1546 return createComplex(sc2r.sin().divide(d), FastMath.sinh(imaginary2).divide(d));
1547
1548 }
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581 @Override
1582 public FieldComplex<T> tanh() {
1583 if (isNaN || imaginary.isInfinite()) {
1584 return getNaN(getPartsField());
1585 }
1586 if (real.getReal() > 20.0) {
1587 return getOne(getPartsField());
1588 }
1589 if (real.getReal() < -20.0) {
1590 return getMinusOne(getPartsField());
1591 }
1592 T real2 = real.multiply(2);
1593 final FieldSinCos<T> sc2i = FastMath.sinCos(imaginary.multiply(2));
1594 T d = FastMath.cosh(real2).add(sc2i.cos());
1595
1596 return createComplex(FastMath.sinh(real2).divide(d), sc2i.sin().divide(d));
1597 }
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618 public T getArgument() {
1619 return FastMath.atan2(getImaginaryPart(), getRealPart());
1620 }
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643 public List<FieldComplex<T>> nthRoot(int n) throws MathIllegalArgumentException {
1644
1645 if (n <= 0) {
1646 throw new MathIllegalArgumentException(LocalizedCoreFormats.CANNOT_COMPUTE_NTH_ROOT_FOR_NEGATIVE_N,
1647 n);
1648 }
1649
1650 final List<FieldComplex<T>> result = new ArrayList<>();
1651
1652 if (isNaN) {
1653 result.add(getNaN(getPartsField()));
1654 return result;
1655 }
1656 if (isInfinite()) {
1657 result.add(getInf(getPartsField()));
1658 return result;
1659 }
1660
1661
1662 final T nthRootOfAbs = FastMath.pow(FastMath.hypot(real, imaginary), 1.0 / n);
1663
1664
1665 final T nthPhi = getArgument().divide(n);
1666 final double slice = 2 * FastMath.PI / n;
1667 T innerPart = nthPhi;
1668 for (int k = 0; k < n ; k++) {
1669
1670 final FieldSinCos<T> scInner = FastMath.sinCos(innerPart);
1671 final T realPart = nthRootOfAbs.multiply(scInner.cos());
1672 final T imaginaryPart = nthRootOfAbs.multiply(scInner.sin());
1673 result.add(createComplex(realPart, imaginaryPart));
1674 innerPart = innerPart.add(slice);
1675 }
1676
1677 return result;
1678 }
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689 protected FieldComplex<T> createComplex(final T realPart, final T imaginaryPart) {
1690 return new FieldComplex<>(realPart, imaginaryPart);
1691 }
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701 public static <T extends CalculusFieldElement<T>> FieldComplex<T>
1702 valueOf(T realPart, T imaginaryPart) {
1703 if (realPart.isNaN() || imaginaryPart.isNaN()) {
1704 return getNaN(realPart.getField());
1705 }
1706 return new FieldComplex<>(realPart, imaginaryPart);
1707 }
1708
1709
1710
1711
1712
1713
1714
1715
1716 public static <T extends CalculusFieldElement<T>> FieldComplex<T>
1717 valueOf(T realPart) {
1718 if (realPart.isNaN()) {
1719 return getNaN(realPart.getField());
1720 }
1721 return new FieldComplex<>(realPart);
1722 }
1723
1724
1725 @Override
1726 public FieldComplex<T> newInstance(double realPart) {
1727 return valueOf(getPartsField().getZero().newInstance(realPart));
1728 }
1729
1730
1731 @Override
1732 public FieldComplexField<T> getField() {
1733 return FieldComplexField.getField(getPartsField());
1734 }
1735
1736
1737
1738
1739 public Field<T> getPartsField() {
1740 return real.getField();
1741 }
1742
1743
1744 @Override
1745 public String toString() {
1746 return "(" + real + ", " + imaginary + ")";
1747 }
1748
1749
1750 @Override
1751 public FieldComplex<T> scalb(int n) {
1752 return createComplex(FastMath.scalb(real, n), FastMath.scalb(imaginary, n));
1753 }
1754
1755
1756 @Override
1757 public FieldComplex<T> ulp() {
