This file is indexed.

/usr/lib/python3/dist-packages/pyqtgraph/functions.py is in python3-pyqtgraph 0.10.0-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   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
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
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
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
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
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
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
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
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
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
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
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
# -*- coding: utf-8 -*-
"""
functions.py -  Miscellaneous functions with no other home
Copyright 2010  Luke Campagnola
Distributed under MIT/X11 license. See license.txt for more infomation.
"""

from __future__ import division
import warnings
import numpy as np
import decimal, re
import ctypes
import sys, struct
from .python2_3 import asUnicode, basestring
from .Qt import QtGui, QtCore, USE_PYSIDE
from . import getConfigOption, setConfigOptions
from . import debug



Colors = {
    'b': QtGui.QColor(0,0,255,255),
    'g': QtGui.QColor(0,255,0,255),
    'r': QtGui.QColor(255,0,0,255),
    'c': QtGui.QColor(0,255,255,255),
    'm': QtGui.QColor(255,0,255,255),
    'y': QtGui.QColor(255,255,0,255),
    'k': QtGui.QColor(0,0,0,255),
    'w': QtGui.QColor(255,255,255,255),
    'd': QtGui.QColor(150,150,150,255),
    'l': QtGui.QColor(200,200,200,255),
    's': QtGui.QColor(100,100,150,255),
}  

SI_PREFIXES = asUnicode('yzafpnµm kMGTPEZY')
SI_PREFIXES_ASCII = 'yzafpnum kMGTPEZY'




def siScale(x, minVal=1e-25, allowUnicode=True):
    """
    Return the recommended scale factor and SI prefix string for x.
    
    Example::
    
        siScale(0.0001)   # returns (1e6, 'μ')
        # This indicates that the number 0.0001 is best represented as 0.0001 * 1e6 = 100 μUnits
    """
    
    if isinstance(x, decimal.Decimal):
        x = float(x)
        
    try:
        if np.isnan(x) or np.isinf(x):
            return(1, '')
    except:
        print(x, type(x))
        raise
    if abs(x) < minVal:
        m = 0
        x = 0
    else:
        m = int(np.clip(np.floor(np.log(abs(x))/np.log(1000)), -9.0, 9.0))
    
    if m == 0:
        pref = ''
    elif m < -8 or m > 8:
        pref = 'e%d' % (m*3)
    else:
        if allowUnicode:
            pref = SI_PREFIXES[m+8]
        else:
            pref = SI_PREFIXES_ASCII[m+8]
    p = .001**m
    
    return (p, pref)    

def siFormat(x, precision=3, suffix='', space=True, error=None, minVal=1e-25, allowUnicode=True):
    """
    Return the number x formatted in engineering notation with SI prefix.
    
    Example::
        siFormat(0.0001, suffix='V')  # returns "100 μV"
    """
    
    if space is True:
        space = ' '
    if space is False:
        space = ''
        
    
    (p, pref) = siScale(x, minVal, allowUnicode)
    if not (len(pref) > 0 and pref[0] == 'e'):
        pref = space + pref
    
    if error is None:
        fmt = "%." + str(precision) + "g%s%s"
        return fmt % (x*p, pref, suffix)
    else:
        if allowUnicode:
            plusminus = space + asUnicode("±") + space
        else:
            plusminus = " +/- "
        fmt = "%." + str(precision) + "g%s%s%s%s"
        return fmt % (x*p, pref, suffix, plusminus, siFormat(error, precision=precision, suffix=suffix, space=space, minVal=minVal))
    
def siEval(s):
    """
    Convert a value written in SI notation to its equivalent prefixless value
    
    Example::
    
        siEval("100 μV")  # returns 0.0001
    """
    
    s = asUnicode(s)
    m = re.match(r'(-?((\d+(\.\d*)?)|(\.\d+))([eE]-?\d+)?)\s*([u' + SI_PREFIXES + r']?).*$', s)
    if m is None:
        raise Exception("Can't convert string '%s' to number." % s)
    v = float(m.groups()[0])
    p = m.groups()[6]
    #if p not in SI_PREFIXES:
        #raise Exception("Can't convert string '%s' to number--unknown prefix." % s)
    if p ==  '':
        n = 0
    elif p == 'u':
        n = -2
    else:
        n = SI_PREFIXES.index(p) - 8
    return v * 1000**n
    

class Color(QtGui.QColor):
    def __init__(self, *args):
        QtGui.QColor.__init__(self, mkColor(*args))
        
    def glColor(self):
        """Return (r,g,b,a) normalized for use in opengl"""
        return (self.red()/255., self.green()/255., self.blue()/255., self.alpha()/255.)
        
    def __getitem__(self, ind):
        return (self.red, self.green, self.blue, self.alpha)[ind]()
        
    
def mkColor(*args):
    """
    Convenience function for constructing QColor from a variety of argument types. Accepted arguments are:
    
    ================ ================================================
     'c'             one of: r, g, b, c, m, y, k, w                      
     R, G, B, [A]    integers 0-255
     (R, G, B, [A])  tuple of integers 0-255
     float           greyscale, 0.0-1.0
     int             see :func:`intColor() <pyqtgraph.intColor>`
     (int, hues)     see :func:`intColor() <pyqtgraph.intColor>`
     "RGB"           hexadecimal strings; may begin with '#'
     "RGBA"          
     "RRGGBB"       
     "RRGGBBAA"     
     QColor          QColor instance; makes a copy.
    ================ ================================================
    """
    err = 'Not sure how to make a color from "%s"' % str(args)
    if len(args) == 1:
        if isinstance(args[0], basestring):
            c = args[0]
            if c[0] == '#':
                c = c[1:]
            if len(c) == 1:
                try:
                    return Colors[c]
                except KeyError:
                    raise Exception('No color named "%s"' % c)
            if len(c) == 3:
                r = int(c[0]*2, 16)
                g = int(c[1]*2, 16)
                b = int(c[2]*2, 16)
                a = 255
            elif len(c) == 4:
                r = int(c[0]*2, 16)
                g = int(c[1]*2, 16)
                b = int(c[2]*2, 16)
                a = int(c[3]*2, 16)
            elif len(c) == 6:
                r = int(c[0:2], 16)
                g = int(c[2:4], 16)
                b = int(c[4:6], 16)
                a = 255
            elif len(c) == 8:
                r = int(c[0:2], 16)
                g = int(c[2:4], 16)
                b = int(c[4:6], 16)
                a = int(c[6:8], 16)
        elif isinstance(args[0], QtGui.QColor):
            return QtGui.QColor(args[0])
        elif isinstance(args[0], float):
            r = g = b = int(args[0] * 255)
            a = 255
        elif hasattr(args[0], '__len__'):
            if len(args[0]) == 3:
                (r, g, b) = args[0]
                a = 255
            elif len(args[0]) == 4:
                (r, g, b, a) = args[0]
            elif len(args[0]) == 2:
                return intColor(*args[0])
            else:
                raise Exception(err)
        elif type(args[0]) == int:
            return intColor(args[0])
        else:
            raise Exception(err)
    elif len(args) == 3:
        (r, g, b) = args
        a = 255
    elif len(args) == 4:
        (r, g, b, a) = args
    else:
        raise Exception(err)
    
    args = [r,g,b,a]
    args = [0 if np.isnan(a) or np.isinf(a) else a for a in args]
    args = list(map(int, args))
    return QtGui.QColor(*args)


def mkBrush(*args, **kwds):
    """
    | Convenience function for constructing Brush.
    | This function always constructs a solid brush and accepts the same arguments as :func:`mkColor() <pyqtgraph.mkColor>`
    | Calling mkBrush(None) returns an invisible brush.
    """
    if 'color' in kwds:
        color = kwds['color']
    elif len(args) == 1:
        arg = args[0]
        if arg is None:
            return QtGui.QBrush(QtCore.Qt.NoBrush)
        elif isinstance(arg, QtGui.QBrush):
            return QtGui.QBrush(arg)
        else:
            color = arg
    elif len(args) > 1:
        color = args
    return QtGui.QBrush(mkColor(color))


def mkPen(*args, **kargs):
    """
    Convenience function for constructing QPen. 
    
    Examples::
    
        mkPen(color)
        mkPen(color, width=2)
        mkPen(cosmetic=False, width=4.5, color='r')
        mkPen({'color': "FF0", width: 2})
        mkPen(None)   # (no pen)
    
    In these examples, *color* may be replaced with any arguments accepted by :func:`mkColor() <pyqtgraph.mkColor>`    """
    
    color = kargs.get('color', None)
    width = kargs.get('width', 1)
    style = kargs.get('style', None)
    dash = kargs.get('dash', None)
    cosmetic = kargs.get('cosmetic', True)
    hsv = kargs.get('hsv', None)
    
    if len(args) == 1:
        arg = args[0]
        if isinstance(arg, dict):
            return mkPen(**arg)
        if isinstance(arg, QtGui.QPen):
            return QtGui.QPen(arg)  ## return a copy of this pen
        elif arg is None:
            style = QtCore.Qt.NoPen
        else:
            color = arg
    if len(args) > 1:
        color = args
        
    if color is None:
        color = mkColor('l')
    if hsv is not None:
        color = hsvColor(*hsv)
    else:
        color = mkColor(color)
        
    pen = QtGui.QPen(QtGui.QBrush(color), width)
    pen.setCosmetic(cosmetic)
    if style is not None:
        pen.setStyle(style)
    if dash is not None:
        pen.setDashPattern(dash)
    return pen


def hsvColor(hue, sat=1.0, val=1.0, alpha=1.0):
    """Generate a QColor from HSVa values. (all arguments are float 0.0-1.0)"""
    c = QtGui.QColor()
    c.setHsvF(hue, sat, val, alpha)
    return c

    
def colorTuple(c):
    """Return a tuple (R,G,B,A) from a QColor"""
    return (c.red(), c.green(), c.blue(), c.alpha())


def colorStr(c):
    """Generate a hex string code from a QColor"""
    return ('%02x'*4) % colorTuple(c)


def intColor(index, hues=9, values=1, maxValue=255, minValue=150, maxHue=360, minHue=0, sat=255, alpha=255, **kargs):
    """
    Creates a QColor from a single index. Useful for stepping through a predefined list of colors.
    
