angles.py 36.3 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171
import math
import doctest

# ========================================================
# ========================================================
# === ANGLE
# ========================================================
# ========================================================

class Angle:
    """ Class to convert angles for astronomy

    Angle formats are:
    -----------------
    
    deg = degrees. e.g.
    rad = radian. e.g.
    
    Usage:
    ------

    First, instanciate an object from the class:    
    angle = Angle()

    Second, assign a date in any angle format:
    angle.angle("-0d3m28.56s")

    Third, get the converted angle:    
    rad = angle.rad()
    deg = angle.deg()
    arcmin = angle.arcmin()
    arcsec = angle.arcsec()
    dms = angle.dms()
    uspzad = angle.sexagesimal(sexagesimal_format)

    Informations:
    -------------
    
    help(Angle)
    Angle().infos("doctest")
    Angle().infos("doc_methods")
    """
# ========================================================
# === attributs
# ========================================================

    # --- multiplicators for units
    _r2d = 180.0/math.pi
    _d2r = 1./_r2d    
    _r2h = _r2d/15.0
    _h2r = 1./_r2h
    _r2m = _r2d*60.0
    _m2r = 1./_r2m
    _r2s = _r2d*3600.0
    _s2r = 1./_r2s
    _r2mh = _r2m/15.0
    _mh2r = 1./_r2mh
    _r2sh = _r2s/15.0
    _sh2r = 1./_r2sh

    # --- correspondances between units and multiplicator ->r
    _u2r = {}
    _u2r["R"] = 1
    _u2r["D"] = _d2r
    _u2r["M"] = _m2r
    _u2r["S"] = _s2r
    _u2r["H"] = _h2r
    _u2r["MH"] = _mh2r
    _u2r["SH"] = _sh2r
    
# ========================================================
# === internal methods
# ========================================================

    def _init(self,angle=""):
        """ Initialize internal attributes.

        Inputs:
        -------
        angle is an angle in any supported format (cf. help(Angle))
        
        Usage:
        ------        
        objangle = Angle()
        objangle._init()
        """
        self._init_angle = angle
        self._init_angleformat = []
        self._computed_rad = 0
        self._angle_redefined()        
        self._computed_sexagesimal_format = "D.3"
        self._rad = 0

    def _angle_redefined(self):
        """ Initialize internal attributes when a radian angle is just defined or redefined.
        """
        self._computed_deg = 0
        self._computed_arcmin = 0
        self._computed_arcsec = 0
        self._computed_sexagesimal = 0
        self._deg = 0
        self._arcmin = 0
        self._arcsec = 0
        self._sexagesimal = 0
        # Attention, python3.5+ only:
        self._cos_rad_modulo = math.nan
        self._sin_rad_modulo = math.nan

    def _is_number(self,s):
        """ Return True if the string is a number else return False.

        Usage:
        ------    
        >>> objangle = Angle()
        >>> objangle._is_number("3e5")
        True
        >>> objangle._is_number("3a5")
        False
        """
        try:
            float(s)
            return True
        except ValueError:
            pass 
        try:
            import unicodedata
            unicodedata.numeric(s)
            return True
        except (TypeError, ValueError):
            pass 
        return False

    def _angle_compare(self, angle, operator):
        """ Comparaison of angles for various operators.

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :param operator : Operator such as == != > >= < <=
        :type operator : string
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1._angle_compare(objangle2,">")
        12.345
        '56d28m'
        False
        
        .. note:: Does not account for the modulo.
        """
        if isinstance(angle, Angle) == False:
            angle =  Angle(angle)
        if self._computed_rad == 0:
            self.rad()
        if angle._computed_rad == 0:
            angle.rad()
        res = False
        if (self._computed_rad == 1) and (angle._computed_rad == 1):
            toeval = str(self._rad)+" "+operator+" "+str(angle._rad)
            res = eval(toeval)
        return res
    
# ========================================================
# === angle methods
# ========================================================

    def angle_angle2rad(self,angle):
        """ Compute radian from any angle format
        
        Inputs:
        -------
        angle is an angle in any supported format (cf. help(Angle))
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle_angle2rad("-57d45m34s")
        ([('-57', 'D'), ('45', 'M'), ('34', 'S')], -1.0080924796783026)
        
        First integer is used to check the recognized input date format:
        0 = Error, format not known
        
