Source code for rwt.wavelets

"""
wavelets - A wavelet libray.
============================

A library of functions that create different kinds of wavelets.

.. codeauthor:: Amit Aides <amitibo@tx.technion.ac.il>
"""

from __future__ import division
import numpy as np
import scipy as sp


WAVELETS_DICT = {
    "db1" : (
        (0.70710678118654757, 0.70710678118654757),
        (-0.70710678118654757, 0.70710678118654757),
        (0.70710678118654757, 0.70710678118654757),
        (0.70710678118654757, -0.70710678118654757)
    ),
    "db2" : (
        (-0.12940952255092145, 0.22414386804185735, 0.83651630373746899, 0.48296291314469025),
        (-0.48296291314469025, 0.83651630373746899, -0.22414386804185735, -0.12940952255092145),
        (0.48296291314469025, 0.83651630373746899, 0.22414386804185735, -0.12940952255092145),
        (-0.12940952255092145, -0.22414386804185735, 0.83651630373746899, -0.48296291314469025)
    ),
    "db3" : (
        (0.035226291882100656, -0.085441273882241486, -0.13501102001039084, 0.45987750211933132, 0.80689150931333875, 0.33267055295095688),
        (-0.33267055295095688, 0.80689150931333875, -0.45987750211933132, -0.13501102001039084, 0.085441273882241486, 0.035226291882100656),
        (0.33267055295095688, 0.80689150931333875, 0.45987750211933132, -0.13501102001039084, -0.085441273882241486, 0.035226291882100656),
        (0.035226291882100656, 0.085441273882241486, -0.13501102001039084, -0.45987750211933132, 0.80689150931333875, -0.33267055295095688)
    ),
    "db4" : (
        (-0.010597401784997278, 0.032883011666982945, 0.030841381835986965, -0.18703481171888114, -0.027983769416983849, 0.63088076792959036, 0.71484657055254153, 0.23037781330885523),
        (-0.23037781330885523, 0.71484657055254153, -0.63088076792959036, -0.027983769416983849, 0.18703481171888114, 0.030841381835986965, -0.032883011666982945, -0.010597401784997278),
        (0.23037781330885523, 0.71484657055254153, 0.63088076792959036, -0.027983769416983849, -0.18703481171888114, 0.030841381835986965, 0.032883011666982945, -0.010597401784997278),
        (-0.010597401784997278, -0.032883011666982945, 0.030841381835986965, 0.18703481171888114, -0.027983769416983849, -0.63088076792959036, 0.71484657055254153, -0.23037781330885523)
    ),
    "db5" : (
        (0.0033357252850015492, -0.012580751999015526, -0.0062414902130117052, 0.077571493840065148, -0.03224486958502952, -0.24229488706619015, 0.13842814590110342, 0.72430852843857441, 0.60382926979747287, 0.16010239797412501),
        (-0.16010239797412501, 0.60382926979747287, -0.72430852843857441, 0.13842814590110342, 0.24229488706619015, -0.03224486958502952, -0.077571493840065148, -0.0062414902130117052, 0.012580751999015526, 0.0033357252850015492),
        (0.16010239797412501, 0.60382926979747287, 0.72430852843857441, 0.13842814590110342, -0.24229488706619015, -0.03224486958502952, 0.077571493840065148, -0.0062414902130117052, -0.012580751999015526, 0.0033357252850015492),
        (0.0033357252850015492, 0.012580751999015526, -0.0062414902130117052, -0.077571493840065148, -0.03224486958502952, 0.24229488706619015, 0.13842814590110342, -0.72430852843857441, 0.60382926979747287, -0.16010239797412501)
    ),
    "db6" : (
        (-0.0010773010849955799, 0.0047772575110106514, 0.0005538422009938016, -0.031582039318031156, 0.027522865530016288, 0.097501605587079362, -0.12976686756709563, -0.22626469396516913, 0.3152503517092432, 0.75113390802157753, 0.49462389039838539, 0.11154074335008017),
        (-0.11154074335008017, 0.49462389039838539, -0.75113390802157753, 0.3152503517092432, 0.22626469396516913, -0.12976686756709563, -0.097501605587079362, 0.027522865530016288, 0.031582039318031156, 0.0005538422009938016, -0.0047772575110106514, -0.0010773010849955799),
        (0.11154074335008017, 0.49462389039838539, 0.75113390802157753, 0.3152503517092432, -0.22626469396516913, -0.12976686756709563, 0.097501605587079362, 0.027522865530016288, -0.031582039318031156, 0.0005538422009938016, 0.0047772575110106514, -0.0010773010849955799),
        (-0.0010773010849955799, -0.0047772575110106514, 0.0005538422009938016, 0.031582039318031156, 0.027522865530016288, -0.097501605587079362, -0.12976686756709563, 0.22626469396516913, 0.3152503517092432, -0.75113390802157753, 0.49462389039838539, -0.11154074335008017)