    The argument *index* determines which color from the set will be returned. All other arguments determine what the set of predefined colors will be
     
    Colors are chosen by cycling across hues while varying the value (brightness). 
    By default, this selects from a list of 9 hues."""
    hues = int(hues)
    values = int(values)
    ind = int(index) % (hues * values)
    indh = ind % hues
    indv = ind / hues
    if values > 1:
        v = minValue + indv * ((maxValue-minValue) / (values-1))
    else:
        v = maxValue
    h = minHue + (indh * (maxHue-minHue)) / hues
    
    c = QtGui.QColor()
    c.setHsv(h, sat, v)
    c.setAlpha(alpha)
    return c


def glColor(*args, **kargs):
    """
    Convert a color to OpenGL color format (r,g,b,a) floats 0.0-1.0
    Accepts same arguments as :func:`mkColor <pyqtgraph.mkColor>`.
    """
    c = mkColor(*args, **kargs)
    return (c.red()/255., c.green()/255., c.blue()/255., c.alpha()/255.)

    

def makeArrowPath(headLen=20, tipAngle=20, tailLen=20, tailWidth=3, baseAngle=0):
    """
    Construct a path outlining an arrow with the given dimensions.
    The arrow points in the -x direction with tip positioned at 0,0.
    If *tipAngle* is supplied (in degrees), it overrides *headWidth*.
    If *tailLen* is None, no tail will be drawn.
    """
    headWidth = headLen * np.tan(tipAngle * 0.5 * np.pi/180.)
    path = QtGui.QPainterPath()
    path.moveTo(0,0)
    path.lineTo(headLen, -headWidth)
    if tailLen is None:
        innerY = headLen - headWidth * np.tan(baseAngle*np.pi/180.)
        path.lineTo(innerY, 0)
    else:
        tailWidth *= 0.5
        innerY = headLen - (headWidth-tailWidth) * np.tan(baseAngle*np.pi/180.)
        path.lineTo(innerY, -tailWidth)
        path.lineTo(headLen + tailLen, -tailWidth)
        path.lineTo(headLen + tailLen, tailWidth)
        path.lineTo(innerY, tailWidth)
    path.lineTo(headLen, headWidth)
    path.lineTo(0,0)
    return path
    
    
def eq(a, b):
    """The great missing equivalence function: Guaranteed evaluation to a single bool value."""
    if a is b:
        return True
        
    try:
        with warnings.catch_warnings(module=np):  # ignore numpy futurewarning (numpy v. 1.10)
            e = a==b
    except ValueError:
        return False
    except AttributeError: 
        return False
    except:
        print('failed to evaluate equivalence for:')
        print("  a:", str(type(a)), str(a))
        print("  b:", str(type(b)), str(b))
        raise
    t = type(e)
    if t is bool:
        return e
    elif t is np.bool_:
        return bool(e)
    elif isinstance(e, np.ndarray) or (hasattr(e, 'implements') and e.implements('MetaArray')):
        try:   ## disaster: if a is an empty array and b is not, then e.all() is True
            if a.shape != b.shape:
                return False
        except:
            return False
        if (hasattr(e, 'implements') and e.implements('MetaArray')):
            return e.asarray().all()
        else:
            return e.all()
    else:
        raise Exception("== operator returned type %s" % str(type(e)))

    
def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False, **kargs):
    """
    Take a slice of any orientation through an array. This is useful for extracting sections of multi-dimensional arrays such as MRI images for viewing as 1D or 2D data.
    
    The slicing axes are aribtrary; they do not need to be orthogonal to the original data or even to each other. It is possible to use this function to extract arbitrary linear, rectangular, or parallelepiped shapes from within larger datasets. The original data is interpolated onto a new array of coordinates using scipy.ndimage.map_coordinates if it is available (see the scipy documentation for more information about this). If scipy is not available, then a slower implementation of map_coordinates is used.
    
    For a graphical interface to this function, see :func:`ROI.getArrayRegion <pyqtgraph.ROI.getArrayRegion>`
    
    ==============  ====================================================================================================
    **Arguments:**
    *data*          (ndarray) the original dataset
    *shape*         the shape of the slice to take (Note the return value may have more dimensions than len(shape))
    *origin*        the location in the original dataset that will become the origin of the sliced data.
    *vectors*       list of unit vectors which point in the direction of the slice axes. Each vector must have the same 
                    length as *axes*. If the vectors are not unit length, the result will be scaled relative to the 
                    original data. If the vectors are not orthogonal, the result will be sheared relative to the 
                    original data.
    *axes*          The axes in the original dataset which correspond to the slice *vectors*
    *order*         The order of spline interpolation. Default is 1 (linear). See scipy.ndimage.map_coordinates
                    for more information.
    *returnCoords*  If True, return a tuple (result, coords) where coords is the array of coordinates used to select
                    values from the original dataset.
    *All extra keyword arguments are passed to scipy.ndimage.map_coordinates.*
    --------------------------------------------------------------------------------------------------------------------
    ==============  ====================================================================================================
    
    Note the following must be true: 
        
        | len(shape) == len(vectors) 
        | len(origin) == len(axes) == len(vectors[i])
        
    Example: start with a 4D fMRI data set, take a diagonal-planar slice out of the last 3 axes
        
        * data = array with dims (time, x, y, z) = (100, 40, 40, 40)
        * The plane to pull out is perpendicular to the vector (x,y,z) = (1,1,1) 
        * The origin of the slice will be at (x,y,z) = (40, 0, 0)
        * We will slice a 20x20 plane from each timepoint, giving a final shape (100, 20, 20)
        
    The call for this example would look like::
        
        affineSlice(data, shape=(20,20), origin=(40,0,0), vectors=((-1, 1, 0), (-1, 0, 1)), axes=(1,2,3))
    
    """
    try:
        import scipy.ndimage
        have_scipy = True
    except ImportError:
        have_scipy = False
    have_scipy = False

    # sanity check
    if len(shape) != len(vectors):
        raise Exception("shape and vectors must have same length.")
    if len(origin) != len(axes):
        raise Exception("origin and axes must have same length.")
    for v in vectors:
        if len(v) != len(axes):
            raise Exception("each vector must be same length as axes.")
        
    shape = list(map(np.ceil, shape))

    ## transpose data so slice axes come first
    trAx = list(range(data.ndim))
    for x in axes:
        trAx.remove(x)
    tr1 = tuple(axes) + tuple(trAx)
    data = data.transpose(tr1)
    #print "tr1:", tr1
    ## dims are now [(slice axes), (other axes)]
    
    ## make sure vectors are arrays
    if not isinstance(vectors, np.ndarray):
        vectors = np.array(vectors)
    if not isinstance(origin, np.ndarray):
        origin = np.array(origin)
    origin.shape = (len(axes),) + (1,)*len(shape)
    
    ## Build array of sample locations. 
    grid = np.mgrid[tuple([slice(0,x) for x in shape])]  ## mesh grid of indexes
    x = (grid[np.newaxis,...] * vectors.transpose()[(Ellipsis,) + (np.newaxis,)*len(shape)]).sum(axis=1)  ## magic
    x += origin

    ## iterate manually over unused axes since map_coordinates won't do it for us
    if have_scipy:
        extraShape = data.shape[len(axes):]
        output = np.empty(tuple(shape) + extraShape, dtype=data.dtype)
        for inds in np.ndindex(*extraShape):
            ind = (Ellipsis,) + inds
            output[ind] = scipy.ndimage.map_coordinates(data[ind], x, order=order, **kargs)
    else:
        # map_coordinates expects the indexes as the first axis, whereas
        # interpolateArray expects indexes at the last axis. 
        tr = tuple(range(1,x.ndim)) + (0,)
        output = interpolateArray(data, x.transpose(tr))
    
    tr = list(range(output.ndim))
    trb = []
    for i in range(min(axes)):
        ind = tr1.index(i) + (len(shape)-len(axes))
        tr.remove(ind)
        trb.append(ind)
    tr2 = tuple(trb+tr)

    ## Untranspose array before returning
    output = output.transpose(tr2)
    if returnCoords:
        return (output, x)
    else:
        return output

def interpolateArray(data, x, default=0.0):
    """
    N-dimensional interpolation similar to scipy.ndimage.map_coordinates.
    
    This function returns linearly-interpolated values sampled from a regular
    grid of data. 
    
    *data* is an array of any shape containing the values to be interpolated.
    *x* is an array with (shape[-1] <= data.ndim) containing the locations
        within *data* to interpolate. 
    
    Returns array of shape (x.shape[:-1] + data.shape[x.shape[-1]:])
    
    For example, assume we have the following 2D image data::
    
        >>> data = np.array([[1,   2,   4  ],
                             [10,  20,  40 ],
                             [100, 200, 400]])
        
    To compute a single interpolated point from this data::
        
        >>> x = np.array([(0.5, 0.5)])
        >>> interpolateArray(data, x)
        array([ 8.25])
        
    To compute a 1D list of interpolated locations:: 
        
        >>> x = np.array([(0.5, 0.5),
                          (1.0, 1.0),
                          (1.0, 2.0),
                          (1.5, 0.0)])
        >>> interpolateArray(data, x)
        array([  8.25,  20.  ,  40.  ,  55.  ])
        
    To compute a 2D array of interpolated locations::
    
        >>> x = np.array([[(0.5, 0.5), (1.0, 2.0)],
                          [(1.0, 1.0), (1.5, 0.0)]])
        >>> interpolateArray(data, x)
        array([[  8.25,  40.  ],
               [ 20.  ,  55.  ]])
               
    ..and so on. The *x* argument may have any shape as long as 
    ```x.shape[-1] <= data.ndim```. In the case that 
    ```x.shape[-1] < data.ndim```, then the remaining axes are simply 
    broadcasted as usual. For example, we can interpolate one location
    from an entire row of the data::
    
        >>> x = np.array([[0.5]])
        >>> interpolateArray(data, x)
        array([[  5.5,  11. ,  22. ]])

    This is useful for interpolating from arrays of colors, vertexes, etc.
    """
    prof = debug.Profiler()
    
    nd = data.ndim
    md = x.shape[-1]
    if md > nd:
        raise TypeError("x.shape[-1] must be less than or equal to data.ndim")

    # First we generate arrays of indexes that are needed to 
    # extract the data surrounding each point
    fields = np.mgrid[(slice(0,2),) * md]
    xmin = np.floor(x).astype(int)
    xmax = xmin + 1
    indexes = np.concatenate([xmin[np.newaxis, ...], xmax[np.newaxis, ...]])
    fieldInds = []
    totalMask = np.ones(x.shape[:-1], dtype=bool) # keep track of out-of-bound indexes
    for ax in range(md):
        mask = (xmin[...,ax] >= 0) & (x[...,ax] <= data.shape[ax]-1) 
        # keep track of points that need to be set to default
        totalMask &= mask
        
        # ..and keep track of indexes that are out of bounds 
        # (note that when x[...,ax] == data.shape[ax], then xmax[...,ax] will be out
        #  of bounds, but the interpolation will work anyway)
        mask &= (xmax[...,ax] < data.shape[ax])
        axisIndex = indexes[...,ax][fields[ax]]
        axisIndex[axisIndex < 0] = 0
        axisIndex[axisIndex >= data.shape[ax]] = 0
        fieldInds.append(axisIndex)
    prof()

    # Get data values surrounding each requested point
    fieldData = data[tuple(fieldInds)]
    prof()
    
    ## Interpolate
    s = np.empty((md,) + fieldData.shape, dtype=float)
    dx = x - xmin
    # reshape fields for arithmetic against dx
    for ax in range(md):
        f1 = fields[ax].reshape(fields[ax].shape + (1,)*(dx.ndim-1))
        sax = f1 * dx[...,ax] + (1-f1) * (1-dx[...,ax])
        sax = sax.reshape(sax.shape + (1,) * (s.ndim-1-sax.ndim))
        s[ax] = sax
    s = np.product(s, axis=0)
    result = fieldData * s
    for i in range(md):
        result = result.sum(axis=0)

    prof()

    if totalMask.ndim > 0:
        result[~totalMask] = default
    else:
        if totalMask is False:
            result[:] = default

    prof()
    return result


def subArray(data, offset, shape, stride):
    """
    Unpack a sub-array from *data* using the specified offset, shape, and stride.
    
