Tue May 20 21:19:13 2025 c8lib_test(): python version: 3.10.12 numpy version: 1.26.4 Test c8lib(). c8_aBS_test c8_aBS computes the absolute value of a C8. C1=c8_uniform_01 R2=c8_aBS(C1) R3=ABS(C1) --------------------- --------------------- --------------------- ( 0.696485, -0.027303) 0.697020 0.697020 ( -0.488513, 0.606421) 0.778712 0.778712 ( -0.478854, 0.754308) 0.893466 0.893466 ( 0.260932, 0.570531) 0.627369 0.627369 ( -0.931787, 0.051723) 0.933221 0.933221 ( -0.659056, 0.661486) 0.933766 0.933766 ( -0.712816, -0.526603) 0.886238 0.886238 ( 0.666054, -0.026244) 0.666571 0.666571 ( -0.338582, -0.593476) 0.683265 0.683265 ( 0.648701, 0.347538) 0.735932 0.735932 c8_acos_test c8_acos computes the inverse cosine of a C8. C1=c8_uniform_01 C2=c8_acos(C1) C3=c8_cos(C2) --------------------- --------------------- --------------------- ( 0.120642, -0.057960) ( 1.450066, 0.058352) ( 0.120642, -0.057960) ( -0.100564, 0.805340) ( 1.649104, -0.738759) ( -0.100564, 0.805340) ( -0.247529, -0.728370) ( 1.770798, 0.687685) ( -0.247529, -0.728370) ( 0.829043, -0.558086) ( 0.844234, 0.690458) ( 0.829043, -0.558086) ( -0.523104, 0.431832) ( 2.059962, -0.471534) ( -0.523104, 0.431832) ( 0.666392, 0.548707) ( 0.981085, -0.619771) ( 0.666392, 0.548707) ( -0.783698, -0.594120) ( 2.244501, 0.701300) ( -0.783698, -0.594120) ( 0.669201, -0.666200) ( 1.016067, 0.719909) ( 0.669201, -0.666200) ( -0.045497, -0.592941) ( 1.609933, 0.563153) ( -0.045497, -0.592941) ( 0.316968, 0.585818) ( 1.296602, -0.576144) ( 0.316968, 0.585818) c8_acosh_test c8_acosh computes the inverse hyperbolic cosine of a C8. C1=c8_uniform_01 C2=c8_acosh(C1) C3=c8_cosh(C2) --------------------- --------------------- --------------------- ( -0.630869, -0.246179) ( -0.303848, 2.217835) ( -0.630869, -0.246179) ( -0.463119, -0.090181) ( -0.101434, 2.049633) ( -0.463119, -0.090181) ( -0.009811, 0.037557) ( 0.037550, 1.580600) ( -0.009811, 0.037557) ( -0.859839, 0.462085) ( 0.621802, 2.369933) ( -0.859839, 0.462085) ( 0.204470, 0.350160) ( 0.349670, 1.377009) ( 0.204470, 0.350160) ( 0.444210, -0.387326) ( -0.412622, 1.149544) ( 0.444210, -0.387326) ( -0.006396, -0.982481) ( -0.868939, 1.575359) ( -0.006396, -0.982481) ( 0.616676, 0.431275) ( 0.495144, 0.990701) ( 0.616676, 0.431275) ( 0.119480, 0.307080) ( 0.304379, 1.456396) ( 0.119480, 0.307080) ( 0.203061, 0.623919) ( 0.597175, 1.398392) ( 0.203061, 0.623919) c8_add_test c8_add adds two C8s. C1=c8_uniform_01 C2=c8_uniform_01 C3=c8_add(C1,C2) --------------------- --------------------- --------------------- ( 0.067773, 0.271867) ( 0.687888, 0.218203) ( 0.755661, 0.490069) ( 0.039133, 0.687522) ( 0.463408, 0.427726) ( 0.502541, 1.115248) ( -0.302773, 0.370024) ( -0.010405, -0.592382) ( -0.313178, -0.222358) ( 0.255677, -0.577719) ( -0.031563, -0.912069) ( 0.224114, -1.489788) ( -0.845886, -0.191786) ( 0.886019, 0.086504) ( 0.040133, -0.105282) ( -0.460349, 0.467964) ( 0.338259, -0.361604) ( -0.122090, 0.106360) ( -0.490652, -0.517779) ( -0.205533, 0.081397) ( -0.696185, -0.436382) ( -0.907557, 0.267331) ( 0.590895, 0.674737) ( -0.316661, 0.942068) ( -0.641589, -0.025153) ( -0.489883, -0.438619) ( -1.131473, -0.463772) ( -0.698079, -0.456599) ( -0.321876, 0.840847) ( -1.019955, 0.384247) c8_arg_test c8_arg computes the argument of a C8. C1=c8_uniform_01 R2=c8_arg(C1) R3=NP.ANGLE(C1) --------------------- --------------------- --------------------- ( -0.540089, -0.312839) -2.616581 -2.616581 ( -0.028102, 0.875762) 1.602873 1.602873 ( -0.725241, -0.098831) -3.006154 -3.006154 ( 0.562018, -0.539080) -0.764570 -0.764570 ( -0.126158, 0.983164) 1.698417 1.698417 ( -0.507698, 0.477604) 2.386728 2.386728 ( -0.166972, -0.954983) -1.743890 -1.743890 ( 0.442398, -0.031409) -0.070879 -0.070879 ( -0.583862, -0.230260) -2.765946 -2.765946 ( 0.789528, -0.234819) -0.289086 -0.289086 c8_asin_test c8_asin computes the inverse sine of a C8. C1=c8_uniform_01 C2=c8_asin(C1) C3=c8_sin(C2) --------------------- --------------------- --------------------- ( 0.863781, -0.309975) ( 0.887346, -0.473037) ( 0.863781, -0.309975) ( 0.424879, -0.538096) ( 0.376588, -0.550426) ( 0.424879, -0.538096) ( 0.451931, -0.034137) ( 0.468559, -0.038252) ( 0.451931, -0.034137) ( -0.074860, 0.859734) ( -0.056757, 0.779688) ( -0.074860, 0.859734) ( -0.527891, -0.040150) ( -0.555423, -0.047236) ( -0.527891, -0.040150) ( -0.600290, -0.176115) ( -0.626831, -0.215777) ( -0.600290, -0.176115) ( -0.150869, -0.899150) ( -0.112105, -0.812453) ( -0.150869, -0.899150) ( 0.317377, 0.654195) ( 0.265809, 0.634556) ( 0.317377, 0.654195) ( -0.614537, 0.472510) ( -0.565968, 0.534049) ( -0.614537, 0.472510) ( -0.497024, 0.070958) ( -0.518265, 0.081594) ( -0.497024, 