        Related topics:
        ---------------
        Prefer using objangle.angle() followed by objangle.rad()            
        """
        str_angle = str(angle).upper()  
        #print("str_angle = "+str_angle)
        cars = "+-.0123456789"
        # --- eliminate leading characters before the first numeric cheracter
        k = 0
        for car in str_angle:
            if (car in cars):
                break
            k += 1
        if (k==0):
            # problem, no valid numeric value found.
            pass
        str_angle = str_angle[k:]
        # --- 
        # "-0   45 ' 34 sec"
        # angle_numb = [ "-0", "45", "34" ]
        # angle_numb = [ "   ", " ' ", " sec" ]
        ind_numb = -1
        ind_unit = -1       
        angle_numbs = []
        angle_units = []
        knumb = 0
        kunit = 0
        for car in str_angle:
            if (car in cars) or (car=='E' and knumb>0):
                # --- numeric case for value
                if (knumb==0):
                    ind_numb += 1
                    angle_numbs.append('')
                angle_numbs[ind_numb] += car
                knumb += 1
                kunit = 0
            else:
                # --- alpha case for units
                if (kunit==0):
                    ind_unit += 1
                    angle_units.append('')
                if ( (car!=" ") and (car!=":") ):
                    if (car=="'"):
                        car = "M"
                    if (car=='"'):
                        car = "S"
                    angle_units[ind_unit] += car
                kunit += 1
                knumb = 0        
        # --- reformat units
        #print("angle_numbs={}".format(angle_numbs))
        #print("angle_units={}".format(angle_units))
        n_numb = len(angle_numbs)
        n_unit = len(angle_units)
        tmps = [];
        for angle_unit in angle_units:
            if angle_unit is '':
                angle_unit = ' '
            tmps.append(angle_unit)
        angle_units = tmps.copy()
        # --- simplify units
        angle_fnumbs = []
        angle_funits = []
        if (n_unit==0) and (n_numb==0):
            angle_fnumbs.append("0")
            angle_funits.append("R")
        elif (n_unit==0):
            angle_fnumbs.append(angle_numbs[0])
            angle_funits.append("D")
        elif (n_unit==1):
            angle_fnumbs.append(angle_numbs[0])
            u1 = angle_units[0]
            if (u1[0]=="R"):            
                angle_funits.append("R")
            elif (u1[0]=="M"):            
                angle_funits.append("M")
                if (n_numb==2):
                    angle_funits.append("S")
                    angle_fnumbs.append(angle_numbs[1])
            elif (u1[0]=="S"):
                angle_funits.append("S")
            elif (u1[0]=="H"):
                angle_funits.append("H")
                if (n_numb==2):
                    angle_funits.append("MH")
                    angle_fnumbs.append(angle_numbs[1])
            else:
                angle_funits.append("D")                
                if (n_numb==2):
                    angle_funits.append("M")
                    angle_fnumbs.append(angle_numbs[1])
        elif (n_numb==2):
            # cases DM or MS HM
            angle_fnumbs.append(angle_numbs[0])
            angle_fnumbs.append(angle_numbs[1])
            u1 = angle_units[0]
            u2 = angle_units[1]
            if (u1[0]=="M"):
                angle_funits.append("M")
                angle_funits.append("S")
            elif (u1[0]=="H" and u2[0]=="S"):
                angle_funits.append("H")
                angle_funits.append("SH")
            elif (u1[0]=="H"):
                angle_funits.append("H")
                angle_funits.append("MH")
            else:
                angle_funits.append("D")
                angle_funits.append("M")
        elif (n_numb==3):
            # cases DMS or HMS 
            angle_fnumbs.append(angle_numbs[0])
            angle_fnumbs.append(angle_numbs[1])
            angle_fnumbs.append(angle_numbs[2])
            u1 = angle_units[0]
            if (u1[0]=="H"):
                angle_funits.append("H")
                angle_funits.append("MH")
                angle_funits.append("SH")
            else:
                angle_funits.append("D")
                angle_funits.append("M")
                angle_funits.append("S")
        # --- compute the angle
        if (angle_fnumbs=="."):
            angle_fnumbs="0."
        #print(angle_fnumbs)
        #print(angle_funits)
        init_angleformat = list ( zip (angle_fnumbs, angle_funits) )
        sign = 1
        k=0
        rad = 0
        for init_angle in init_angleformat:
            numb = init_angle[0]
            unit = init_angle[1]
            if (k==0) and ('-' in numb):
                sign = -1
            fnumb = math.fabs(float(numb))
            mult = self._u2r[unit]
            rad += fnumb*mult
        rad *= sign
        self._rad = rad
        self._rad_modulo_2pi = math.fmod(rad,2*math.pi)
        if (self._rad_modulo_2pi<0):
            self._rad_modulo_2pi += (2*math.pi)
        return init_angleformat, rad

    def angle_rad2deg(self,rad):
        """ Compute a angle in degrees from a angle in radian
        
        Inputs:
        -------
        rad is an angle in radian.
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle_rad2deg(1)
        (0, 57.29577951308232)
        
        First integer is an error code. 0 = no problem.
            