    Note that *stride* is specified in array elements, not bytes.
    For example, we have a 2x3 array packed in a 1D array as follows::
    
        data = [_, _, 00, 01, 02, _, 10, 11, 12, _]
        
    Then we can unpack the sub-array with this call::
    
        subArray(data, offset=2, shape=(2, 3), stride=(4, 1))
        
    ..which returns::
    
        [[00, 01, 02],
         [10, 11, 12]]
         
    This function operates only on the first axis of *data*. So changing 
    the input in the example above to have shape (10, 7) would cause the
    output to have shape (2, 3, 7).
    """
    #data = data.flatten()
    data = data[offset:]
    shape = tuple(shape)
    stride = tuple(stride)
    extraShape = data.shape[1:]
    #print data.shape, offset, shape, stride
    for i in range(len(shape)):
        mask = (slice(None),) * i + (slice(None, shape[i] * stride[i]),)
        newShape = shape[:i+1]
        if i < len(shape)-1:
            newShape += (stride[i],)
        newShape += extraShape 
        #print i, mask, newShape
        #print "start:\n", data.shape, data
        data = data[mask]
        #print "mask:\n", data.shape, data
        data = data.reshape(newShape)
        #print "reshape:\n", data.shape, data
    
    return data


def transformToArray(tr):
    """
    Given a QTransform, return a 3x3 numpy array.
    Given a QMatrix4x4, return a 4x4 numpy array.
    
    Example: map an array of x,y coordinates through a transform::
    
        ## coordinates to map are (1,5), (2,6), (3,7), and (4,8)
        coords = np.array([[1,2,3,4], [5,6,7,8], [1,1,1,1]])  # the extra '1' coordinate is needed for translation to work
        
        ## Make an example transform
        tr = QtGui.QTransform()
        tr.translate(3,4)
        tr.scale(2, 0.1)
        
        ## convert to array
        m = pg.transformToArray()[:2]  # ignore the perspective portion of the transformation
        
        ## map coordinates through transform
        mapped = np.dot(m, coords)
    """
    #return np.array([[tr.m11(), tr.m12(), tr.m13()],[tr.m21(), tr.m22(), tr.m23()],[tr.m31(), tr.m32(), tr.m33()]])
    ## The order of elements given by the method names m11..m33 is misleading--
    ## It is most common for x,y translation to occupy the positions 1,3 and 2,3 in
    ## a transformation matrix. However, with QTransform these values appear at m31 and m32.
    ## So the correct interpretation is transposed:
    if isinstance(tr, QtGui.QTransform):
        return np.array([[tr.m11(), tr.m21(), tr.m31()], [tr.m12(), tr.m22(), tr.m32()], [tr.m13(), tr.m23(), tr.m33()]])
    elif isinstance(tr, QtGui.QMatrix4x4):
        return np.array(tr.copyDataTo()).reshape(4,4)
    else:
        raise Exception("Transform argument must be either QTransform or QMatrix4x4.")

def transformCoordinates(tr, coords, transpose=False):
    """
    Map a set of 2D or 3D coordinates through a QTransform or QMatrix4x4.
    The shape of coords must be (2,...) or (3,...)
    The mapping will _ignore_ any perspective transformations.
    
    For coordinate arrays with ndim=2, this is basically equivalent to matrix multiplication.
    Most arrays, however, prefer to put the coordinate axis at the end (eg. shape=(...,3)). To 
    allow this, use transpose=True.
    
    """
    
    if transpose:
        ## move last axis to beginning. This transposition will be reversed before returning the mapped coordinates.
        coords = coords.transpose((coords.ndim-1,) + tuple(range(0,coords.ndim-1)))
    
    nd = coords.shape[0]
    if isinstance(tr, np.ndarray):
        m = tr
    else:
        m = transformToArray(tr)
        m = m[:m.shape[0]-1]  # remove perspective
    
    ## If coords are 3D and tr is 2D, assume no change for Z axis
    if m.shape == (2,3) and nd == 3:
        m2 = np.zeros((3,4))
        m2[:2, :2] = m[:2,:2]
        m2[:2, 3] = m[:2,2]
        m2[2,2] = 1
        m = m2
    
    ## if coords are 2D and tr is 3D, ignore Z axis
    if m.shape == (3,4) and nd == 2:
        m2 = np.empty((2,3))
        m2[:,:2] = m[:2,:2]
        m2[:,2] = m[:2,3]
        m = m2
    
    ## reshape tr and coords to prepare for multiplication
    m = m.reshape(m.shape + (1,)*(coords.ndim-1))
    coords = coords[np.newaxis, ...]
    
    # separate scale/rotate and translation    
    translate = m[:,-1]  
    m = m[:, :-1]
    
    ## map coordinates and return
    mapped = (m*coords).sum(axis=1)  ## apply scale/rotate
    mapped += translate
    
    if transpose:
        ## move first axis to end.
        mapped = mapped.transpose(tuple(range(1,mapped.ndim)) + (0,))
    return mapped
    
    

    
def solve3DTransform(points1, points2):
    """
    Find a 3D transformation matrix that maps points1 onto points2.
    Points must be specified as either lists of 4 Vectors or 
    (4, 3) arrays.
    """
    import numpy.linalg
    pts = []
    for inp in (points1, points2):
        if isinstance(inp, np.ndarray):
            A = np.empty((4,4), dtype=float)
            A[:,:3] = inp[:,:3]
            A[:,3] = 1.0
        else:
            A = np.array([[inp[i].x(), inp[i].y(), inp[i].z(), 1] for i in range(4)])
        pts.append(A)
    
    ## solve 3 sets of linear equations to determine transformation matrix elements
    matrix = np.zeros((4,4))
    for i in range(3):
        ## solve Ax = B; x is one row of the desired transformation matrix
        matrix[i] = numpy.linalg.solve(pts[0], pts[1][:,i])  
    
    return matrix
    
def solveBilinearTransform(points1, points2):
    """
    Find a bilinear transformation matrix (2x4) that maps points1 onto points2.
    Points must be specified as a list of 4 Vector, Point, QPointF, etc.
    
    To use this matrix to map a point [x,y]::
    
        mapped = np.dot(matrix, [x*y, x, y, 1])
    """
    import numpy.linalg
    ## A is 4 rows (points) x 4 columns (xy, x, y, 1)
    ## B is 4 rows (points) x 2 columns (x, y)
    A = np.array([[points1[i].x()*points1[i].y(), points1[i].x(), points1[i].y(), 1] for i in range(4)])
    B = np.array([[points2[i].x(), points2[i].y()] for i in range(4)])
    
    ## solve 2 sets of linear equations to determine transformation matrix elements
    matrix = np.zeros((2,4))
    for i in range(2):
        matrix[i] = numpy.linalg.solve(A, B[:,i])  ## solve Ax = B; x is one row of the desired transformation matrix
    
    return matrix
    
def rescaleData(data, scale, offset, dtype=None, clip=None):
    """Return data rescaled and optionally cast to a new dtype::
    
        data => (data-offset) * scale
        
    """
    if dtype is None:
        dtype = data.dtype
    else:
        dtype = np.dtype(dtype)
    
    try:
        if not getConfigOption('useWeave'):
            raise Exception('Weave is disabled; falling back to slower version.')
        try:
            import scipy.weave
        except ImportError:
            raise Exception('scipy.weave is not importable; falling back to slower version.')
        
        ## require native dtype when using weave
        if not data.dtype.isnative:
            data = data.astype(data.dtype.newbyteorder('='))
        if not dtype.isnative:
            weaveDtype = dtype.newbyteorder('=')
        else:
            weaveDtype = dtype
        
        newData = np.empty((data.size,), dtype=weaveDtype)
        flat = np.ascontiguousarray(data).reshape(data.size)
        size = data.size
        
        code = """
        double sc = (double)scale;
        double off = (double)offset;
        for( int i=0; i<size; i++ ) {
            newData[i] = ((double)flat[i] - off) * sc;
        }
        """
        scipy.weave.inline(code, ['flat', 'newData', 'size', 'offset', 'scale'], compiler='gcc')
        if dtype != weaveDtype:
            newData = newData.astype(dtype)
        data = newData.reshape(data.shape)
    except:
        if getConfigOption('useWeave'):
            if getConfigOption('weaveDebug'):
                debug.printExc("Error; disabling weave.")
            setConfigOptions(useWeave=False)
        
        #p = np.poly1d([scale, -offset*scale])
        #d2 = p(data)
        d2 = data - float(offset)
        d2 *= scale
        
        # Clip before converting dtype to avoid overflow
        if dtype.kind in 'ui':
            lim = np.iinfo(dtype)
            if clip is None:
                # don't let rescale cause integer overflow
                d2 = np.clip(d2, lim.min, lim.max)
            else:
                d2 = np.clip(d2, max(clip[0], lim.min), min(clip[1], lim.max))
        else:
            if clip is not None:
                d2 = np.clip(d2, *clip)
        data = d2.astype(dtype)
    return data
    
def applyLookupTable(data, lut):
    """
    Uses values in *data* as indexes to select values from *lut*.
    The returned data has shape data.shape + lut.shape[1:]
    
    Note: color gradient lookup tables can be generated using GradientWidget.
    """
    if data.dtype.kind not in ('i', 'u'):
        data = data.astype(int)
    
    return np.take(lut, data, axis=0, mode='clip')  
    

def makeRGBA(*args, **kwds):
    """Equivalent to makeARGB(..., useRGBA=True)"""
    kwds['useRGBA'] = True
    return makeARGB(*args, **kwds)


def makeARGB(data, lut=None, levels=None, scale=None, useRGBA=False): 
    """ 
    Convert an array of values into an ARGB array suitable for building QImages,
    OpenGL textures, etc.
    