1758 return createComplex(FastMath.ulp(real), FastMath.ulp(imaginary));
1759 }
1760
1761
1762 @Override
1763 public FieldComplex<T> hypot(FieldComplex<T> y) {
1764 if (isInfinite() || y.isInfinite()) {
1765 return getInf(getPartsField());
1766 } else if (isNaN() || y.isNaN()) {
1767 return getNaN(getPartsField());
1768 } else {
1769 return multiply(this).add(y.multiply(y)).sqrt();
1770 }
1771 }
1772
1773
1774 @Override
1775 public FieldComplex<T> linearCombination(final FieldComplex<T>[] a, final FieldComplex<T>[] b)
1776 throws MathIllegalArgumentException {
1777 final int n = 2 * a.length;
1778 final T[] realA = MathArrays.buildArray(getPartsField(), n);
1779 final T[] realB = MathArrays.buildArray(getPartsField(), n);
1780 final T[] imaginaryA = MathArrays.buildArray(getPartsField(), n);
1781 final T[] imaginaryB = MathArrays.buildArray(getPartsField(), n);
1782 for (int i = 0; i < a.length; ++i) {
1783 final FieldComplex<T> ai = a[i];
1784 final FieldComplex<T> bi = b[i];
1785 realA[2 * i ] = ai.real;
1786 realA[2 * i + 1] = ai.imaginary.negate();
1787 realB[2 * i ] = bi.real;
1788 realB[2 * i + 1] = bi.imaginary;
1789 imaginaryA[2 * i ] = ai.real;
1790 imaginaryA[2 * i + 1] = ai.imaginary;
1791 imaginaryB[2 * i ] = bi.imaginary;
1792 imaginaryB[2 * i + 1] = bi.real;
1793 }
1794 return createComplex(real.linearCombination(realA, realB),
1795 real.linearCombination(imaginaryA, imaginaryB));
1796 }
1797
1798
1799 @Override
1800 public FieldComplex<T> linearCombination(final double[] a, final FieldComplex<T>[] b)
1801 throws MathIllegalArgumentException {
1802 final int n = a.length;
1803 final T[] realB = MathArrays.buildArray(getPartsField(), n);
1804 final T[] imaginaryB = MathArrays.buildArray(getPartsField(), n);
1805 for (int i = 0; i < a.length; ++i) {
1806 final FieldComplex<T> bi = b[i];
1807 realB[i] = bi.real;
1808 imaginaryB[i] = bi.imaginary;
1809 }
1810 return createComplex(real.linearCombination(a, realB),
1811 real.linearCombination(a, imaginaryB));
1812 }
1813
1814
1815 @Override
1816 public FieldComplex<T> linearCombination(final FieldComplex<T> a1, final FieldComplex<T> b1, final FieldComplex<T> a2, final FieldComplex<T> b2) {
1817 return createComplex(real.linearCombination(a1.real, b1.real,
1818 a1.imaginary.negate(), b1.imaginary,
1819 a2.real, b2.real,
1820 a2.imaginary.negate(), b2.imaginary),
1821 real.linearCombination(a1.real, b1.imaginary,
1822 a1.imaginary, b1.real,
1823 a2.real, b2.imaginary,
1824 a2.imaginary, b2.real));
1825 }
1826
1827
1828 @Override
1829 public FieldComplex<T> linearCombination(final double a1, final FieldComplex<T> b1, final double a2, final FieldComplex<T> b2) {
1830 return createComplex(real.linearCombination(a1, b1.real,
1831 a2, b2.real),
1832 real.linearCombination(a1, b1.imaginary,
1833 a2, b2.imaginary));
1834 }
1835
1836
1837 @Override
1838 public FieldComplex<T> linearCombination(final FieldComplex<T> a1, final FieldComplex<T> b1,
1839 final FieldComplex<T> a2, final FieldComplex<T> b2,
1840 final FieldComplex<T> a3, final FieldComplex<T> b3) {
1841 FieldComplex<T>[] a = MathArrays.buildArray(getField(), 3);
1842 a[0] = a1;
1843 a[1] = a2;
1844 a[2] = a3;
1845 FieldComplex<T>[] b = MathArrays.buildArray(getField(), 3);
1846 b[0] = b1;
1847 b[1] = b2;
1848 b[2] = b3;
1849 return linearCombination(a, b);
1850 }
1851
1852
1853 @Override
1854 public FieldComplex<T> linearCombination(final double a1, final FieldComplex<T> b1,
1855 final double a2, final FieldComplex<T> b2,
1856 final double a3, final FieldComplex<T> b3) {