0.070958) c8_asinh_test c8_asinh computes the inverse sine of a C8. C1=c8_uniform_01 C2=c8_asinh(C1) C3=sinh(C2) --------------------- --------------------- --------------------- ( 0.223096, 0.118319) ( 0.222751, 0.115701) ( 0.223096, 0.118319) ( 0.477452, -0.665631) ( 0.554648, -0.612494) ( 0.477452, -0.665631) ( -0.085638, -0.768413) ( -0.131811, -0.866066) ( -0.085638, -0.768413) ( 0.527232, -0.236667) ( 0.515872, -0.209863) ( 0.527232, -0.236667) ( 0.063799, -0.803394) ( 0.105878, -0.925484) ( 0.063799, -0.803394) ( 0.298482, 0.362606) ( 0.312942, 0.352822) ( 0.298482, 0.362606) ( -0.128769, -0.936727) ( -0.289636, -1.116943) ( -0.128769, -0.936727) ( -0.141348, 0.036191) ( -0.140972, 0.035842) ( -0.141348, 0.036191) ( -0.906789, -0.125687) ( -0.816821, -0.093059) ( -0.906789, -0.125687) ( -0.032866, 0.408202) ( -0.035989, 0.420194) ( -0.032866, 0.408202) c8_atan_test c8_atan computes the inverse tangent of a C8. C1=c8_uniform_01 C2=c8_atan(C1) C3=c8_tan(C2) --------------------- --------------------- --------------------- ( 0.238195, 0.176035) ( 0.240625, 0.167874) ( 0.238195, 0.176035) ( 0.671478, -0.268281) ( 0.614707, -0.184056) ( 0.671478, -0.268281) ( -0.523392, 0.767891) ( -0.720609, 0.584725) ( -0.523392, 0.767891) ( 0.189847, -0.917007) ( 0.628692, -1.114870) ( 0.189847, -0.917007) ( 0.884720, 0.240688) ( 0.740494, 0.133871) ( 0.884720, 0.240688) ( -0.272568, 0.145333) ( -0.271178, 0.135927) ( -0.272568, 0.145333) ( -0.591378, -0.356848) ( -0.577253, -0.263565) ( -0.591378, -0.356848) ( 0.411509, -0.809919) ( 0.680821, -0.704855) ( 0.411509, -0.809919) ( 0.724912, 0.452185) ( 0.693328, 0.290070) ( 0.724912, 0.452185) ( -0.552389, 0.689635) ( -0.687434, 0.515804) ( -0.552389, 0.689635) c8_atanh_test c8_atanh computes the inverse hyperbolic tangent of a C8. C1=c8_uniform_01 C2=c8_atanh(C1) C3=c8_tanh(C2) --------------------- --------------------- --------------------- ( -0.012055, 0.704476) ( -0.008056, 0.613769) ( -0.012055, 0.704476) ( -0.043767, 0.729086) ( -0.028572, 0.630577) ( -0.043767, 0.729086) ( -0.556525, -0.009900) ( -0.627671, -0.014340) ( -0.556525, -0.009900) ( 0.385377, 0.604414) ( 0.280785, 0.594205) ( 0.385377, 0.604414) ( -0.072444, -0.659474) ( -0.050474, -0.584690) ( -0.072444, -0.659474) ( 0.286436, 0.273959) ( 0.271392, 0.288201) ( 0.286436, 0.273959) ( 0.083766, -0.174314) ( 0.081459, -0.173739) ( 0.083766, -0.174314) ( 0.274634, -0.736963) ( 0.176685, -0.658773) ( 0.274634, -0.736963) ( 0.020028, 0.859876) ( 0.011514, 0.710314) ( 0.020028, 0.859876) ( -0.479703, -0.573318) ( -0.358843, -0.601744) ( -0.479703, -0.573318) c8_conj_test c8_conj computes the conjugate of a C8. C1=c8_uniform_01 C2=c8_conj(C1) C3=c8_conj(C2) --------------------- --------------------- --------------------- ( 0.208261, -0.841826) ( 0.208261, 0.841826) ( 0.208261, -0.841826) ( 0.831846, -0.108185) ( 0.831846, 0.108185) ( 0.831846, -0.108185) ( 0.258920, -0.411811) ( 0.258920, 0.411811) ( 0.258920, -0.411811) ( 0.410299, 0.770860) ( 0.410299, -0.770860) ( 0.410299, 0.770860) ( -0.649961, 0.358977) ( -0.649961, -0.358977) ( -0.649961, 0.358977) ( -0.257476, 0.706432) ( -0.257476, -0.706432) ( -0.257476, 0.706432) ( -0.226057, 0.602057) ( -0.226057, -0.602057) ( -0.226057, 0.602057) ( -0.337683, -0.755374) ( -0.337683, 0.755374) ( -0.337683, -0.755374) ( -0.613136, 0.498748) ( -0.613136, -0.498748) ( -0.613136, 0.498748) ( 0.709502, 0.562839) ( 0.709502, -0.562839) ( 0.709502, 0.562839) c8_cos_test c8_cos computes the cosine of a C8. C1=c8_uniform_01 C2=c8_cos(C1) C3=c8_acos(C2) --------------------- --------------------- --------------------- ( 0.660743, -0.651679) ( 0.963207, 0.428853) ( 0.660743, -0.651679) ( -0.832459, -0.137333) ( 0.679416, -0.101889) ( 0.832459, 0.137333) ( 0.042616, -0.028734) ( 0.999505, 0.001224) ( 0.042616, -0.028734) ( -0.812604, -0.291536) ( 0.717039, -0.214690) ( 0.812604, 0.291536) ( -0.079302, -0.193151) ( 1.015510, -0.015396) ( 0.079302, 0.193151) ( -0.321387, 0.520448) ( 1.080223, 0.171924) ( 0.321387, -0.520448) ( -0.601489, 0.738812) ( 1.059940, 0.457157) ( 0.601489, -0.738812) ( 0.120227, -0.198078) ( 1.012321, 0.023913) ( 0.120227, -0.198078) ( 0.758633, -0.357428) ( 0.772633, 0.251154) ( 0.758633, -0.357428) ( -0.067321, 0.921601) ( 1.452299, 0.071152) ( 0.067321, -0.921601) c8_cosh_test c8_cosh computes the cosine of a C8. C1=c8_uniform_01 C2=c8_cosh(C1) C3=c8_acosh(C2) --------------------- --------------------- --------------------- ( -0.188044, 0.329321) ( 0.963042, -0.061173) ( -0.188044, 0.329321) ( -0.397324, 0.431153) ( 0.981142, -0.170452) ( -0.397324, 0.431153) ( -0.776610, -0.343921) ( 1.239901, 0.288986) ( 0.776610, 0.343921) ( 0.141037, 0.637411) ( 