    Returns the ARGB array (unsigned byte) and a boolean indicating whether
    there is alpha channel data. This is a two stage process:
    
        1) Rescale the data based on the values in the *levels* argument (min, max).
        2) Determine the final output by passing the rescaled values through a
           lookup table.
   
    Both stages are optional.
    
    ============== ==================================================================================
    **Arguments:**
    data           numpy array of int/float types. If 
    levels         List [min, max]; optionally rescale data before converting through the
                   lookup table. The data is rescaled such that min->0 and max->*scale*::
                   
                      rescaled = (clip(data, min, max) - min) * (*scale* / (max - min))
                   
                   It is also possible to use a 2D (N,2) array of values for levels. In this case,
                   it is assumed that each pair of min,max values in the levels array should be 
                   applied to a different subset of the input data (for example, the input data may 
                   already have RGB values and the levels are used to independently scale each 
                   channel). The use of this feature requires that levels.shape[0] == data.shape[-1].
    scale          The maximum value to which data will be rescaled before being passed through the 
                   lookup table (or returned if there is no lookup table). By default this will
                   be set to the length of the lookup table, or 255 if no lookup table is provided.
    lut            Optional lookup table (array with dtype=ubyte).
                   Values in data will be converted to color by indexing directly from lut.
                   The output data shape will be input.shape + lut.shape[1:].
                   Lookup tables can be built using ColorMap or GradientWidget.
    useRGBA        If True, the data is returned in RGBA order (useful for building OpenGL textures). 
                   The default is False, which returns in ARGB order for use with QImage 
                   (Note that 'ARGB' is a term used by the Qt documentation; the *actual* order 
                   is BGRA).
    ============== ==================================================================================
    """
    profile = debug.Profiler()

    if data.ndim not in (2, 3):
        raise TypeError("data must be 2D or 3D")
    if data.ndim == 3 and data.shape[2] > 4:
        raise TypeError("data.shape[2] must be <= 4")
    
    if lut is not None and not isinstance(lut, np.ndarray):
        lut = np.array(lut)
    
    if levels is None:
        # automatically decide levels based on data dtype
        if data.dtype.kind == 'u':
            levels = np.array([0, 2**(data.itemsize*8)-1])
        elif data.dtype.kind == 'i':
            s = 2**(data.itemsize*8 - 1)
            levels = np.array([-s, s-1])
        elif data.dtype.kind == 'b':
            levels = np.array([0,1])
        else:
            raise Exception('levels argument is required for float input types')
    if not isinstance(levels, np.ndarray):
        levels = np.array(levels)
    if levels.ndim == 1:
        if levels.shape[0] != 2:
            raise Exception('levels argument must have length 2')
    elif levels.ndim == 2:
        if lut is not None and lut.ndim > 1:
            raise Exception('Cannot make ARGB data when both levels and lut have ndim > 2')
        if levels.shape != (data.shape[-1], 2):
            raise Exception('levels must have shape (data.shape[-1], 2)')
    else:
        raise Exception("levels argument must be 1D or 2D (got shape=%s)." % repr(levels.shape))

    profile()

    # Decide on maximum scaled value
    if scale is None:
        if lut is not None:
            scale = lut.shape[0] - 1
        else:
            scale = 255.

    # Decide on the dtype we want after scaling
    if lut is None:
        dtype = np.ubyte
    else:
        dtype = np.min_scalar_type(lut.shape[0]-1)
            
    # Apply levels if given
    if levels is not None:
        if isinstance(levels, np.ndarray) and levels.ndim == 2:
            # we are going to rescale each channel independently
            if levels.shape[0] != data.shape[-1]:
                raise Exception("When rescaling multi-channel data, there must be the same number of levels as channels (data.shape[-1] == levels.shape[0])")
            newData = np.empty(data.shape, dtype=int)
            for i in range(data.shape[-1]):
                minVal, maxVal = levels[i]
                if minVal == maxVal:
                    maxVal += 1e-16
                newData[...,i] = rescaleData(data[...,i], scale/(maxVal-minVal), minVal, dtype=dtype)
            data = newData
        else:
            # Apply level scaling unless it would have no effect on the data
            minVal, maxVal = levels
            if minVal != 0 or maxVal != scale:
                if minVal == maxVal:
                    maxVal += 1e-16
                data = rescaleData(data, scale/(maxVal-minVal), minVal, dtype=dtype)
            

    profile()

    # apply LUT if given
    if lut is not None:
        data = applyLookupTable(data, lut)
    else:
        if data.dtype is not np.ubyte:
            data = np.clip(data, 0, 255).astype(np.ubyte)

    profile()

    # this will be the final image array
    imgData = np.empty(data.shape[:2]+(4,), dtype=np.ubyte)

    profile()

    # decide channel order
    if useRGBA:
        order = [0,1,2,3] # array comes out RGBA
    else:
        order = [2,1,0,3] # for some reason, the colors line up as BGR in the final image.
        
    # copy data into image array
    if data.ndim == 2:
        # This is tempting:
        #   imgData[..., :3] = data[..., np.newaxis]
        # ..but it turns out this is faster:
        for i in range(3):
            imgData[..., i] = data
    elif data.shape[2] == 1:
        for i in range(3):
            imgData[..., i] = data[..., 0]
    else:
        for i in range(0, data.shape[2]):
            imgData[..., i] = data[..., order[i]] 
        
    profile()
    
    # add opaque alpha channel if needed
    if data.ndim == 2 or data.shape[2] == 3:
        alpha = False
        imgData[..., 3] = 255
    else:
        alpha = True
        
    profile()
    return imgData, alpha


def makeQImage(imgData, alpha=None, copy=True, transpose=True):
    """
    Turn an ARGB array into QImage.
    By default, the data is copied; changes to the array will not
    be reflected in the image. The image will be given a 'data' attribute
    pointing to the array which shares its data to prevent python
    freeing that memory while the image is in use.
    
    ============== ===================================================================
    **Arguments:**
    imgData        Array of data to convert. Must have shape (width, height, 3 or 4) 
                   and dtype=ubyte. The order of values in the 3rd axis must be 
                   (b, g, r, a).
    alpha          If True, the QImage returned will have format ARGB32. If False,
                   the format will be RGB32. By default, _alpha_ is True if
                   array.shape[2] == 4.
    copy           If True, the data is copied before converting to QImage.
                   If False, the new QImage points directly to the data in the array.
                   Note that the array must be contiguous for this to work
                   (see numpy.ascontiguousarray).
    transpose      If True (the default), the array x/y axes are transposed before 
                   creating the image. Note that Qt expects the axes to be in 
                   (height, width) order whereas pyqtgraph usually prefers the 
                   opposite.
    ============== ===================================================================    
    """
    ## create QImage from buffer
    profile = debug.Profiler()
    
    ## If we didn't explicitly specify alpha, check the array shape.
    if alpha is None:
        alpha = (imgData.shape[2] == 4)
        
    copied = False
    if imgData.shape[2] == 3:  ## need to make alpha channel (even if alpha==False; QImage requires 32 bpp)
        if copy is True:
            d2 = np.empty(imgData.shape[:2] + (4,), dtype=imgData.dtype)
            d2[:,:,:3] = imgData
            d2[:,:,3] = 255
            imgData = d2
            copied = True
        else:
            raise Exception('Array has only 3 channels; cannot make QImage without copying.')
    
    if alpha:
        imgFormat = QtGui.QImage.Format_ARGB32
    else:
        imgFormat = QtGui.QImage.Format_RGB32
        
    if transpose:
        imgData = imgData.transpose((1, 0, 2))  ## QImage expects the row/column order to be opposite

    profile()

    if not imgData.flags['C_CONTIGUOUS']:
        if copy is False:
            extra = ' (try setting transpose=False)' if transpose else ''
            raise Exception('Array is not contiguous; cannot make QImage without copying.'+extra)
        imgData = np.ascontiguousarray(imgData)
        copied = True
        
    if copy is True and copied is False:
        imgData = imgData.copy()
        
    if USE_PYSIDE:
        ch = ctypes.c_char.from_buffer(imgData, 0)
        img = QtGui.QImage(ch, imgData.shape[1], imgData.shape[0], imgFormat)
    else:
        #addr = ctypes.addressof(ctypes.c_char.from_buffer(imgData, 0))
        ## PyQt API for QImage changed between 4.9.3 and 4.9.6 (I don't know exactly which version it was)
        ## So we first attempt the 4.9.6 API, then fall back to 4.9.3
        #addr = ctypes.c_char.from_buffer(imgData, 0)
        #try:
            #img = QtGui.QImage(addr, imgData.shape[1], imgData.shape[0], imgFormat)
        #except TypeError:  
            #addr = ctypes.addressof(addr)
            #img = QtGui.QImage(addr, imgData.shape[1], imgData.shape[0], imgFormat)
        try:
            img = QtGui.QImage(imgData.ctypes.data, imgData.shape[1], imgData.shape[0], imgFormat)
        except:
            if copy:
                # does not leak memory, is not mutable
                img = QtGui.QImage(buffer(imgData), imgData.shape[1], imgData.shape[0], imgFormat)
            else:
                # mutable, but leaks memory
                img = QtGui.QImage(memoryview(imgData), imgData.shape[1], imgData.shape[0], imgFormat)
                
    img.data = imgData
    return img
    #try:
        #buf = imgData.data
    #except AttributeError:  ## happens when image data is non-contiguous
        #buf = imgData.data
        
    #profiler()
    #qimage = QtGui.QImage(buf, imgData.shape[1], imgData.shape[0], imgFormat)
    #profiler()
    #qimage.data = imgData
    #return qimage

def imageToArray(img, copy=False, transpose=True):
    """
    Convert a QImage into numpy array. The image must have format RGB32, ARGB32, or ARGB32_Premultiplied.
    By default, the image is not copied; changes made to the array will appear in the QImage as well (beware: if 
    the QImage is collected before the array, there may be trouble).
    The array will have shape (width, height, (b,g,r,a)).
    """
    fmt = img.format()
    ptr = img.bits()
    if USE_PYSIDE:
        arr = np.frombuffer(ptr, dtype=np.ubyte)
    else:
        ptr.setsize(img.byteCount())
        arr = np.asarray(ptr)
        if img.byteCount() != arr.size * arr.itemsize:
            # Required for Python 2.6, PyQt 4.10
            # If this works on all platforms, then there is no need to use np.asarray..
            arr = np.frombuffer(ptr, np.ubyte, img.byteCount())
    
    arr = arr.reshape(img.height(), img.width(), 4)
    if fmt == img.Format_RGB32:
        arr[...,3] = 255
    
    if copy:
        arr = arr.copy()
        
    if transpose:
        return arr.transpose((1,0,2))
    else:
        return arr
    
def colorToAlpha(data, color):
    """
    Given an RGBA image in *data*, convert *color* to be transparent. 
    *data* must be an array (w, h, 3 or 4) of ubyte values and *color* must be 
    an array (3) of ubyte values.
    This is particularly useful for use with images that have a black or white background.
    