        Related topics:
        ---------------
        Prefer using objangle.angle() followed by objangle.deg()            
        """
        error = 0
        res = rad * self._r2d
        return error, res

    def angle_rad2sexagesimal(self,rad, sexagesimal_format):
        """ Compute a sexagesimal format string from radian
        
        Inputs:
        -------
        rad is an angle in radian
        sexagesimal_format is
        u (unit) = h,H,d,D (default=D). Capital mean module [0:360[, lower case means module [-180:180[ 
        s (separator) = " ",:,"" (default="" means letters hms or dms)
        p (plus/minus) = +,"" (default="")
        z (zeros) = 0,"" (default="")
        a (angle_limits) = "",90, (+/-limit if unit D,H, default="" means 360)
        d (sec_digits) = "",".1",".2",... (default="")
        --- style 1:
        E.g. To Display a R.A.: "H0.2" =>  23h07m42.49s
        E.g. To Display a Decl.: "d+090.1" => +00d34m22.6s
        E.g. To Display a H.A.: "h0.2" => -08h43m16.05s
        --- style 2:
        E.g. To Display a R.A.: "H 0.2" =>  23 07 42.49
        E.g. To Display a Decl.: "d +090.1" => -00 34 22.6
        E.g. To Display a H.A.: "h 0.2" => -08 43 16.05
        --- style 3:
        E.g. To Display a R.A.: "H:0.2" =>  23:07:42.49
        E.g. To Display a Decl.: "d:+090.1" => -00:34:22.6
        E.g. To Display a H.A.: "h:0.2" => -08:43:16.05
                
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle_rad2sexagesimal(-0.01,"d:-090.1")
        (0, '-00:34:22.6')
        
        First integer is used to check the recognized input date format:
        0 = Error, format not known
        