0.811645, 0.084212) ( 0.141037, 0.637411) ( 0.014146, 0.532161) ( 0.861799, 0.007178) ( 0.014146, 0.532161) ( 0.665610, 0.215152) ( 1.201463, 0.152833) ( 0.665610, 0.215152) ( -0.348422, -0.245451) ( 1.029506, 0.086388) ( 0.348422, 0.245451) ( -0.211837, 0.193950) ( 1.003350, -0.041135) ( -0.211837, 0.193950) ( 0.037526, -0.609201) ( 0.820683, -0.021478) ( -0.037526, 0.609201) ( 0.861291, 0.131790) ( 1.382323, 0.127703) ( 0.861291, 0.131790) c8_cube_root_test c8_cube_root computes the cube root of a C8. C1=c8_uniform_01 C2=c8_cube_root(C1) C3=C2*C2*C2 --------------------- --------------------- --------------------- ( -0.196412, 0.523669) ( 0.659272, 0.494153) ( -0.196412, 0.523669) ( 0.046575, -0.612513) ( 0.746700, -0.406278) ( 0.046575, -0.612513) ( -0.656413, -0.465339) ( 0.619674, -0.693610) ( -0.656413, -0.465339) ( -0.041878, 0.629699) ( 0.733164, 0.445215) ( -0.041878, 0.629699) ( 0.795680, -0.172587) ( 0.931406, -0.066427) ( 0.795680, -0.172587) ( 0.315692, -0.480554) ( 0.786710, -0.269339) ( 0.315692, -0.480554) ( -0.901064, 0.191253) ( 0.544011, 0.806698) ( -0.901064, 0.191253) ( 0.525353, 0.055172) ( 0.807880, 0.028189) ( 0.525353, 0.055172) ( -0.834766, 0.202976) ( 0.539202, 0.782919) ( -0.834766, 0.202976) ( -0.912098, -0.074252) ( 0.508017, -0.827343) ( -0.912098, -0.074252) c8_div_test c8_div divides two C8s. C1=c8_uniform_01 C2=c8_uniform_01 C3=c8_div(C1,C2) C4=C1/C2 --------------------- --------------------- --------------------- --------------------- ( 0.231545, -0.331831) ( -0.746026, -0.137032) ( -0.221207, 0.485430) ( -0.221207, 0.485430) ( -0.160983, 0.859895) ( -0.787865, -0.144378) ( 0.004182, -1.092190) ( 0.004182, -1.092190) ( 0.110530, 0.489944) ( -0.815711, -0.437865) ( -0.355485, -0.409814) ( -0.355485, -0.409814) ( -0.516143, 0.337024) ( -0.210410, -0.806651) ( -0.234919, -0.701136) ( -0.234919, -0.701136) ( 0.922029, 0.314780) ( -0.384255, 0.777355) ( -0.145755, -1.114062) ( -0.145755, -1.114062) ( 0.044316, -0.689493) ( 0.006726, 0.466696) ( -1.475718, -0.116226) ( -1.475718, -0.116226) ( 0.107672, 0.789051) ( 0.255215, 0.322239) ( 1.667384, 0.986441) ( 1.667384, 0.986441) ( -0.367735, -0.678813) ( 0.234005, -0.866852) ( 0.623152, -0.592438) ( 0.623152, -0.592438) ( 0.333282, 0.618815) ( -0.483559, 0.085111) ( -0.450044, -1.358921) ( -0.450044, -1.358921) ( 0.810117, 0.076384) ( -0.707808, -0.381702) ( -0.931767, 0.394561) ( -0.931767, 0.394561) c8_div_r8_test c8_div_r8 divides a C8 by an R8. C1=c8_uniform_01 R2=R8_uniform_01 C3=c8_div_r8(C1,RC2) C4=C1/R2 --------------------- --------------------- --------------------- --------------------- ( -0.485770, 0.685883) 0.283051 ( -1.716195, 2.423181) ( -1.716195, 2.423181) ( 0.292948, -0.483230) 0.233631 ( 1.253895, -2.068352) ( 1.253895, -2.068352) ( 0.440763, -0.342153) 0.246955 ( 1.784791, -1.385488) ( 1.784791, -1.385488) ( -0.054926, -0.521877) 0.270642 ( -0.202945, -1.928288) ( -0.202945, -1.928288) ( 0.706693, 0.213240) 0.703776 ( 1.004145, 0.302995) ( 1.004145, 0.302995) ( -0.795805, -0.303134) 0.879876 ( -0.904451, -0.344519) ( -0.904451, -0.344519) ( 0.132446, 0.113125) 0.334646 ( 0.395778, 0.338045) ( 0.395778, 0.338045) ( 0.400076, -0.489457) 0.625162 ( 0.639956, -0.782928) ( 0.639956, -0.782928) ( 0.874900, -0.058506) 0.032711 ( 26.746537, -1.788590) ( 26.746537, -1.788590) ( -0.501214, 0.720511) 0.433971 ( -1.154950, 1.660275) ( -1.154950, 1.660275) c8_exp_test c8_exp computes the exponential of a C8. C1=c8_uniform_01 C2=c8_exp(C1) C3=c8_log(C2) --------------------- --------------------- --------------------- ( -0.047184, -0.782548) ( 0.676438, -0.672592) ( -0.047184, -0.782548) ( 0.248052, 0.470778) ( 1.142117, 0.581274) ( 0.248052, 0.470778) ( -0.387411, 0.786879) ( 0.479281, 0.480703) ( -0.387411, 0.786879) ( 0.436534, -0.856556) ( 1.013571, -1.169152) ( 0.436534, -0.856556) ( 0.915200, -0.370856) ( 2.327505, -0.905045) ( 0.915200, -0.370856) ( 0.232635, -0.841663) ( 0.840721, -0.941080) ( 0.232635, -0.841663) ( -0.434722, 0.114162) ( 0.643230, 0.073753) ( -0.434722, 0.114162) ( -0.426383, -0.673076) ( 0.510481, -0.406993) ( -0.426383, -0.673076) ( 0.123357, 0.310640) ( 1.077142, 0.345798) ( 0.123357, 0.310640) ( -0.976307, -0.172606) ( 0.371102, -0.064698) ( -0.976307, -0.172606) c8_i_test c8_i returns the value of the imaginary unit. C1=c8_i ( ) = (0,1) C2= C1 * C1 = (-1,0) c8_imag_test c8_imag computes the imaginary part of a C8. C1=c8_uniform_01 R2=c8_imag(C1) R3=C1.Imag --------------------- --------------------- ------------ ( -0.580867, -0.185213) -0.185213 -0.185213 ( -0.653258, 0.237643) 0.237643 0.237643 ( 0.190684, -0.726719) -0.726719 -0.726719 ( -0.943852, -0.325551) -0.325551 -0.325551 ( -0.470796, 0.783218) 0.783218 0.783218 ( -0.053383, -0.944045) -0.944045 -0.944045 ( 0.174015, 0.577354) 0.577354 0.577354 ( -0.165470, -0.402559) -0.402559 -0.402559 ( -0.120669, 0.794841) 0.794841 0.794841 ( 0.033970, -0.205174) -0.205174 -0.205174 c8_inv_test c8_inv computes the inverse of a C8. C1=c8_uniform_01 C2=c8_inv(C1) C3=c8_inv(C2) --------------------- --------------------- --------------------- ( -0.427924, 0.829566) ( -0.491133, -0.952102) ( -0.427924, 0.829566) ( -0.625623, -0.665521) ( -0.749858, 0.797679) ( -0.625623, -0.665521) ( 0.924116, -0.037471) ( 1.080339, 0.043805) ( 0.924116, -0.037471) ( -0.236916, 0.090625) ( -3.682126, -1.408488) ( -0.236916, 0.090625) ( -0.258387, -0.361382) ( -1.309209, 1.831072) ( -0.258387, -0.361382) ( -0.225726, 0.619993) ( -0.518501, -1.424147) ( -0.225726, 0.619993) ( 0.413714, 0.125354) ( 2.213880, -0.670800) ( 0.413714, 0.125354) ( 0.762153, 0.071483) ( 1.300632, -0.121988) ( 0.762153, 0.071483) ( -0.166890, -0.844030) ( -0.225454, 1.140213) ( -0.166890, -0.844030) ( -0.581965, 0.266968) ( -1.419582, -0.651211) ( -0.581965, 0.266968) c8_le_l1_test c8_le_l1 evalues (C1 <= C2) using the L1 norm. C1=c8_uniform_01 C2=c8_uniform_01 L3=c8_le_l1(C1,C2) --------------------- --------------------- --------------------- ( 0.961372, -0.104144) ( -0.177244, -0.414648) False ( 0.925152, -0.108376) ( -0.975087, -0.104473) True ( 0.228526, -0.542987) ( -0.525703, 0.625835) True ( 0.307565, -0.657088) ( -0.489729, -0.544258) True ( -0.309322, -0.737718) ( -0.679581, 0.239539) False ( 0.091997, 0.092622) ( -0.761580, 0.401654) True ( 0.634577, 0.105915) ( 0.328507, -0.350292) False ( -0.391356, 0.378167) ( -0.601488, 0.287135) True ( -0.407384, -0.623166) ( -0.475139, 0.533062) False ( 0.145501, 0.709101) ( -0.042613, 0.611356) False c8_le_l2_test c8_le_l2 evalues (C1 <= C2) using the L2 norm. C1=c8_uniform_01 C2=c8_uniform_01 L3=c8_le_l2(C1,C2) --------------------- --------------------- --------------------- ( -0.012951, -0.089077) ( 0.478664, -0.143720) True ( -0.059829, 0.824963) ( -0.759177, -0.174974) False ( 0.842464, 0.068577) ( -0.173869, -0.819892) False ( 0.462408, 0.607693) ( 0.474999, 0.193975) False ( -0.588390, 0.661299) ( 0.456942, 0.388962) False ( 0.020160, 0.567843) ( 0.823797, 0.442547) True ( -0.973044, 0.198682) ( -0.556732, 0.230884) False ( -0.393551, -0.219526) ( 0.063705, -0.416695) False ( -0.033784, -0.064711) ( 0.677083, -0.485062) True ( 0.612799, 0.365242) ( -0.674247, 0.058137) False c8_le_li_test c8_le_li evalues (C1 <= C2) using the Loo norm. C1=c8_uniform_01 C2=c8_uniform_01 L3=c8_le_li(C1,C2) --------------------- --------------------- --------------------- ( 0.307816, -0.413659) ( -0.740079, 0.054285) True ( -0.106146, -0.958017) ( 0.896704, -0.008252) False ( 0.169159, -0.681384) ( -0.849525, 0.499749) True ( 0.009849, 0.029246) ( -0.299184, 0.167102) True ( 0.677106, 0.263826) ( -0.213787, -0.057754) False ( -0.548693, 0.157620) ( 0.309256, -0.542604) False ( -0.261505, -0.885372) ( -0.552218, 0.420646) False ( 0.330431, 0.126094) ( 0.422553, -0.593849) True ( 0.690157, -0.344860) ( 0.933647, -0.342654) True ( -0.566521, -0.114012) ( 0.545448, -0.016073) False c8_log_test c8_log computes the logarithm of a C8. C1=c8_uniform_01 C2=c8_log(C1) C3=c8_exp(C2) --------------------- --------------------- --------------------- ( -0.683078, -0.266423) ( -0.310342, -2.769708) ( -0.683078, -0.266423) ( 0.772075, -0.063225) ( -0.255332, -0.081707) ( 0.772075, -0.063225) ( -0.746661, 0.065637) ( -0.288296, 3.053911) ( -0.746661, 0.065637) ( 0.106064, 0.630602) ( -0.447133, 1.404161) ( 0.106064, 0.630602) ( -0.187053, 0.755083) ( -0.251149, 1.813633) ( -0.187053, 0.755083) ( 0.769198, -0.492326) ( -0.090730, -0.569349) ( 0.769198, -0.492326) ( -0.709901, -0.576655) ( -0.089270, -2.459395) ( -0.709901, -0.576655) ( 0.919557, 0.134178) ( -0.073330, 0.144893) ( 0.919557, 0.134178) ( -0.241410, -0.267542) ( -1.020659, -2.304895) ( -0.241410, -0.267542) ( 0.181171, -0.423311) ( -0.775549, -1.166400) ( 0.181171, -0.423311) c8_mag_test c8_mag computes the magnitude of a C8. C1=c8_uniform_01 R2=c8_mag(C1) R3=NP.ABSOLUTE(C1) --------------------- --------------------- --------------------- ( -0.305725, 0.120997) 0.328798 0.328798 ( 0.093944, 0.956404) 0.961007 0.961007 ( 0.190199, 0.961875) 0.980500 0.980500 ( -0.152667, 0.193467) 0.246449 0.246449 ( 0.129577, 0.024255) 0.131828 0.131828 ( -0.383376, 0.081733) 0.391992 0.391992 ( -0.913849, 0.326164) 0.970311 0.970311 ( 0.127200, 0.164320) 0.207801 0.207801 ( 0.088877, 0.742621) 0.747920 0.747920 ( 0.659706, -0.202599) 0.690114 0.690114 c8_mul_test c8_mul multiplies two C8s. C1=c8_uniform_01 