    Algorithm is taken from Gimp's color-to-alpha function in plug-ins/common/colortoalpha.c
    Credit:
        /*
        * Color To Alpha plug-in v1.0 by Seth Burgess, sjburges@gimp.org 1999/05/14
        *  with algorithm by clahey
        */
    
    """
    data = data.astype(float)
    if data.shape[-1] == 3:  ## add alpha channel if needed
        d2 = np.empty(data.shape[:2]+(4,), dtype=data.dtype)
        d2[...,:3] = data
        d2[...,3] = 255
        data = d2
    
    color = color.astype(float)
    alpha = np.zeros(data.shape[:2]+(3,), dtype=float)
    output = data.copy()
    
    for i in [0,1,2]:
        d = data[...,i]
        c = color[i]
        mask = d > c
        alpha[...,i][mask] = (d[mask] - c) / (255. - c)
        imask = d < c
        alpha[...,i][imask] = (c - d[imask]) / c
    
    output[...,3] = alpha.max(axis=2) * 255.
    
    mask = output[...,3] >= 1.0  ## avoid zero division while processing alpha channel
    correction = 255. / output[...,3][mask]  ## increase value to compensate for decreased alpha
    for i in [0,1,2]:
        output[...,i][mask] = ((output[...,i][mask]-color[i]) * correction) + color[i]
        output[...,3][mask] *= data[...,3][mask] / 255.  ## combine computed and previous alpha values
    
    #raise Exception()
    return np.clip(output, 0, 255).astype(np.ubyte)

def gaussianFilter(data, sigma):
    """
    Drop-in replacement for scipy.ndimage.gaussian_filter.
    
    (note: results are only approximately equal to the output of
     gaussian_filter)
    """
    if np.isscalar(sigma):
        sigma = (sigma,) * data.ndim
        
    baseline = data.mean()
    filtered = data - baseline
    for ax in range(data.ndim):
        s = sigma[ax]
        if s == 0:
            continue
        
        # generate 1D gaussian kernel
        ksize = int(s * 6)
        x = np.arange(-ksize, ksize)
        kernel = np.exp(-x**2 / (2*s**2))
        kshape = [1,] * data.ndim
        kshape[ax] = len(kernel)
        kernel = kernel.reshape(kshape)
        
        # convolve as product of FFTs
        shape = data.shape[ax] + ksize
        scale = 1.0 / (abs(s) * (2*np.pi)**0.5)
        filtered = scale * np.fft.irfft(np.fft.rfft(filtered, shape, axis=ax) * 
                                        np.fft.rfft(kernel, shape, axis=ax), 
                                        axis=ax)
        
        # clip off extra data
        sl = [slice(None)] * data.ndim
        sl[ax] = slice(filtered.shape[ax]-data.shape[ax],None,None)
        filtered = filtered[sl]
    return filtered + baseline
    
    
def downsample(data, n, axis=0, xvals='subsample'):
    """Downsample by averaging points together across axis.
    If multiple axes are specified, runs once per axis.
    If a metaArray is given, then the axis values can be either subsampled
    or downsampled to match.
    """
    ma = None
    if (hasattr(data, 'implements') and data.implements('MetaArray')):
        ma = data
        data = data.view(np.ndarray)
        
    
    if hasattr(axis, '__len__'):
        if not hasattr(n, '__len__'):
            n = [n]*len(axis)
        for i in range(len(axis)):
            data = downsample(data, n[i], axis[i])
        return data
    
    if n <= 1:
        return data
    nPts = int(data.shape[axis] / n)
    s = list(data.shape)
    s[axis] = nPts
    s.insert(axis+1, n)
    sl = [slice(None)] * data.ndim
    sl[axis] = slice(0, nPts*n)
    d1 = data[tuple(sl)]
    #print d1.shape, s
    d1.shape = tuple(s)
    d2 = d1.mean(axis+1)
    
    if ma is None:
        return d2
    else:
        info = ma.infoCopy()
        if 'values' in info[axis]:
            if xvals == 'subsample':
                info[axis]['values'] = info[axis]['values'][::n][:nPts]
            elif xvals == 'downsample':
                info[axis]['values'] = downsample(info[axis]['values'], n)
        return MetaArray(d2, info=info)


def arrayToQPath(x, y, connect='all'):
    """Convert an array of x,y coordinats to QPainterPath as efficiently as possible.
    The *connect* argument may be 'all', indicating that each point should be
    connected to the next; 'pairs', indicating that each pair of points
    should be connected, or an array of int32 values (0 or 1) indicating
    connections.
    """

    ## Create all vertices in path. The method used below creates a binary format so that all
    ## vertices can be read in at once. This binary format may change in future versions of Qt,
    ## so the original (slower) method is left here for emergencies:
        #path.moveTo(x[0], y[0])
        #if connect == 'all':
            #for i in range(1, y.shape[0]):
                #path.lineTo(x[i], y[i])
        #elif connect == 'pairs':
            #for i in range(1, y.shape[0]):
                #if i%2 == 0:
                    #path.lineTo(x[i], y[i])
                #else:
                    #path.moveTo(x[i], y[i])
        #elif isinstance(connect, np.ndarray):
            #for i in range(1, y.shape[0]):
                #if connect[i] == 1:
                    #path.lineTo(x[i], y[i])
                #else:
                    #path.moveTo(x[i], y[i])
        #else:
            #raise Exception('connect argument must be "all", "pairs", or array')

    ## Speed this up using >> operator
    ## Format is:
    ##    numVerts(i4)   0(i4)
    ##    x(f8)   y(f8)   0(i4)    <-- 0 means this vertex does not connect
    ##    x(f8)   y(f8)   1(i4)    <-- 1 means this vertex connects to the previous vertex
    ##    ...
    ##    0(i4)
    ##
    ## All values are big endian--pack using struct.pack('>d') or struct.pack('>i')

    path = QtGui.QPainterPath()

    #profiler = debug.Profiler()
    n = x.shape[0]
    # create empty array, pad with extra space on either end
    arr = np.empty(n+2, dtype=[('x', '>f8'), ('y', '>f8'), ('c', '>i4')])
    # write first two integers
    #profiler('allocate empty')
    byteview = arr.view(dtype=np.ubyte)
    byteview[:12] = 0
    byteview.data[12:20] = struct.pack('>ii', n, 0)
    #profiler('pack header')
    # Fill array with vertex values
    arr[1:-1]['x'] = x
    arr[1:-1]['y'] = y

    # decide which points are connected by lines
    if eq(connect, 'all'):
        arr[1:-1]['c'] = 1
    elif eq(connect, 'pairs'):
        arr[1:-1]['c'][::2] = 1
        arr[1:-1]['c'][1::2] = 0
    elif eq(connect, 'finite'):
        arr[1:-1]['c'] = np.isfinite(x) & np.isfinite(y)
    elif isinstance(connect, np.ndarray):
        arr[1:-1]['c'] = connect
    else:
        raise Exception('connect argument must be "all", "pairs", "finite", or array')

    #profiler('fill array')
    # write last 0
    lastInd = 20*(n+1)
    byteview.data[lastInd:lastInd+4] = struct.pack('>i', 0)
    #profiler('footer')
    # create datastream object and stream into path

    ## Avoiding this method because QByteArray(str) leaks memory in PySide
    #buf = QtCore.QByteArray(arr.data[12:lastInd+4])  # I think one unnecessary copy happens here

    path.strn = byteview.data[12:lastInd+4] # make sure data doesn't run away
    try:
        buf = QtCore.QByteArray.fromRawData(path.strn)
    except TypeError:
        buf = QtCore.QByteArray(bytes(path.strn))
    #profiler('create buffer')
    ds = QtCore.QDataStream(buf)

    ds >> path
    #profiler('load')

    return path

#def isosurface(data, level):
    #"""
    #Generate isosurface from volumetric data using marching tetrahedra algorithm.
    #See Paul Bourke, "Polygonising a Scalar Field Using Tetrahedrons"  (http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/)
    
    #*data*   3D numpy array of scalar values
    #*level*  The level at which to generate an isosurface
    #"""
    
    #facets = []
    
    ### mark everything below the isosurface level
    #mask = data < level
    
    #### make eight sub-fields 
    #fields = np.empty((2,2,2), dtype=object)
    #slices = [slice(0,-1), slice(1,None)]
    #for i in [0,1]:
        #for j in [0,1]:
            #for k in [0,1]:
                #fields[i,j,k] = mask[slices[i], slices[j], slices[k]]
    
    
    
    ### split each cell into 6 tetrahedra
    ### these all have the same 'orienation'; points 1,2,3 circle 
    ### clockwise around point 0
    #tetrahedra = [
        #[(0,1,0), (1,1,1), (0,1,1), (1,0,1)],
        #[(0,1,0), (0,1,1), (0,0,1), (1,0,1)],
        #[(0,1,0), (0,0,1), (0,0,0), (1,0,1)],
        #[(0,1,0), (0,0,0), (1,0,0), (1,0,1)],
        #[(0,1,0), (1,0,0), (1,1,0), (1,0,1)],
        #[(0,1,0), (1,1,0), (1,1,1), (1,0,1)]
    #]
    
    ### each tetrahedron will be assigned an index
    ### which determines how to generate its facets.
    ### this structure is: 
    ###    facets[index][facet1, facet2, ...]
    ### where each facet is triangular and its points are each 
    ### interpolated between two points on the tetrahedron
    ###    facet = [(p1a, p1b), (p2a, p2b), (p3a, p3b)]
    ### facet points always circle clockwise if you are looking 
    ### at them from below the isosurface.
    #indexFacets = [
        #[],  ## all above
        #[[(0,1), (0,2), (0,3)]],  # 0 below
        #[[(1,0), (1,3), (1,2)]],   # 1 below
        #[[(0,2), (1,3), (1,2)], [(0,2), (0,3), (1,3)]],   # 0,1 below
        #[[(2,0), (2,1), (2,3)]],   # 2 below
        #[[(0,3), (1,2), (2,3)], [(0,3), (0,1), (1,2)]],   # 0,2 below
        #[[(1,0), (2,3), (2,0)], [(1,0), (1,3), (2,3)]],   # 1,2 below
        #[[(3,0), (3,1), (3,2)]],   # 3 above
        #[[(3,0), (3,2), (3,1)]],   # 3 below
        #[[(1,0), (2,0), (2,3)], [(1,0), (2,3), (1,3)]],   # 0,3 below
        #[[(0,3), (2,3), (1,2)], [(0,3), (1,2), (0,1)]],   # 1,3 below
        #[[(2,0), (2,3), (2,1)]], # 0,1,3 below
        #[[(0,2), (1,2), (1,3)], [(0,2), (1,3), (0,3)]],   # 2,3 below
        #[[(1,0), (1,2), (1,3)]], # 0,2,3 below
        #[[(0,1), (0,3), (0,2)]], # 1,2,3 below
        #[]  ## all below
    #]
    