1857 FieldComplex<T>[] b = MathArrays.buildArray(getField(), 3);
1858 b[0] = b1;
1859 b[1] = b2;
1860 b[2] = b3;
1861 return linearCombination(new double[] { a1, a2, a3 }, b);
1862 }
1863
1864
1865 @Override
1866 public FieldComplex<T> linearCombination(final FieldComplex<T> a1, final FieldComplex<T> b1,
1867 final FieldComplex<T> a2, final FieldComplex<T> b2,
1868 final FieldComplex<T> a3, final FieldComplex<T> b3,
1869 final FieldComplex<T> a4, final FieldComplex<T> b4) {
1870 FieldComplex<T>[] a = MathArrays.buildArray(getField(), 4);
1871 a[0] = a1;
1872 a[1] = a2;
1873 a[2] = a3;
1874 a[3] = a4;
1875 FieldComplex<T>[] b = MathArrays.buildArray(getField(), 4);
1876 b[0] = b1;
1877 b[1] = b2;
1878 b[2] = b3;
1879 b[3] = b4;
1880 return linearCombination(a, b);
1881 }
1882
1883
1884 @Override
1885 public FieldComplex<T> linearCombination(final double a1, final FieldComplex<T> b1,
1886 final double a2, final FieldComplex<T> b2,
1887 final double a3, final FieldComplex<T> b3,
1888 final double a4, final FieldComplex<T> b4) {
1889 FieldComplex<T>[] b = MathArrays.buildArray(getField(), 4);
1890 b[0] = b1;
1891 b[1] = b2;
1892 b[2] = b3;
1893 b[3] = b4;
1894 return linearCombination(new double[] { a1, a2, a3, a4 }, b);
1895 }
1896
1897
1898 @Override
1899 public FieldComplex<T> ceil() {
1900 return createComplex(FastMath.ceil(getRealPart()), FastMath.ceil(getImaginaryPart()));
1901 }
1902
1903
1904 @Override
1905 public FieldComplex<T> floor() {
1906 return createComplex(FastMath.floor(getRealPart()), FastMath.floor(getImaginaryPart()));
1907 }
1908
1909
1910 @Override
1911 public FieldComplex<T> rint() {
1912 return createComplex(FastMath.rint(getRealPart()), FastMath.rint(getImaginaryPart()));
1913 }
1914
1915
1916
1917
1918
1919
1920
1921 @Override
1922 public FieldComplex<T> remainder(final double a) {
1923 return createComplex(FastMath.IEEEremainder(getRealPart(), a), FastMath.IEEEremainder(getImaginaryPart(), a));
1924 }
1925
1926
1927
1928
1929
1930
1931
1932 @Override
1933 public FieldComplex<T> remainder(final FieldComplex<T> a) {
1934 final FieldComplex<T> complexQuotient = divide(a);
1935 final T qRInt = FastMath.rint(complexQuotient.real);
1936 final T qIInt = FastMath.rint(complexQuotient.imaginary);
1937 return createComplex(real.subtract(qRInt.multiply(a.real)).add(qIInt.multiply(a.imaginary)),
1938 imaginary.subtract(qRInt.multiply(a.imaginary)).subtract(qIInt.multiply(a.real)));
1939 }
1940
1941
1942 @Override
1943 public FieldComplex<T> sign() {
1944 if (isNaN() || isZero()) {
1945 return this;
1946 } else {
1947 return this.divide(FastMath.hypot(real, imaginary));
1948 }
1949 }
1950
1951
1952
1953
1954
1955
1956 @Override
1957 public FieldComplex<T> copySign(final FieldComplex<T> z) {
1958 return createComplex(FastMath.copySign(getRealPart(), z.getRealPart()),
1959 FastMath.copySign(getImaginaryPart(), z.getImaginaryPart()));
1960 }
1961
1962
1963 @Override
1964 public FieldComplex<T> copySign(double r) {
1965 return createComplex(FastMath.copySign(getRealPart(), r), FastMath.copySign(getImaginaryPart(), r));
1966 }
1967
1968
1969 @Override
1970 public FieldComplex<T> toDegrees() {
1971 return createComplex(FastMath.toDegrees(getRealPart()), FastMath.toDegrees(getImaginaryPart()));
1972 }
1973
1974
1975 @Override
1976 public FieldComplex<T> toRadians() {
1977 return createComplex(FastMath.toRadians(getRealPart()), FastMath.toRadians(getImaginaryPart()));
1978 }
1979
1980
1981 @Override
1982 public FieldComplex<T> getPi() {
1983 return getPi(getPartsField());
1984 }
1985
1986 }