        Related topics:
        ---------------
        Prefer using objangle.angle() followed by objangle.sexagesimal()            
        """
        symbols = str(sexagesimal_format)       
        digits = ""
        unit=0; # 0=deg 1=hours
        separator=0; # 0=hdms 1=space 2=:
        modulo=0; # 0=360 1=180
        sign=0; # 0=[0:modulo] 1=[-modulo/2:modulo/2]
        zeros=0; # 0=spaces 1=leading zeros
        k=0
        for car in symbols:
            if (car=='D'): 
                unit=0
                modulo=0
            if (car=='d'): 
                unit=0
                modulo=1
            if (car=='H'): 
                unit=1 
                modulo=0
            if (car=='h'):
                unit=1 
                modulo=1
            if (car==' '): 
                separator=1
            if (car=='_'): 
                separator=1
            if (car==':'): 
                separator=2
            if (car=='+'): 
                sign=1
            if (self._is_number(car)) or car=='.': 
                digits = symbols[k:]
                break
            k += 1
        #	int unit=0; // 0=deg 1=hours
        #	int modulo=0; // 0=360 1=180
        #	int separator=0; // 0=hdms 1=space 2=:
        #	int sign=0; // 0=[0:modulo] 1=[-modulo/2:modulo/2]
        # === trailing format (digits)
        angle_limit = 360
        nb_decimalsec = 2
        ld = len(digits)
        if (ld>0):
            # e.g. digits = "090.3"
            car = digits[0]
            if car=='0':
                zeros=1
                digits = digits[1:]
            # now digits = "90.3" and zeros=1
            kd = digits.find(".")
            if kd==-1:
                if (self._is_number(digits)==True):
                    angle_limit = int(digits)
            else:
                if (self._is_number(digits[0:kd])==True):
                    angle_limit = int(digits[0:kd])
                if (self._is_number(digits[kd+1:])==True):
                    nb_decimalsec = int(digits[kd+1:])
                # now digits_angle_limit = "90", digits_nb_decimal="3"
        #print("ld="+str(ld))            
        #print("symbols="+symbols)
        #print("digits="+digits)
        #print("unit="+str(unit))
        #print("modulo="+str(modulo))
        #print("separator="+str(separator))
        #print("sign="+str(sign))
        #print("zeros="+str(zeros))
        #print("angle_limit="+str(angle_limit))
        #print("nb_decimal="+str(nb_decimalsec))
        error, deg = self.angle_rad2deg(rad)
        # --- all angle in [0:360[
        deg = math.fmod(deg, 360)
        if (deg<0):
            deg = math.fmod(deg+360, 360)
        #print("deg 1 ="+str(deg))
        # --- case modulo [-180:180[
        if modulo==1:
            if deg>180:
                deg-=360
        #print("deg 2 ="+str(deg))
        # --- limit angle
        if deg>angle_limit:
            deg = angle_limit
        elif deg<-angle_limit:
            deg = -angle_limit
        #print("deg 3 ="+str(deg))
        # --- sign of the input angle
        s = 1
        if deg<0:
            s = -1
            deg = -deg
        # --- case hour/deg
        if (unit==1):
            angle = deg/15
            angle_limit = angle_limit/15
        else:
            angle = deg
        #print("angle 1 ="+str(angle))
        # --- compute the trheee components of xx mm ss
        r = angle
        xx = int(math.floor(r))
        mm = 0
        ss = 0
        r = (r-xx)*60
        mm = int(math.floor(r))
        ss = (r-mm)*60
        #print("xx ="+str(xx))
        #print("mm ="+str(mm))
        #print("ss ="+str(ss))
        # === Compute the result
        result = ""
        # --- sign
        if sign==1 and s>=0:
            result += "+"
        elif s<0:
            result += "-"
        # --- xx
        n = 1+int(math.log10(angle_limit))
        if zeros==0:
            fstring  = "{:d}"
        else:
            fstring  = "{:0"+str(n)+"d}"
        result += fstring.format(xx)
        # --- separator xx mm
        if separator==1:
            result += " "
        elif separator==2:
            result += ":"
        else:
            if unit==0:
                result += "d"
            else:
                result += "h"
        # --- mm
        if zeros==0:
            fstring  = "{:d}"
        else:
            fstring  = "{:02d}"
        result += fstring.format(mm)
        # --- separator mm ss
        if separator==1:
            result += " "
        elif separator==2:
            result += ":"
        else:
            result += "m"
        # --- ss
        if zeros==0:
            fstring  = "{:."+str(nb_decimalsec)+"f}"
        else:
            if nb_decimalsec==0:
                fstring  = "{:0"+str(nb_decimalsec+2)+".0f}"
            else:
                fstring  = "{:0"+str(nb_decimalsec+3)+"."+str(nb_decimalsec)+"f}"
        #print("fstring="+fstring)
        result += fstring.format(ss)
        # --- separator ss
        if separator==0:
            result += "s"
        # -- end
        return 0, result
        
# ========================================================
# === get/set methods
# ========================================================

    def angle(self, angle=""):
        """ Set the input angle in any format
        
        Inputs:
        -------
        angle is an angle in any supported format (cf. help(Angle))
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle("23d 27m")
        '23d 27m'
        
        Related topics:
        ---------------
        After using objangle.angle() get conversions with methods as objangle.deg()
        or objdate.rad().            
        """
        if isinstance(angle, Angle) == False:
            if angle != "":
                if (angle != self._init_angle):
                    self._init(angle)
        else:
            self = angle
        return self._init_angle

    def rad(self):
        """ Get the angle in radian
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle("-23 d 56'")
        "-23 d 56'"
        >>> objangle.rad()
        -0.4177154676439762
        
        Related topics:
        ---------------
        Before use objdate.angle() to set the input angle.
        """
        if (self._computed_rad == 0):
            init_angleformat, rad = self.angle_angle2rad(self._init_angle)
            self._init_angleformat = init_angleformat
            self._computed_rad = 1        
            self._rad = rad
        return self._rad

    def deg(self):
        """ Get the angle in degrees
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle("-23 d 56'")
        "-23 d 56'"
        >>> objangle.deg()
        -23.933333333333334
        