C2=c8_uniform_01 C3=c8_mul(C1,C2) C4=C1*C2 --------------------- --------------------- --------------------- --------------------- ( 0.297923, -0.541024) ( 0.826585, -0.212919) ( 0.131064, -0.510636) ( 0.131064, -0.510636) ( -0.536681, -0.576948) ( -0.038882, -0.179984) ( -0.082974, 0.119027) ( -0.082974, 0.119027) ( 0.733071, 0.142495) ( -0.650597, -0.045059) ( -0.470513, -0.125738) ( -0.470513, -0.125738) ( 0.438369, -0.773726) ( -0.288940, 0.552381) ( 0.300729, 0.465707) ( 0.300729, 0.465707) ( 0.348537, 0.881766) ( 0.393697, -0.625595) ( 0.688846, 0.129106) ( 0.688846, 0.129106) ( -0.287318, 0.603391) ( -0.730867, -0.111337) ( 0.277171, -0.409009) ( 0.277171, -0.409009) ( -0.426276, -0.382403) ( -0.305415, -0.036621) ( 0.116187, 0.132402) ( 0.116187, 0.132402) ( -0.261429, -0.433379) ( -0.092382, 0.186479) ( 0.104967, -0.008714) ( 0.104967, -0.008714) ( 0.065774, -0.485157) ( 0.481823, -0.058147) ( 0.003481, -0.237585) ( 0.003481, -0.237585) ( -0.431095, 0.822675) ( 0.951302, -0.152549) ( -0.284603, 0.848375) ( -0.284603, 0.848375) c8_nint_test c8_nint computes the nearest integer to a C8. C1=10*c8_uniform_01 C2=c8_nint(C1) --------------------- --------------------- ( -0.842466, -9.542685) ( -1.000000, -10.000000) ( -8.372556, -1.073274) ( -8.000000, -1.000000) ( -8.790761, 3.526635) ( -9.000000, 4.000000) ( -8.438030, 2.006563) ( -8.000000, 2.000000) ( 3.800815, -3.189210) ( 4.000000, -3.000000) ( 0.182690, -4.927413) ( 0.000000, -5.000000) ( -1.386138, -7.327970) ( -1.000000, -7.000000) ( 0.767627, 9.729882) ( 1.000000, 10.000000) ( -6.614063, -4.658781) ( -7.000000, -5.000000) ( 1.639297, -7.057626) ( 2.000000, -7.000000) c8_norm_l1_test c8_norm_l1 computes the L1 norm of a C8. C1=c8_uniform_01 R2=c8_norm_l1(C1) --------------------- --------------------- ( -0.354592, -0.436444) 0.791036 ( -0.392813, -0.836525) 1.229337 ( 0.202112, -0.763549) 0.965662 ( -0.440397, -0.676630) 1.117028 ( -0.380015, 0.357616) 0.737631 ( -0.882932, 0.222189) 1.105121 ( -0.616204, 0.531291) 1.147496 ( -0.651058, 0.703979) 1.355037 ( 0.042329, 0.393271) 0.435600 ( -0.067664, -0.693905) 0.761569 c8_norm_l2_test c8_norm_l2 computes the L2 norm of a C8. C1=c8_uniform_01 R2=c8_norm_l21(C1) --------------------- --------------------- ( 0.412563, 0.393164) 0.569900 ( -0.809823, 0.144499) 0.822614 ( -0.199087, -0.219584) 0.296399 ( 0.452073, 0.274062) 0.528659 ( -0.591080, -0.567962) 0.819730 ( -0.507601, -0.347774) 0.615309 ( 0.937853, 0.138648) 0.948046 ( -0.769041, 0.279534) 0.818269 ( 0.282341, -0.459107) 0.538977 ( 0.515498, -0.326082) 0.609974 c8_norm_li_test c8_norm_l1 computes the Loo norm of a C8. C1=c8_uniform_01 R2=c8_norm_li(C1) --------------------- --------------------- ( -0.744843, 0.471959) 0.744843 ( -0.500159, 0.122644) 0.500159 ( 0.350872, 0.848868) 0.848868 ( -0.038852, 0.573287) 0.573287 ( -0.179305, 0.404813) 0.404813 ( -0.291569, -0.136067) 0.291569 ( 0.818444, -0.350451) 0.818444 ( 0.702825, -0.164787) 0.702825 ( -0.024282, -0.824671) 0.824671 ( 0.951928, -0.222217) 0.951928 c8_normal_01_test Python version: 3.10.12 c8_normal_01 computes pseudonormal complex values. 1 ( -0.260161, -0.722597 ) 2 ( -1.306529, 1.043562 ) 3 ( 0.385506, -1.043445 ) 4 ( 0.767224, -2.031315 ) 5 ( 0.050341, -0.794832 ) 6 ( 0.286324, 0.299133 ) 7 ( -0.880010, -0.163719 ) 8 ( -0.146244, -0.449426 ) 9 ( -0.057647, -0.632224 ) 10 ( 1.667414, 0.659982 ) c8_one_test Python version: 3.10.12 c8_one returns the value of one as a C8 C1=c8_one ( ) = (1,0) C2= C1 + C1 = (2,0) c8_print_test c8_print prints a C8. zero: ( 0, 0 ) One: ( 1, 0 ) Pi: ( 3.14159, 0 ) i: ( 0, 1 ) 1+2i: ( 1, 2 ) -12.34 + 56.78i: ( -12.34, 56.78 ) 1E-3 + 2E-6i ( 0.001, 2e-06 ) 3E8 - 4.5E9i: ( 3e+08, -4.5e+09 ) c8_real_test c8_real computes the real part of a C8. C1=c8_uniform_01 R2=c8_real(C1) R3=C1.real --------------------- --------------------- ------------ ( 0.853914, 0.159154) 0.853914 0.853914 ( 0.695217, 0.437182) 0.695217 0.695217 ( 0.899597, -0.346053) 0.899597 0.899597 ( 0.665771, 0.001500) 0.665771 0.665771 ( -0.302328, 0.765762) -0.302328 -0.302328 ( 0.530486, 0.346456) 0.530486 0.530486 ( 0.491200, -0.785131) 0.491200 0.491200 ( -0.082548, -0.670207) -0.082548 -0.082548 ( -0.459047, 0.161093) -0.459047 -0.459047 ( -0.337119, 0.510454) -0.337119 -0.337119 c8_sin_test c8_sin computes the sine of a C8. C1=c8_uniform_01 C2=c8_sin(C1) C3=c8_asin(C2) --------------------- --------------------- --------------------- ( -0.802369, -0.242604) ( -0.740268, -0.170270) ( -0.802369, -0.242604) ( 0.730689, -0.143825) ( 0.674297, -0.107479) ( 0.730689, -0.143825) ( -0.925918, 0.137881) ( -0.806782, 0.083143) ( -0.925918, 0.137881) ( 0.424061, -0.338312) ( 0.435238, -0.314262) ( 