    #for tet in tetrahedra:
        
        ### get the 4 fields for this tetrahedron
        #tetFields = [fields[c] for c in tet]
        
        ### generate an index for each grid cell
        #index = tetFields[0] + tetFields[1]*2 + tetFields[2]*4 + tetFields[3]*8
        
        ### add facets
        #for i in xrange(index.shape[0]):                 # data x-axis
            #for j in xrange(index.shape[1]):             # data y-axis
                #for k in xrange(index.shape[2]):         # data z-axis
                    #for f in indexFacets[index[i,j,k]]:  # faces to generate for this tet
                        #pts = []
                        #for l in [0,1,2]:      # points in this face
                            #p1 = tet[f[l][0]]  # tet corner 1
                            #p2 = tet[f[l][1]]  # tet corner 2
                            #pts.append([(p1[x]+p2[x])*0.5+[i,j,k][x]+0.5 for x in [0,1,2]]) ## interpolate between tet corners
                        #facets.append(pts)

    #return facets
    

def isocurve(data, level, connected=False, extendToEdge=False, path=False):
    """
    Generate isocurve from 2D data using marching squares algorithm.
    
    ============== =========================================================
    **Arguments:**
    data           2D numpy array of scalar values
    level          The level at which to generate an isosurface
    connected      If False, return a single long list of point pairs
                   If True, return multiple long lists of connected point 
                   locations. (This is slower but better for drawing 
                   continuous lines)
    extendToEdge   If True, extend the curves to reach the exact edges of 
                   the data. 
    path           if True, return a QPainterPath rather than a list of 
                   vertex coordinates. This forces connected=True.
    ============== =========================================================
    
    This function is SLOW; plenty of room for optimization here.
    """    
    
    if path is True:
        connected = True
    
    if extendToEdge:
        d2 = np.empty((data.shape[0]+2, data.shape[1]+2), dtype=data.dtype)
        d2[1:-1, 1:-1] = data
        d2[0, 1:-1] = data[0]
        d2[-1, 1:-1] = data[-1]
        d2[1:-1, 0] = data[:, 0]
        d2[1:-1, -1] = data[:, -1]
        d2[0,0] = d2[0,1]
        d2[0,-1] = d2[1,-1]
        d2[-1,0] = d2[-1,1]
        d2[-1,-1] = d2[-1,-2]
        data = d2
    
    sideTable = [
        [],
        [0,1],
        [1,2],
        [0,2],
        [0,3],
        [1,3],
        [0,1,2,3],
        [2,3],
        [2,3],
        [0,1,2,3],
        [1,3],
        [0,3],
        [0,2],
        [1,2],
        [0,1],
        []
        ]
    
    edgeKey=[
        [(0,1), (0,0)],
        [(0,0), (1,0)],
        [(1,0), (1,1)],
        [(1,1), (0,1)]
        ]
    
    
    lines = []
    
    ## mark everything below the isosurface level
    mask = data < level
    
    ### make four sub-fields and compute indexes for grid cells
    index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte)
    fields = np.empty((2,2), dtype=object)
    slices = [slice(0,-1), slice(1,None)]
    for i in [0,1]:
        for j in [0,1]:
            fields[i,j] = mask[slices[i], slices[j]]
            #vertIndex = i - 2*j*i + 3*j + 4*k  ## this is just to match Bourk's vertex numbering scheme
            vertIndex = i+2*j
            #print i,j,k," : ", fields[i,j,k], 2**vertIndex
            np.add(index, fields[i,j] * 2**vertIndex, out=index, casting='unsafe')
            #print index
    #print index
    
    ## add lines
    for i in range(index.shape[0]):                 # data x-axis
        for j in range(index.shape[1]):             # data y-axis     
            sides = sideTable[index[i,j]]
            for l in range(0, len(sides), 2):     ## faces for this grid cell
                edges = sides[l:l+2]
                pts = []
                for m in [0,1]:      # points in this face
                    p1 = edgeKey[edges[m]][0] # p1, p2 are points at either side of an edge
                    p2 = edgeKey[edges[m]][1]
                    v1 = data[i+p1[0], j+p1[1]] # v1 and v2 are the values at p1 and p2
                    v2 = data[i+p2[0], j+p2[1]]
                    f = (level-v1) / (v2-v1)
                    fi = 1.0 - f
                    p = (    ## interpolate between corners
                        p1[0]*fi + p2[0]*f + i + 0.5, 
                        p1[1]*fi + p2[1]*f + j + 0.5
                        )
                    if extendToEdge:
                        ## check bounds
                        p = (
                            min(data.shape[0]-2, max(0, p[0]-1)),
                            min(data.shape[1]-2, max(0, p[1]-1)),                        
                        )
                    if connected:
                        gridKey = i + (1 if edges[m]==2 else 0), j + (1 if edges[m]==3 else 0), edges[m]%2
                        pts.append((p, gridKey))  ## give the actual position and a key identifying the grid location (for connecting segments)
                    else:
                        pts.append(p)
                
                lines.append(pts)

    if not connected:
        return lines
                
    ## turn disjoint list of segments into continuous lines

    #lines = [[2,5], [5,4], [3,4], [1,3], [6,7], [7,8], [8,6], [11,12], [12,15], [11,13], [13,14]]
    #lines = [[(float(a), a), (float(b), b)] for a,b in lines]
    points = {}  ## maps each point to its connections
    for a,b in lines:
        if a[1] not in points:
            points[a[1]] = []
        points[a[1]].append([a,b])
        if b[1] not in points:
            points[b[1]] = []
        points[b[1]].append([b,a])

    ## rearrange into chains
    for k in list(points.keys()):
        try:
            chains = points[k]
        except KeyError:   ## already used this point elsewhere
            continue
        #print "===========", k
        for chain in chains:
            #print "  chain:", chain
            x = None
            while True:
                if x == chain[-1][1]:
                    break ## nothing left to do on this chain
                    
                x = chain[-1][1]
                if x == k:  
                    break ## chain has looped; we're done and can ignore the opposite chain
                y = chain[-2][1]
                connects = points[x]
                for conn in connects[:]:
                    if conn[1][1] != y:
                        #print "    ext:", conn
                        chain.extend(conn[1:])
                #print "    del:", x
                del points[x]
            if chain[0][1] == chain[-1][1]:  # looped chain; no need to continue the other direction
                chains.pop()
                break
                

    ## extract point locations 
    lines = []
    for chain in points.values():
        if len(chain) == 2:
            chain = chain[1][1:][::-1] + chain[0]  # join together ends of chain
        else:
            chain = chain[0]
        lines.append([p[0] for p in chain])
    
    if not path:
        return lines ## a list of pairs of points
    
    path = QtGui.QPainterPath()
    for line in lines:
        path.moveTo(*line[0])
        for p in line[1:]:
            path.lineTo(*p)
    
    return path
    
    
def traceImage(image, values, smooth=0.5):
    """
    Convert an image to a set of QPainterPath curves.
    One curve will be generated for each item in *values*; each curve outlines the area
    of the image that is closer to its value than to any others.
    
    If image is RGB or RGBA, then the shape of values should be (nvals, 3/4)
    The parameter *smooth* is expressed in pixels.
    """
    try:
        import scipy.ndimage as ndi
    except ImportError:
        raise Exception("traceImage() requires the package scipy.ndimage, but it is not importable.")
    
    if values.ndim == 2:
        values = values.T
    values = values[np.newaxis, np.newaxis, ...].astype(float)
    image = image[..., np.newaxis].astype(float)
    diff = np.abs(image-values)
    if values.ndim == 4:
        diff = diff.sum(axis=2)
        
    labels = np.argmin(diff, axis=2)
    
    paths = []
    for i in range(diff.shape[-1]):    
        d = (labels==i).astype(float)
        d = gaussianFilter(d, (smooth, smooth))
        lines = isocurve(d, 0.5, connected=True, extendToEdge=True)
        path = QtGui.QPainterPath()
        for line in lines:
            path.moveTo(*line[0])
            for p in line[1:]:
                path.lineTo(*p)
        
        paths.append(path)
    return paths
    
    
    
IsosurfaceDataCache = None
def isosurface(data, level):
    """
    Generate isosurface from volumetric data using marching cubes algorithm.
    See Paul Bourke, "Polygonising a Scalar Field"  
    (http://paulbourke.net/geometry/polygonise/)
    
    *data*   3D numpy array of scalar values. Must be contiguous.
    *level*  The level at which to generate an isosurface
    
    Returns an array of vertex coordinates (Nv, 3) and an array of 
    per-face vertex indexes (Nf, 3)    
    """
    ## For improvement, see:
    ## 
    ## Efficient implementation of Marching Cubes' cases with topological guarantees.
    ## Thomas Lewiner, Helio Lopes, Antonio Wilson Vieira and Geovan Tavares.
    ## Journal of Graphics Tools 8(2): pp. 1-15 (december 2003)
    
    ## Precompute lookup tables on the first run
    global IsosurfaceDataCache
    if IsosurfaceDataCache is None:
        ## map from grid cell index to edge index.
        ## grid cell index tells us which corners are below the isosurface,
        ## edge index tells us which edges are cut by the isosurface.
        ## (Data stolen from Bourk; see above.)
        edgeTable = np.array([
            0x0  , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
            0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
            0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
            0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
            0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
            0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
            0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
            0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
            0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
            0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
            0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
            0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
            0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
            0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
            0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
            0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
            0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
            0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
            0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
            0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
            0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
            0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
            0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
            0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
            0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
            0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
            0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
            0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
            0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
            0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
            0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
            0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0   
            ], dtype=np.uint16)
        