        Related topics:
        ---------------
        Before use objdate.angle() to set the input angle.
        """
        if (self._computed_deg == 0):
            if (self._computed_rad == 0):
                self.rad()
            if (len(self._init_angleformat) > 0):                    
                error, deg = self.angle_rad2deg(self._rad)
                if error==0:
                    self._computed_deg = 1
                    self._deg = deg
                    return self._deg
            return -1            
        return self._deg

    def arcmin(self):
        """ Get the angle in arcmin
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle("-23 d 56'")
        "-23 d 56'"
        >>> objangle.arcmin()
        -1436.0
        
        Related topics:
        ---------------
        Before use objdate.angle() to set the input angle.
        """
        if (self._computed_arcmin == 0):
            if (self._computed_rad == 0):
                self.rad()
            if (len(self._init_angleformat) > 0):                    
                error, deg = self.angle_rad2deg(self._rad)
                arcmin = deg*60
                if error==0:
                    self._computed_arcmin = 1
                    self._arcmin = arcmin
                    return self._arcmin
            return -1            
        return self._arcmin

    def arcsec(self):
        """ Get the angle in arcsec
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle("-23 d 56'")
        "-23 d 56'"
        >>> objangle.arcsec()
        -86160.0
        
        Related topics:
        ---------------
        Before use objdate.angle() to set the input angle.
        """
        if (self._computed_arcsec == 0):
            if (self._computed_rad == 0):
                self.rad()
            if (len(self._init_angleformat) > 0):                    
                error, deg = self.angle_rad2deg(self._rad)
                arcsec = deg*3600
                if error==0:
                    self._computed_arcsec = 1
                    self._arcsec = arcsec
                    return self._arcsec
            return -1            
        return self._arcsec

    def sexagesimal(self,sexagesimal_format):
        """ Get the angle in sexagesimal
        
        Inputs:
        -------
        rad is an angle in radian
        sexagesimal_format is
        u (unit) = h,H,d,D (default=D). Capital mean module [0:360[, lower case means module [-180:180[ 
        s (separator) = " ",:,"" (default="" means letters hms or dms)
        p (plus/minus) = +,"" (default="")
        z (zeros) = 0,"" (default="")
        a (angle_limits) = "",90, (+/-limit if unit D,H, default="" means 360)
        d (sec_digits) = "",".1",".2",... (default="")
        --- style 1:
        E.g. To Display a R.A.: "H0.2" =>  23h07m42.49s
        E.g. To Display a Decl.: "d+090.1" => +00d34m22.6s
        E.g. To Display a H.A.: "h0.2" => -08h43m16.05s
        --- style 2:
        E.g. To Display a R.A.: "H 0.2" =>  23 07 42.49
        E.g. To Display a Decl.: "d +090.1" => -00 34 22.6
        E.g. To Display a H.A.: "h 0.2" => -08 43 16.05
        --- style 3:
        E.g. To Display a R.A.: "H:0.2" =>  23:07:42.49
        E.g. To Display a Decl.: "d:+090.1" => -00:34:22.6
        E.g. To Display a H.A.: "h:0.2" => -08:43:16.05
        
        Usage:
        ------
        >>> objangle = Angle()
        >>> objangle.angle(-0.57)
        -0.57
        >>> objangle.sexagesimal("d:-090.1")
        '-00:34:12.0'
                
        Related topics:
        ---------------
        Before use objdate.angle() to set the input angle.
        """
        if (self._computed_sexagesimal == 0) or (sexagesimal_format != self._computed_sexagesimal_format):
            if (self._computed_rad == 0):
                self.rad()
            if (len(self._init_angleformat) > 0):                    
                error, sexagesimal = self.angle_rad2sexagesimal(self._rad, sexagesimal_format)
                if error==0:
                    self._computed_sexagesimal = 1
                    self._sexagesimal = sexagesimal
                    self._computed_sexagesimal_format = sexagesimal_format
                    return self._sexagesimal
            return -1            
        return self._sexagesimal

# ========================================================
# === debug methods
# ========================================================
    
    def infos(self, action) -> None:
        """ To get informations about this class
        
        :param action: A command to run a debug action (see examples).
        :type action: string
        
        :Example:
            