0.424061, -0.338312) ( 0.588907, -0.418019) ( 0.604693, -0.357815) ( 0.588907, -0.418019) ( 0.129021, -0.469985) ( 0.143137, -0.483427) ( 0.129021, -0.469985) ( 0.598901, 0.554022) ( 0.652487, 0.481369) ( 0.598901, 0.554022) ( 0.717729, 0.506278) ( 0.743778, 0.397883) ( 0.717729, 0.506278) ( 0.093527, -0.243781) ( 0.096180, -0.245127) ( 0.093527, -0.243781) ( -0.263522, 0.275448) ( -0.270427, 0.269315) ( -0.263522, 0.275448) c8_sinh_test c8_sinh computes the hyperbolic sine of a C8. C1=c8_uniform_01 C2=c8_sinh(C1) C3=c8_asinh(C2) --------------------- --------------------- --------------------- ( -0.822742, 0.059551) ( -0.917125, 0.080821) ( -0.822742, 0.059551) ( -0.055351, 0.329809) ( -0.052395, 0.324358) ( -0.055351, 0.329809) ( 0.625876, 0.210970) ( 0.652745, 0.251780) ( 0.625876, 0.210970) ( 0.804919, -0.120084) ( 0.888253, -0.160744) ( 0.804919, -0.120084) ( 0.363359, -0.232545) ( 0.361410, -0.245837) ( 0.363359, -0.232545) ( -0.255895, -0.059621) ( -0.258237, -0.061547) ( -0.255895, -0.059621) ( -0.227214, -0.328346) ( -0.216931, -0.330838) ( -0.227214, -0.328346) ( 0.743511, 0.303759) ( 0.776670, 0.385664) ( 0.743511, 0.303759) ( -0.378367, 0.002120) ( -0.387459, 0.002273) ( -0.378367, 0.002120) ( 0.303370, -0.135591) ( 0.305217, -0.141444) ( 0.303370, -0.135591) c8_sqrt_test c8_sqrt computes the square root of a C8. C1=c8_uniform_01 C2=c8_sqrt(C1) C3=C2*C2 --------------------- --------------------- --------------------- ( 0.459389, -0.020322) ( 0.677948, -0.014988) ( 0.459389, -0.020322) ( 0.757981, -0.182499) ( 0.876819, -0.104069) ( 0.757981, -0.182499) ( -0.126361, -0.457981) ( 0.417572, -0.548386) ( -0.126361, -0.457981) ( 0.060413, 0.150104) ( 0.333330, 0.225158) ( 0.060413, 0.150104) ( 0.179694, 0.071241) ( 0.431854, 0.082483) ( 0.179694, 0.071241) ( 0.799278, -0.273479) ( 0.906655, -0.150817) ( 0.799278, -0.273479) ( 0.816514, -0.394898) ( 0.928307, -0.212698) ( 0.816514, -0.394898) ( 0.460647, 0.314597) ( 0.713607, 0.220427) ( 0.460647, 0.314597) ( 0.120959, 0.677850) ( 0.636206, 0.532728) ( 0.120959, 0.677850) ( 0.000556, -0.369833) ( 0.430343, -0.429696) ( 0.000556, -0.369833) c8_tan_test c8_tan computes the tangent of a C8. C1=c8_uniform_01 C2=c8_tan(C1) C3=c8_atan(C2) --------------------- --------------------- --------------------- ( 0.819681, -0.153378) ( 1.019146, -0.318303) ( 0.819681, -0.153378) ( 0.483599, 0.512812) ( 0.384484, 0.567470) ( 0.483599, 0.512812) ( -0.824443, 0.286792) ( -0.913757, 0.555023) ( -0.824443, 0.286792) ( 0.627540, -0.365697) ( 0.597807, -0.502086) ( 0.627540, -0.365697) ( -0.383194, 0.528875) ( -0.297148, 0.542560) ( -0.383194, 0.528875) ( -0.308258, -0.014991) ( -0.318329, -0.016509) ( -0.308258, -0.014991) ( -0.658703, 0.589802) ( -0.476662, 0.725205) ( -0.658703, 0.589802) ( 0.548947, 0.259941) ( 0.558612, 0.341109) ( 0.548947, 0.259941) ( -0.575310, 0.536187) ( -0.447520, 0.632327) ( -0.575310, 0.536187) ( -0.785017, 0.294539) ( -0.847929, 0.528890) ( -0.785017, 0.294539) c8_tanh_test c8_tanh computes the hyperbolic tangent of a C8. C1=c8_uniform_01 C2=c8_tanh(C1) C3=c8_atanh(C2) --------------------- --------------------- --------------------- ( -0.444262, 0.726281) ( -0.656207, 0.645086) ( -0.444262, 0.726281) ( 0.369792, -0.269940) ( 0.377282, -0.239759) ( 0.369792, -0.269940) ( 0.948292, -0.287819) ( 0.767061, -0.128225) ( 0.948292, -0.287819) ( 0.440146, -0.723414) ( 0.649715, -0.645716) ( 0.440146, -0.723414) ( 0.572722, 0.376459) ( 0.574187, 0.277881) ( 0.572722, 0.376459) ( 0.006076, 0.829124) ( 0.013313, 1.091424) ( 0.006076, 0.829124) ( -0.115688, -0.466312) ( -0.143871, -0.494994) ( -0.115688, -0.466312) ( -0.661857, -0.455016) ( -0.664873, -0.300717) ( -0.661857, -0.455016) ( -0.246030, -0.830623) ( -0.495702, -0.963913) ( -0.246030, -0.830623) ( -0.287575, -0.625114) ( -0.408983, -0.639046) ( -0.287575, -0.625114) c8_to_cartesian_test c8_to_cartesian computes the cartesian form of a C8. C1=c8_uniform_01 (X2,Y2)=c8_to_cartesian(C1) C3=cartesian_to_c8(X2,Y2) --------------------- --------------------- --------------------- ( -0.402289, -0.055969) ( -0.402289, -0.055969) ( -0.402289, -0.055969) ( -0.410712, 0.600221) ( -0.410712, 0.600221) ( -0.410712, 0.600221) ( -0.247137, 0.633139) ( -0.247137, 0.633139) ( -0.247137, 0.633139) ( 0.436374, -0.623822) ( 0.436374, -0.623822) ( 0.436374, -0.623822) ( 0.052377, 0.766477) ( 0.052377, 0.766477) ( 0.052377, 0.766477) ( 0.913771, -0.143264) ( 0.913771, -0.143264) ( 0.913771, -0.143264) ( 0.395148, -0.746789) ( 0.395148, -0.746789) ( 0.395148, -0.746789) ( 0.117749, -0.494862) ( 0.117749, -0.494862) ( 0.117749, -0.494862) ( 0.635397, -0.337364) ( 0.635397, -0.337364) ( 0.635397, -0.337364) ( 