        ## Table of triangles to use for filling each grid cell.
        ## Each set of three integers tells us which three edges to
        ## draw a triangle between.
        ## (Data stolen from Bourk; see above.)
        triTable = [
            [],
            [0, 8, 3],
            [0, 1, 9],
            [1, 8, 3, 9, 8, 1],
            [1, 2, 10],
            [0, 8, 3, 1, 2, 10],
            [9, 2, 10, 0, 2, 9],
            [2, 8, 3, 2, 10, 8, 10, 9, 8],
            [3, 11, 2],
            [0, 11, 2, 8, 11, 0],
            [1, 9, 0, 2, 3, 11],
            [1, 11, 2, 1, 9, 11, 9, 8, 11],
            [3, 10, 1, 11, 10, 3],
            [0, 10, 1, 0, 8, 10, 8, 11, 10],
            [3, 9, 0, 3, 11, 9, 11, 10, 9],
            [9, 8, 10, 10, 8, 11],
            [4, 7, 8],
            [4, 3, 0, 7, 3, 4],
            [0, 1, 9, 8, 4, 7],
            [4, 1, 9, 4, 7, 1, 7, 3, 1],
            [1, 2, 10, 8, 4, 7],
            [3, 4, 7, 3, 0, 4, 1, 2, 10],
            [9, 2, 10, 9, 0, 2, 8, 4, 7],
            [2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4],
            [8, 4, 7, 3, 11, 2],
            [11, 4, 7, 11, 2, 4, 2, 0, 4],
            [9, 0, 1, 8, 4, 7, 2, 3, 11],
            [4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1],
            [3, 10, 1, 3, 11, 10, 7, 8, 4],
            [1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4],
            [4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3],
            [4, 7, 11, 4, 11, 9, 9, 11, 10],
            [9, 5, 4],
            [9, 5, 4, 0, 8, 3],
            [0, 5, 4, 1, 5, 0],
            [8, 5, 4, 8, 3, 5, 3, 1, 5],
            [1, 2, 10, 9, 5, 4],
            [3, 0, 8, 1, 2, 10, 4, 9, 5],
            [5, 2, 10, 5, 4, 2, 4, 0, 2],
            [2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8],
            [9, 5, 4, 2, 3, 11],
            [0, 11, 2, 0, 8, 11, 4, 9, 5],
            [0, 5, 4, 0, 1, 5, 2, 3, 11],
            [2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5],
            [10, 3, 11, 10, 1, 3, 9, 5, 4],
            [4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10],
            [5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3],
            [5, 4, 8, 5, 8, 10, 10, 8, 11],
            [9, 7, 8, 5, 7, 9],
            [9, 3, 0, 9, 5, 3, 5, 7, 3],
            [0, 7, 8, 0, 1, 7, 1, 5, 7],
            [1, 5, 3, 3, 5, 7],
            [9, 7, 8, 9, 5, 7, 10, 1, 2],
            [10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3],
            [8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2],
            [2, 10, 5, 2, 5, 3, 3, 5, 7],
            [7, 9, 5, 7, 8, 9, 3, 11, 2],
            [9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11],
            [2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7],
            [11, 2, 1, 11, 1, 7, 7, 1, 5],
            [9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11],
            [5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0],
            [11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0],
            [11, 10, 5, 7, 11, 5],
            [10, 6, 5],
            [0, 8, 3, 5, 10, 6],
            [9, 0, 1, 5, 10, 6],
            [1, 8, 3, 1, 9, 8, 5, 10, 6],
            [1, 6, 5, 2, 6, 1],
            [1, 6, 5, 1, 2, 6, 3, 0, 8],
            [9, 6, 5, 9, 0, 6, 0, 2, 6],
            [5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8],
            [2, 3, 11, 10, 6, 5],
            [11, 0, 8, 11, 2, 0, 10, 6, 5],
            [0, 1, 9, 2, 3, 11, 5, 10, 6],
            [5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11],
            [6, 3, 11, 6, 5, 3, 5, 1, 3],
            [0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6],
            [3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9],
            [6, 5, 9, 6, 9, 11, 11, 9, 8],
            [5, 10, 6, 4, 7, 8],
            [4, 3, 0, 4, 7, 3, 6, 5, 10],
            [1, 9, 0, 5, 10, 6, 8, 4, 7],
            [10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4],
            [6, 1, 2, 6, 5, 1, 4, 7, 8],
            [1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7],
            [8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6],
            [7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9],
            [3, 11, 2, 7, 8, 4, 10, 6, 5],
            [5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11],
            [0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6],
            [9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6],
            [8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6],
            [5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11],
            [0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7],
            [6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9],
            [10, 4, 9, 6, 4, 10],
            [4, 10, 6, 4, 9, 10, 0, 8, 3],
            [10, 0, 1, 10, 6, 0, 6, 4, 0],
            [8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10],
            [1, 4, 9, 1, 2, 4, 2, 6, 4],
            [3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4],
            [0, 2, 4, 4, 2, 6],
            [8, 3, 2, 8, 2, 4, 4, 2, 6],
            [10, 4, 9, 10, 6, 4, 11, 2, 3],
            [0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6],
            [3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10],
            [6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1],
            [9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3],
            [8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1],
            [3, 11, 6, 3, 6, 0, 0, 6, 4],
            [6, 4, 8, 11, 6, 8],
            [7, 10, 6, 7, 8, 10, 8, 9, 10],
            [0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10],
            [10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0],
            [10, 6, 7, 10, 7, 1, 1, 7, 3],
            [1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7],
            [2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9],
            [7, 8, 0, 7, 0, 6, 6, 0, 2],
            [7, 3, 2, 6, 7, 2],
            [2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7],
            [2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7],
            [1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11],
            [11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1],
            [8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6],
            [0, 9, 1, 11, 6, 7],
            [7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0],
            [7, 11, 6],
            [7, 6, 11],
            [3, 0, 8, 11, 7, 6],
            [0, 1, 9, 11, 7, 6],
            [8, 1, 9, 8, 3, 1, 11, 7, 6],
            [10, 1, 2, 6, 11, 7],
            [1, 2, 10, 3, 0, 8, 6, 11, 7],
            [2, 9, 0, 2, 10, 9, 6, 11, 7],
            [6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8],
            [7, 2, 3, 6, 2, 7],
            [7, 0, 8, 7, 6, 0, 6, 2, 0],
            [2, 7, 6, 2, 3, 7, 0, 1, 9],
            [1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6],
            [10, 7, 6, 10, 1, 7, 1, 3, 7],
            [10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8],
            [0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7],
            [7, 6, 10, 7, 10, 8, 8, 10, 9],
            [6, 8, 4, 11, 8, 6],
            [3, 6, 11, 3, 0, 6, 0, 4, 6],
            [8, 6, 11, 8, 4, 6, 9, 0, 1],
            [9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6],
            [6, 8, 4, 6, 11, 8, 2, 10, 1],
            [1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6],
            [4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9],
            [10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3],
            [8, 2, 3, 8, 4, 2, 4, 6, 2],
            [0, 4, 2, 4, 6, 2],
            [1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8],
            [1, 9, 4, 1, 4, 2, 2, 4, 6],
            [8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1],
            [10, 1, 0, 10, 0, 6, 6, 0, 4],
            [4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3],
            [10, 9, 4, 6, 10, 4],
            [4, 9, 5, 7, 6, 11],
            [0, 8, 3, 4, 9, 5, 11, 7, 6],
            [5, 0, 1, 5, 4, 0, 7, 6, 11],
            [11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5],
            [9, 5, 4, 10, 1, 2, 7, 6, 11],
            [6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5],
            [7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2],
            [3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6],
            [7, 2, 3, 7, 6, 2, 5, 4, 9],
            [9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7],
            [3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0],
            [6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8],
            [9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7],
            [1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4],
            [4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10],
            [7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10],
            [6, 9, 5, 6, 11, 9, 11, 8, 9],
            [3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5],
            [0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11],
            [6, 11, 3, 6, 3, 5, 5, 3, 1],
            [1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6],
            [0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10],
            [11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5],
            [6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3],
            [5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2],
            [9, 5, 6, 9, 6, 0, 0, 6, 2],
            [1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8],
            [1, 5, 6, 2, 1, 6],
            [1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6],
            [10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0],
            [0, 3, 8, 5, 6, 10],
            [10, 5, 6],
            [11, 5, 10, 7, 5, 11],
            [11, 5, 10, 11, 7, 5, 8, 3, 0],
            [5, 11, 7, 5, 10, 11, 1, 9, 0],
            [10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1],
            [11, 1, 2, 11, 7, 1, 7, 5, 1],
            [0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11],
            [9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7],
            [7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2],
            [2, 5, 10, 2, 3, 5, 3, 7, 5],
            [8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5],
            [9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2],
            [9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2],
            [1, 3, 5, 3, 7, 5],
            [0, 8, 7, 0, 7, 1, 1, 7, 5],
            [9, 0, 3, 9, 3, 5, 5, 3, 7],
            [9, 8, 7, 5, 9, 7],
            [5, 8, 4, 5, 10, 8, 10, 11, 8],
            [5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0],
            [0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5],
            [10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4],
            [2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8],
            [0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11],
            [0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5],
            [9, 4, 5, 2, 11, 3],
            [2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4],
            [5, 10, 2, 5, 2, 4, 4, 2, 0],
            [3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9],
            [5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2],
            [8, 4, 5, 8, 5, 3, 3, 5, 1],
            [0, 4, 5, 1, 0, 5],
            [8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5],
            [9, 4, 5],
            [4, 11, 7, 4, 9, 11, 9, 10, 11],
            [0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11],
            [1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11],
            [3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4],
            [4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2],
            [9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3],
            [11, 7, 4, 11, 4, 2, 2, 4, 0],
            [11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4],
            [2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9],
            [9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7],
            [3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10],
            [1, 10, 2, 8, 7, 4],
            [4, 9, 1, 4, 1, 7, 7, 1, 3],
            [4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1],
            [4, 0, 3, 7, 4, 3],
            [4, 8, 7],
            [9, 10, 8, 10, 11, 8],
            [3, 0, 9, 3, 9, 11, 11, 9, 10],
            [0, 1, 10, 0, 10, 8, 8, 10, 11],
            [3, 1, 10, 11, 3, 10],
            [1, 2, 11, 1, 11, 9, 9, 11, 8],
            [3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9],
            [0, 2, 11, 8, 0, 11],
            [3, 2, 11],
            [2, 3, 8, 2, 8, 10, 10, 8, 9],
            [9, 10, 2, 0, 9, 2],
            [2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8],
            [1, 10, 2],
            [1, 3, 8, 9, 1, 8],
            [0, 9, 1],
            [0, 3, 8],
            []
        ]    
        edgeShifts = np.array([  ## maps edge ID (0-11) to (x,y,z) cell offset and edge ID (0-2)
            [0, 0, 0, 0],   
            [1, 0, 0, 1],
            [0, 1, 0, 0],
            [0, 0, 0, 1],
            [0, 0, 1, 0],
            [1, 0, 1, 1],
            [0, 1, 1, 0],
            [0, 0, 1, 1],
            [0, 0, 0, 2],
            [1, 0, 0, 2],
            [1, 1, 0, 2],
            [0, 1, 0, 2],
            #[9, 9, 9, 9]  ## fake
        ], dtype=np.uint16) # don't use ubyte here! This value gets added to cell index later; will need the extra precision.
        nTableFaces = np.array([len(f)/3 for f in triTable], dtype=np.ubyte)
        faceShiftTables = [None]
        for i in range(1,6):
            ## compute lookup table of index: vertexes mapping
            faceTableI = np.zeros((len(triTable), i*3), dtype=np.ubyte)
            faceTableInds = np.argwhere(nTableFaces == i)
            faceTableI[faceTableInds[:,0]] = np.array([triTable[j] for j in faceTableInds])
            faceTableI = faceTableI.reshape((len(triTable), i, 3))
            faceShiftTables.append(edgeShifts[faceTableI])
            