        Angle().infos("doctest")
        Angle().infos("doc_methods")
        Angle().infos("internal_attributes")
        Angle().infos("public_methods")        
        """
        if (action == "doc_methods"):
            publics = [x for x in dir(self) if x[0]!="_"]
            for public in publics:
                varname = "{}".format(public)
                if (callable(getattr(self,varname))==True):
                    print("\n{:=^40}".format(" method "+varname+" "))
                    t = "Angle()."+varname+".__doc__"
                    tt =eval(t)
                    print(tt)
        if (action == "doctest"):
            if __name__ == "__main__":
                print("\n{:~^40}".format("doctest"))
                #doctest.testmod(verbose=True, extraglobs={'objangle': Angle()})
                doctest.testmod(verbose=True)
        if (action == "internal_attributes"):
            internals = [x for x in dir(self) if x[0]=="_" and x[1]!="_"]
            for internal in internals:
                varname = "{}".format(internal)
                #if (hasattr(self,varname)==True):
                if (callable(getattr(self,varname))==False):
                    print(varname + "=" + str(getattr(self,varname)))
        if (action == "public_methods"):
            publics = [x for x in dir(self) if x[0]!="_"]
            for public in publics:
                varname = "{}".format(public)
                if (callable(getattr(self,varname))==True):
                    print(varname)


# ========================================================
# === special methods
# ========================================================
        
    def __init__(self, angle=""):
        """ Object initialization where angle is the input in any format.

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : string
        
        """
        self._init(angle)

    def __add__(self, angle):
        """ Add an angle to an angle.

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The result of the addition
        :rtype: Angle()
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle = objangle1 + objangle2 ; objangle.sexagesimal("D")
        12.345
        '56d28m'
        '68d48m42.00s'
        """
        if isinstance(angle, Angle) == False:
            angle =  Angle(angle)
        res = Angle()
        if self._computed_rad == 0:
            self.rad()
        if angle._computed_rad == 0:
            angle.rad()            
        if (self._computed_rad == 1) and (angle._computed_rad == 1):
            rad = self._rad + angle._rad
            deg = rad * self._r2d
            res = Angle(deg)
        return res

    def __radd__(self, angle):
        """ Right addition an angle to an angle.
        """
        return self + angle    

    def __iadd__(self, angle):
        """ Add an angle to an angle.
        """
        return self + angle
    
    def __sub__(self, angle):
        """ Subtract an angle to an angle.
        
        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The result of the subtraction
        :rtype: Angle()
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle = objangle1 - objangle2 ; objangle.sexagesimal("D")
        12.345
        '56d28m'
        '315d52m42.00s'
        """
        if isinstance(angle, Angle) == False:
            angle =  Angle(angle)
        res = Angle()
        if self._computed_rad == 0:
            self.rad()
        if angle._computed_rad == 0:
            angle.rad()            
        if (self._computed_rad == 1) and (angle._computed_rad == 1):
            rad = self._rad - angle._rad
            deg = rad * self._r2d
            res = Angle(deg)
        return res


    def __rsub__(self, angle):
        """ Right subtraction only an angle to an angle.
        """
        if isinstance(angle, Angle) == True:
            return self - angle    
        else:
            return angle
    
    def __isub__(self, angle):
        """ Subtract  an angle to an angle.
        
        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The result of the subtraction
        :rtype: Angle()
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 -= objangle2 ; objangle1.sexagesimal("D")
        12.345
        '56d28m'
        '315d52m42.00s'
        """
        return self - angle

    def __eq__(self, angle):
        """ Comparaison of angles. Return True if angles are defined and equals.

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 == objangle2
        12.345
        '56d28m'
        False
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle, "==")

    def __ne__(self, angle):
        """ Comparaison of angles. Return True if angles are defined and not equals.

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 != objangle2
        12.345
        '56d28m'
        True
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle, "!=")

    def __gt__(self, angle):
        """ Comparaison of angles. Return True if self > angle

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 > objangle2
        12.345
        '56d28m'
        False
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle,">")
    
    def __ge__(self, angle):
        """ Comparaison of angles. Return True if self >= angle

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 >= objangle2
        12.345
        '56d28m'
        False
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle,">=")

    def __lt__(self, angle):
        """ Comparaison of angles. Return True if self < angle

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 < objangle2
        12.345
        '56d28m'
        True
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle,"<")
        
    def __le__(self, angle):
        """ Comparaison of angles. Return True if self <= angle

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: The logic result of the comparison.
        :rtype: bool
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(12.345) ; objangle2.angle("56d28m") ; objangle1 <= objangle2
        12.345
        '56d28m'
        True
        
        .. note:: Does not account for the modulo.
        """
        return self._angle_compare(angle,"<=")

    def __mod__(self, angle):
        """ Modulo of an angle by another angle. Return an angle