0.600679, 0.276053) ( 0.600679, 0.276053) ( 0.600679, 0.276053) c8_to_polar_test c8_to_polar computes the polar form of a C8. C1=c8_uniform_01 (R2,T2)=c8_to_polar(C1) C3=polar_to_c8(R2,T2) --------------------- --------------------- --------------------- ( -0.392753, 0.593376) ( 0.711583, 2.155489) ( -0.392753, 0.593376) ( 0.495845, -0.420327) ( 0.650029, -0.703156) ( 0.495845, -0.420327) ( 0.309634, 0.550553) ( 0.631650, 1.058478) ( 0.309634, 0.550553) ( -0.205657, 0.844387) ( 0.869070, 1.809702) ( -0.205657, 0.844387) ( -0.461102, -0.808483) ( 0.930731, -2.089113) ( -0.461102, -0.808483) ( 0.750111, -0.603475) ( 0.962730, -0.677487) ( 0.750111, -0.603475) ( -0.882438, 0.394221) ( 0.966492, 2.721453) ( -0.882438, 0.394221) ( 0.268180, 0.469275) ( 0.540500, 1.051614) ( 0.268180, 0.469275) ( 0.182207, -0.394186) ( 0.434260, -1.137813) ( 0.182207, -0.394186) ( 0.825008, 0.113626) ( 0.832796, 0.136867) ( 0.825008, 0.113626) c8_uniform_01_test Python version: 3.10.12 c8_uniform_01 computes pseudorandom complex values in the unit circle. 0 ( 0.0581155, 0.478348 ) 1 ( 0.902044, -0.172199 ) 2 ( 0.494419, 0.251224 ) 3 ( -0.88666, -0.383528 ) 4 ( -0.377593, -0.571387 ) 5 ( 0.4711, 0.0738685 ) 6 ( 0.678027, -0.212121 ) 7 ( -0.330462, 0.368826 ) 8 ( 0.116459, -0.0030316 ) 9 ( -0.566952, -0.446535 ) c8_zero_test Python version: 3.10.12 c8_zero returns the value of zero as a C8 C1=c8_zero ( ) = (0,0) c8mat_identity_test c8mat_identity returns the complex identity matrix. identity matrix: Col: 0 1 2 3 Row 0 : 1 0i 0 0i 0 0i 0 0i 1 : 0 0i 1 0i 0 0i 0 0i 2 : 0 0i 0 0i 1 0i 0 0i 3 : 0 0i 0 0i 0 0i 1 0i c8mat_indicator_test c8mat_indicator returns the complex indicator matrix. indicator matrix: Col: 0 1 2 Row 0 : 1 -1i 1 -2i 1 -3i 1 : 2 -1i 2 -2i 2 -3i 2 : 3 -1i 3 -2i 3 -3i 3 : 4 -1i 4 -2i 4 -3i 4 : 5 -1i 5 -2i 5 -3i c8mat_norm_fro_test c8mat_norm_fro computes the Frobenius norm of a C8MAT. The indicator matrix: Col: 0 1 2 3 Row 0 : 1 -1i 1 -2i 1 -3i 1 -4i 1 : 2 -1i 2 -2i 2 -3i 2 -4i 2 : 3 -1i 3 -2i 3 -3i 3 -4i 3 : 4 -1i 4 -2i 4 -3i 4 -4i 4 : 5 -1i 5 -2i 5 -3i 5 -4i Frobenius norm = 19.2354 c8mat_norm_l1_test c8mat_norm_l1 computes the L1 norm of a C8MAT. The indicator matrix: Col: 0 1 2 3 Row 0 : 1 -1i 1 -2i 1 -3i 1 -4i 1 : 2 -1i 2 -2i 2 -3i 2 -4i 2 : 3 -1i 3 -2i 3 -3i 3 -4i 3 : 4 -1i 4 -2i 4 -3i 4 -4i 4 : 5 -1i 5 -2i 5 -3i 5 -4i L1 norm = 25.6552 c8mat_norm_li_test c8mat_norm_li computes the Loo norm of a C8MAT. The indicator matrix: Col: 0 1 2 3 Row 0 : 1 -1i 1 -2i 1 -3i 1 -4i 1 : 2 -1i 2 -2i 2 -3i 2 -4i 2 : 3 -1i 3 -2i 3 -3i 3 -4i 3 : 4 -1i 4 -2i 4 -3i 4 -4i 4 : 5 -1i 5 -2i 5 -3i 5 -4i Loo norm = 22.7183 c8mat_print_test Python version: 3.10.12 c8mat_print prints an C8MAT. Here is a C8MAT: Col: 0 1 2 Row 0 : 10 1i 10 2i 10 3i 1 : 20 1i 20 2i 20 3i 2 : 30 1i 30 2i 30 3i 3 : 40 1i 40 2i 40 3i c8mat_print_some_test Python version: 3.10.12 c8mat_print_some prints some of an C8MAT. Here is a C8MAT: Col: 3 4 5 Row 0 : 10 4i 10 5i 10 6i 1 : 20 4i 20 5i 20 6i 2 : 30 4i 30 5i 30 6i c8mat_uniform_01_test c8mat_uniform_01 computes a random C8MAT. 0 <= X <= 1 Random C8MAT: Col: 0 1 2 Row 0 : 0.0989373 0.369563i 0.0441466 0.309507i 0.641107 -0.446064i 1 : 0.269802 -0.0672104i -0.222368 0.850548i 0.106262 0.868865i 2 : 0.759667 -0.35292i 0.296271 0.702083i -0.305866 -0.946557i 3 : 0.786002 -0.567929i 0.876639 -0.463756i -0.0547356 0.152347i 4 : 0.0456766 0.824355i 0.644768 -0.607407i -0.15542 0.36177i c8vec_indicator_test c8vec_indicator returns the indicator vector. The indicator vector: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 5 6 -6 6 7 -7 7 8 -8 8 9 -9 9 10 -10 c8vec_nint_test c8vec_nint rounds a C8VEC. The initial vector: 0 3.92488 0.78998 1 5.56514 -0.590985 2 -0.737322 1.59283 3 -1.69808 0.388799 4 1.42919 5.17498 The rounded vector: 0 4 1 1 6 -1 2 -1 2 3 -2 0 4 1 5 c8vec_norm_l1_test c8vec_norm_l1 computes the L1 norm of a C8VEC. The indicator vector: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 L1 norm = 21.2132 c8vec_norm_l2_test c8vec_norm_l2 computes the L2 norm of a C8VEC. The indicator vector: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 L2 norm = 10.4881 c8vec_norm_li_test c8vec_norm_li computes the Loo norm of a C8VEC. The indicator vector: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 Loo norm = 7.07107 c8vec_print_test Python version: 3.10.12 c8vec_print prints an C8VEC. Here is a C8VEC: 0 1 2 1 3 4 2 5 6 3 7 8 c8vec_print_part_test c8vec_print_part prints part of a C8VEC. Part of the C8VEC: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 5 6 -6 6 7 -7 7 8 -8 ...... .............. .............. 