        ## Let's try something different:
        #faceTable = np.empty((256, 5, 3, 4), dtype=np.ubyte)   # (grid cell index, faces, vertexes, edge lookup)
        #for i,f in enumerate(triTable):
            #f = np.array(f + [12] * (15-len(f))).reshape(5,3)
            #faceTable[i] = edgeShifts[f]
        
        
        IsosurfaceDataCache = (faceShiftTables, edgeShifts, edgeTable, nTableFaces)
    else:
        faceShiftTables, edgeShifts, edgeTable, nTableFaces = IsosurfaceDataCache

    # We use strides below, which means we need contiguous array input.
    # Ideally we can fix this just by removing the dependency on strides.
    if not data.flags['C_CONTIGUOUS']:
        raise TypeError("isosurface input data must be c-contiguous.")
    
    ## mark everything below the isosurface level
    mask = data < level
    
    ### make eight sub-fields and compute indexes for grid cells
    index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte)
    fields = np.empty((2,2,2), dtype=object)
    slices = [slice(0,-1), slice(1,None)]
    for i in [0,1]:
        for j in [0,1]:
            for k in [0,1]:
                fields[i,j,k] = mask[slices[i], slices[j], slices[k]]
                vertIndex = i - 2*j*i + 3*j + 4*k  ## this is just to match Bourk's vertex numbering scheme
                np.add(index, fields[i,j,k] * 2**vertIndex, out=index, casting='unsafe')
    
    ### Generate table of edges that have been cut
    cutEdges = np.zeros([x+1 for x in index.shape]+[3], dtype=np.uint32)
    edges = edgeTable[index]
    for i, shift in enumerate(edgeShifts[:12]):        
        slices = [slice(shift[j],cutEdges.shape[j]+(shift[j]-1)) for j in range(3)]
        cutEdges[slices[0], slices[1], slices[2], shift[3]] += edges & 2**i
    
    ## for each cut edge, interpolate to see where exactly the edge is cut and generate vertex positions
    m = cutEdges > 0
    vertexInds = np.argwhere(m)   ## argwhere is slow!
    vertexes = vertexInds[:,:3].astype(np.float32)
    dataFlat = data.reshape(data.shape[0]*data.shape[1]*data.shape[2])
    
    ## re-use the cutEdges array as a lookup table for vertex IDs
    cutEdges[vertexInds[:,0], vertexInds[:,1], vertexInds[:,2], vertexInds[:,3]] = np.arange(vertexInds.shape[0])
    
    for i in [0,1,2]:
        vim = vertexInds[:,3] == i
        vi = vertexInds[vim, :3]
        viFlat = (vi * (np.array(data.strides[:3]) // data.itemsize)[np.newaxis,:]).sum(axis=1)
        v1 = dataFlat[viFlat]
        v2 = dataFlat[viFlat + data.strides[i]//data.itemsize]
        vertexes[vim,i] += (level-v1) / (v2-v1)
    
    ### compute the set of vertex indexes for each face. 
    
    ## This works, but runs a bit slower.
    #cells = np.argwhere((index != 0) & (index != 255))  ## all cells with at least one face
    #cellInds = index[cells[:,0], cells[:,1], cells[:,2]]
    #verts = faceTable[cellInds]
    #mask = verts[...,0,0] != 9
    #verts[...,:3] += cells[:,np.newaxis,np.newaxis,:]  ## we now have indexes into cutEdges
    #verts = verts[mask]
    #faces = cutEdges[verts[...,0], verts[...,1], verts[...,2], verts[...,3]]  ## and these are the vertex indexes we want.
    
    
    ## To allow this to be vectorized efficiently, we count the number of faces in each 
    ## grid cell and handle each group of cells with the same number together.
    ## determine how many faces to assign to each grid cell
    nFaces = nTableFaces[index]
    totFaces = nFaces.sum()
    faces = np.empty((totFaces, 3), dtype=np.uint32)
    ptr = 0
    #import debug
    #p = debug.Profiler()
    
    ## this helps speed up an indexing operation later on
    cs = np.array(cutEdges.strides)//cutEdges.itemsize
    cutEdges = cutEdges.flatten()

    ## this, strangely, does not seem to help.
    #ins = np.array(index.strides)/index.itemsize
    #index = index.flatten()

    for i in range(1,6):
        ### expensive:
        #profiler()
        cells = np.argwhere(nFaces == i)  ## all cells which require i faces  (argwhere is expensive)
        #profiler()
        if cells.shape[0] == 0:
            continue
        cellInds = index[cells[:,0], cells[:,1], cells[:,2]]   ## index values of cells to process for this round
        #profiler()
        
        ### expensive:
        verts = faceShiftTables[i][cellInds]
        #profiler()
        np.add(verts[...,:3], cells[:,np.newaxis,np.newaxis,:], out=verts[...,:3], casting='unsafe')  ## we now have indexes into cutEdges
        verts = verts.reshape((verts.shape[0]*i,)+verts.shape[2:])
        #profiler()
        
        ### expensive:
        verts = (verts * cs[np.newaxis, np.newaxis, :]).sum(axis=2)
        vertInds = cutEdges[verts]
        #profiler()
        nv = vertInds.shape[0]
        #profiler()
        faces[ptr:ptr+nv] = vertInds #.reshape((nv, 3))
        #profiler()
        ptr += nv
        
    return vertexes, faces


    
def invertQTransform(tr):
    """Return a QTransform that is the inverse of *tr*.
    Rasises an exception if tr is not invertible.
    
    Note that this function is preferred over QTransform.inverted() due to
    bugs in that method. (specifically, Qt has floating-point precision issues
    when determining whether a matrix is invertible)
    """
    try:
        import numpy.linalg
        arr = np.array([[tr.m11(), tr.m12(), tr.m13()], [tr.m21(), tr.m22(), tr.m23()], [tr.m31(), tr.m32(), tr.m33()]])
        inv = numpy.linalg.inv(arr)
        return QtGui.QTransform(inv[0,0], inv[0,1], inv[0,2], inv[1,0], inv[1,1], inv[1,2], inv[2,0], inv[2,1])
    except ImportError:
        inv = tr.inverted()
        if inv[1] is False:
            raise Exception("Transform is not invertible.")
        return inv[0]
    
    
def pseudoScatter(data, spacing=None, shuffle=True, bidir=False):
    """
    Used for examining the distribution of values in a set. Produces scattering as in beeswarm or column scatter plots.
    
    Given a list of x-values, construct a set of y-values such that an x,y scatter-plot
    will not have overlapping points (it will look similar to a histogram).
    """
    inds = np.arange(len(data))
    if shuffle:
        np.random.shuffle(inds)
        
    data = data[inds]
    
    if spacing is None:
        spacing = 2.*np.std(data)/len(data)**0.5
    s2 = spacing**2
    
    yvals = np.empty(len(data))
    if len(data) == 0:
        return yvals
    yvals[0] = 0
    for i in range(1,len(data)):
        x = data[i]     # current x value to be placed
        x0 = data[:i]   # all x values already placed
        y0 = yvals[:i]  # all y values already placed
        y = 0
        
        dx = (x0-x)**2  # x-distance to each previous point
        xmask = dx < s2  # exclude anything too far away
        
        if xmask.sum() > 0:
            if bidir:
                dirs = [-1, 1]
            else:
                dirs = [1]
            yopts = []
            for direction in dirs:
                y = 0
                dx2 = dx[xmask]
                dy = (s2 - dx2)**0.5   
                limits = np.empty((2,len(dy)))  # ranges of y-values to exclude
                limits[0] = y0[xmask] - dy
                limits[1] = y0[xmask] + dy    
                while True:
                    # ignore anything below this y-value
                    if direction > 0:
                        mask = limits[1] >= y
                    else:
                        mask = limits[0] <= y
                        
                    limits2 = limits[:,mask]
                    
                    # are we inside an excluded region?
                    mask = (limits2[0] < y) & (limits2[1] > y)
                    if mask.sum() == 0:
                        break
                        
                    if direction > 0:
                        y = limits2[:,mask].max()
                    else:
                        y = limits2[:,mask].min()
                yopts.append(y)
            if bidir:
                y = yopts[0] if -yopts[0] < yopts[1] else yopts[1]
            else:
                y = yopts[0]
        yvals[i] = y
    
    return yvals[np.argsort(inds)]  ## un-shuffle values before returning



def toposort(deps, nodes=None, seen=None, stack=None, depth=0):
    """Topological sort. Arguments are:
      deps    dictionary describing dependencies where a:[b,c] means "a depends on b and c"
      nodes   optional, specifies list of starting nodes (these should be the nodes 
              which are not depended on by any other nodes). Other candidate starting
              nodes will be ignored.
              
    Example::

        # Sort the following graph:
        # 
        #   B ──┬─────> C <── D
        #       │       │       
        #   E <─┴─> A <─┘
        #     
        deps = {'a': ['b', 'c'], 'c': ['b', 'd'], 'e': ['b']}
        toposort(deps)
         => ['b', 'd', 'c', 'a', 'e']
    """
    # fill in empty dep lists
    deps = deps.copy()
    for k,v in list(deps.items()):
        for k in v:
            if k not in deps:
                deps[k] = []
    
    if nodes is None:
        ## run through deps to find nodes that are not depended upon
        rem = set()
        for dep in deps.values():
            rem |= set(dep)
        nodes = set(deps.keys()) - rem
    if seen is None:
        seen = set()
        stack = []
    sorted = []
    for n in nodes:
        if n in stack:
            raise Exception("Cyclic dependency detected", stack + [n])
        if n in seen:
            continue
        seen.add(n)
        sorted.extend( toposort(deps, deps[n], seen, stack+[n], depth=depth+1))
        sorted.append(n)
    return sorted