        :param angle : An angle in any supported format (cf. help(Angle))
        :type angle : Angle()
        :return: An angle
        :rtype: Angle()
        
        :Example:

        >>> objangle1 = Angle()
        >>> objangle2 = Angle()
        >>> objangle1.angle(30.56) ; objangle2.angle(2.34) ; (objangle1 % objangle2).deg()
        30.56
        2.34
        0.14000000000000412
        
        """
        if isinstance(angle, Angle) == False:
            angle =  Angle(angle)
        if self._computed_deg == 0:
            self.deg()
        if angle._computed_deg == 0:
            angle.deg()
        anglemod = Angle()
        if (self._computed_deg == 1) and (angle._computed_deg == 1):
            deg = math.fmod(self._deg, angle._deg)
            if (deg<0):
                deg += angle._deg
            anglemod.angle(deg)
        return anglemod

    def __mul__(self, multiplier):
        """ multiplication of an angle by a float or int. Return an angle

        :param multiplier: A real number
        :type multiplier: float
        :return: An angle
        :rtype: Angle()
        
        :Example:

        >>> objangle = Angle()
        >>> objangle.angle(30.43) ; (objangle*2).deg()
        30.43
        60.86000000000001
        
        """
        if isinstance(multiplier, (int, float)) == False:
            raise TypeError
            return ""
        if self._computed_deg == 0:
            self.deg()
        anglemult = Angle()
        if (self._computed_deg == 1):
            deg = self._deg * multiplier
            anglemult.angle(deg)
        return anglemult

    def __rmul__(self, multiplier):
        """ Right multiplication of an angle by a float or int.
        """
        return self * multiplier

    def __truediv__(self, divisor):
        """ division of an angle by a float or int. Return an angle

        :param divisor: A real number
        :type divisor: float
        :return: An angle
        :rtype: Angle()
        
        :Example:

        >>> objangle = Angle()
        >>> objangle.angle(30.43) ; (objangle/2).deg()
        30.43
        15.215000000000002
        
        """
        if isinstance(divisor, (int, float)) == False:
            raise TypeError
            return ""
        if (divisor==0):
            raise ZeroDivisionError
        if self._computed_deg == 0:
            self.deg()
        anglediv = Angle()
        if (self._computed_deg == 1):
            deg = self._deg / divisor
            anglediv.angle(deg)
        return anglediv

# ========================================================
# ========================================================
# ========================================================

# Examples of execution

if __name__ == "__main__":

    kex = 0
    print("==========================")
    print("=== Self documentation ===")
    print("==========================")

    kex+=1;
    print("\n=== Example {}: Simple conversion to degrees".format(kex))
    angle_inp = "2h3m27s"
    a = Angle(angle_inp)
    print("{} = {} degrees".format(angle_inp, a.deg()))
    assert a.deg() == 30.862499999999994

    kex+=1;
    print("\n=== Example {}: Simple conversion to radians".format(kex))
    angle_inp = "2h3m27s"
    a = Angle(angle_inp)
    print("{} = {} radians".format(angle_inp, a.rad()))
    assert a.rad() == 0.5386522403967499

    kex+=1;
    print("\n=== Example {}: Simple conversion to sexagesimal".format(kex))
    angle_inp = "2h3m27s"
    a = Angle(angle_inp)
    print("{} = {}".format(angle_inp, a.sexagesimal("H:0.2")))
    print("{} = {}".format(angle_inp, a.sexagesimal("d:+090.1")))
    res = a.sexagesimal("d+090.1")
    print("{} = {}".format(angle_inp, res))
    assert res == '+30d51m45.0s'

    kex+=1;
    print("\n=== Example {}: Addition of angles + format conversion".format(kex))
    angle_inp1 = "2h3m27s"
    angle_inp2 = "-0d28m12.4s"
    a = Angle(angle_inp1)
    b = Angle(angle_inp2)
    c = a + b
    res = c.sexagesimal("H0.2")
    print("{} + {} = {}".format(angle_inp1, angle_inp2, res))
    assert res == '02h01m34.17s'

    cl = "Angle"
    print("\n=== To perform unitary tests: {}().infos(\"doctest\")".format(cl))
    print("=== To list docs of all methods: {}().infos(\"doc_methods\")".format(cl))
    print("\n=== List of public methods using {}().infos(\"public_methods\"):".format(cl))
    Angle().infos("public_methods")