99 100 -100 c8vec_sort_a_l1_test c8vec_sort_a_l1 sorts a C8VEC by L1 norm. The unsorted vector: 0 0.0189422 -0.966304 1 0.0371973 0.0597232 2 -0.35941 0.681056 3 -0.184984 0.294381 4 -0.585428 0.608716 5 0.622918 -0.741237 6 0.0846928 0.418586 7 -0.90237 0.187264 8 -0.511025 0.432269 9 -0.747834 0.0335636 I A(I) ||A(I)|| 0 ( 0.0371973, 0.0597232) 0.0969205 1 ( -0.184984, 0.294381) 0.479365 2 ( 0.0846928, 0.418586) 0.503279 3 ( -0.747834, 0.0335636) 0.781398 4 ( -0.511025, 0.432269) 0.943294 5 ( 0.0189422, -0.966304) 0.985247 6 ( -0.35941, 0.681056) 1.04047 7 ( -0.90237, 0.187264) 1.08963 8 ( -0.585428, 0.608716) 1.19414 9 ( 0.622918, -0.741237) 1.36415 c8vec_sort_a_l2_test c8vec_sort_a_l2 sorts a C8VEC by L2 norm. The unsorted vector: 0 0.178145 -0.602945 1 -0.0205499 0.0846362 2 -0.540553 -0.521933 3 -0.1179 -0.928832 4 0.598063 -0.55006 5 0.0319065 -0.706539 6 0.0934655 0.793005 7 -0.597555 0.178693 8 0.538877 0.810257 9 0.834169 -0.538216 I A(I) ||A(I)|| 0 ( -0.0205499, 0.0846362) 0.0870952 1 ( -0.597555, 0.178693) 0.623701 2 ( 0.178145, -0.602945) 0.628711 3 ( 0.0319065, -0.706539) 0.707259 4 ( -0.540553, -0.521933) 0.751407 5 ( 0.0934655, 0.793005) 0.798494 6 ( 0.598063, -0.55006) 0.812555 7 ( -0.1179, -0.928832) 0.936284 8 ( 0.538877, 0.810257) 0.973091 9 ( 0.834169, -0.538216) 0.992731 c8vec_sort_a_li_test c8vec_sort_a_li sorts a C8VEC by Loo norm. The unsorted vector: 0 -0.354156 -0.267713 1 0.764092 -0.531624 2 0.58261 0.746243 3 -0.14334 0.0895391 4 0.15096 -0.923722 5 0.366923 -0.0257022 6 -0.223434 0.149926 7 0.299318 -0.0881874 8 0.672987 0.250874 9 -0.583796 0.44432 I A(I) ||A(I)|| 0 ( -0.14334, 0.0895391) 0.14334 1 ( -0.223434, 0.149926) 0.223434 2 ( 0.299318, -0.0881874) 0.299318 3 ( -0.354156, -0.267713) 0.354156 4 ( 0.366923, -0.0257022) 0.366923 5 ( -0.583796, 0.44432) 0.583796 6 ( 0.672987, 0.250874) 0.672987 7 ( 0.58261, 0.746243) 0.746243 8 ( 0.764092, -0.531624) 0.764092 9 ( 0.15096, -0.923722) 0.923722 c8vec_spiral_test c8vec_spiral returns N points on a spiral which includes M complete turns. The spiral points: 0 5 0 1 4.18579 2.41667 2 2.33333 4.04145 3 2.75546e-16 4.5 4 -2.16667 3.75278 5 -3.60844 2.08333 6 -4 4.89859e-16 7 -3.31976 -1.91667 8 -1.83333 -3.17543 9 -6.4294e-16 -3.5 10 1.66667 -2.88675 11 2.74241 -1.58333 12 3 -7.34788e-16 c8vec_uniform_01_test Python version: 3.10.12 c8vec_uniform_01 computes pseudorandom complex values in the unit circle. 0 ( 0.800994, 0.429430 ) 1 ( 0.088358, 0.247094 ) 2 ( 0.636033, 0.387099 ) 3 ( -0.436228, -0.010850 ) 4 ( 0.419491, -0.065617 ) 5 ( -0.079931, 0.166081 ) 6 ( -0.137271, -0.405016 ) 7 ( -0.589840, 0.330649 ) 8 ( -0.528263, -0.712635 ) 9 ( -0.503772, 0.160476 ) c8vec_unity_test c8vec_unity returns the N roots of unity. The N roots of unity: 0 1 0 1 0.866025 0.5 2 0.5 0.866025 3 6.12323e-17 1 4 -0.5 0.866025 5 -0.866025 0.5 6 -1 1.22465e-16 7 -0.866025 -0.5 8 -0.5 -0.866025 9 -1.83697e-16 -1 10 0.5 -0.866025 11 0.866025 -0.5 cartesian_to_c8_test cartesian_to_c8 computes the cartesian form of a C8. X1,Y1=r8_uniform_01 C2=cartesian_to_c8(X1,Y1) X3,Y3=c8_to_cartesian(C2) --------------------- --------------------- --------------------- ( 0.032842, 0.101623) ( 0.032842, 0.101623) ( 0.032842, 0.101623) ( 0.320246, 0.803242) ( 0.320246, 0.803242) ( 0.320246, 0.803242) ( 0.776412, 0.439462) ( 0.776412, 0.439462) ( 0.776412, 0.439462) ( 0.333761, 0.144233) ( 0.333761, 0.144233) ( 0.333761, 0.144233) ( 0.772101, 0.087631) ( 0.772101, 0.087631) ( 0.772101, 0.087631) ( 0.252979, 0.987096) ( 0.252979, 0.987096) ( 0.252979, 0.987096) ( 0.783087, 0.298639) ( 0.783087, 0.298639) ( 0.783087, 0.298639) ( 0.621546, 0.439769) ( 0.621546, 0.439769) ( 0.621546, 0.439769) ( 0.543394, 0.084755) ( 0.543394, 0.084755) ( 0.543394, 0.084755) ( 0.542793, 0.946026) ( 0.542793, 0.946026) ( 0.542793, 0.946026) polar_to_c8_test polar_to_c8 computes the polar form of a C8. R1,T1=R8_uniform_01 C2=polar_to_c8(R1,T1) R3,T3=c8_to_polar(C2) --------------------- --------------------- --------------------- ( 0.637935, 5.636222) ( 0.509020, -0.384526) ( 0.637935, -0.646963) ( 0.230206, 3.685248) ( -0.197016, -0.119078) ( 0.230206, -2.597937) ( 0.050440, 3.880012) ( -0.037302, -0.033952) ( 0.050440, -2.403173) ( 0.091717, 3.439921) ( -0.087666, -0.026958) ( 0.091717, -2.843264) ( 0.794115, 1.847274) ( -0.216768, 0.763957) ( 0.794115, 1.847274) ( 0.052366, 5.191992) ( 0.024163, -0.046458) ( 0.052366, -1.091193) ( 0.400787, 3.752333) ( -0.328334, -0.229841) ( 0.400787, -2.530852) ( 0.018150, 5.709188) ( 0.015241, -0.009855) ( 0.018150, -0.573998) ( 0.611644, 0.957300) ( 0.352142, 0.500105) ( 0.611644, 0.957300) ( 0.013685, 1.028299) ( 0.007065, 0.011720) ( 0.013685, 1.028299) c8lib_test(): Normal end of execution. Tue May 20 21:19:13 2025