    ),
    "db7" : (
        (0.00035371380000103988, -0.0018016407039998328, 0.00042957797300470274, 0.012550998556013784, -0.01657454163101562, -0.038029936935034633, 0.080612609151065898, 0.071309219267050042, -0.22403618499416572, -0.14390600392910627, 0.4697822874053586, 0.72913209084655506, 0.39653931948230575, 0.077852054085062364),
        (-0.077852054085062364, 0.39653931948230575, -0.72913209084655506, 0.4697822874053586, 0.14390600392910627, -0.22403618499416572, -0.071309219267050042, 0.080612609151065898, 0.038029936935034633, -0.01657454163101562, -0.012550998556013784, 0.00042957797300470274, 0.0018016407039998328, 0.00035371380000103988),
        (0.077852054085062364, 0.39653931948230575, 0.72913209084655506, 0.4697822874053586, -0.14390600392910627, -0.22403618499416572, 0.071309219267050042, 0.080612609151065898, -0.038029936935034633, -0.01657454163101562, 0.012550998556013784, 0.00042957797300470274, -0.0018016407039998328, 0.00035371380000103988),
        (0.00035371380000103988, 0.0018016407039998328, 0.00042957797300470274, -0.012550998556013784, -0.01657454163101562, 0.038029936935034633, 0.080612609151065898, -0.071309219267050042, -0.22403618499416572, 0.14390600392910627, 0.4697822874053586, -0.72913209084655506, 0.39653931948230575, -0.077852054085062364)
    ),
    "db8" : (
        (-0.00011747678400228192, 0.00067544940599855677, -0.00039174037299597711, -0.0048703529930106603, 0.0087460940470156547, 0.013981027917015516, -0.044088253931064719, -0.017369301002022108, 0.12874742662018601, 0.00047248457399797254, -0.28401554296242809, -0.015829105256023893, 0.58535468365486909, 0.67563073629801285, 0.31287159091446592, 0.054415842243081609),
        (-0.054415842243081609, 0.31287159091446592, -0.67563073629801285, 0.58535468365486909, 0.015829105256023893, -0.28401554296242809, -0.00047248457399797254, 0.12874742662018601, 0.017369301002022108, -0.044088253931064719, -0.013981027917015516, 0.0087460940470156547, 0.0048703529930106603, -0.00039174037299597711, -0.00067544940599855677, -0.00011747678400228192),
        (0.054415842243081609, 0.31287159091446592, 0.67563073629801285, 0.58535468365486909, -0.015829105256023893, -0.28401554296242809, 0.00047248457399797254, 0.12874742662018601, -0.017369301002022108, -0.044088253931064719, 0.013981027917015516, 0.0087460940470156547, -0.0048703529930106603, -0.00039174037299597711, 0.00067544940599855677, -0.00011747678400228192),
        (-0.00011747678400228192, -0.00067544940599855677, -0.00039174037299597711, 0.0048703529930106603, 0.0087460940470156547, -0.013981027917015516, -0.044088253931064719, 0.017369301002022108, 0.12874742662018601, -0.00047248457399797254, -0.28401554296242809, 0.015829105256023893, 0.58535468365486909, -0.67563073629801285, 0.31287159091446592, -0.054415842243081609)
    ),
    "db9" : (
        (3.9347319995026124e-005, -0.00025196318899817888, 0.00023038576399541288, 0.0018476468829611268, -0.0042815036819047227, -0.004723204757894831, 0.022361662123515244, 0.00025094711499193845, -0.067632829059523988, 0.030725681478322865, 0.14854074933476008, -0.096840783220879037, -0.29327378327258685, 0.13319738582208895, 0.65728807803663891, 0.6048231236767786, 0.24383467463766728, 0.038077947363167282),
        (-0.038077947363167282, 0.24383467463766728, -0.6048231236767786, 0.65728807803663891, -0.13319738582208895, -0.29327378327258685, 0.096840783220879037, 0.14854074933476008, -0.030725681478322865, -0.067632829059523988, -0.00025094711499193845, 0.022361662123515244, 0.004723204757894831, -0.0042815036819047227, -0.0018476468829611268, 0.00023038576399541288, 0.00025196318899817888, 3.9347319995026124e-005),
        (0.038077947363167282, 0.24383467463766728, 0.6048231236767786, 0.65728807803663891, 0.13319738582208895, -0.29327378327258685, -0.096840783220879037, 0.14854074933476008, 0.030725681478322865, -0.067632829059523988, 0.00025094711499193845, 0.022361662123515244, -0.004723204757894831, -0.0042815036819047227, 0.0018476468829611268, 0.00023038576399541288, -0.00025196318899817888, 3.9347319995026124e-005),
        (3.9347319995026124e-005, 0.00025196318899817888, 0.00023038576399541288, -0.0018476468829611268, -0.0042815036819047227, 0.004723204757894831, 0.022361662123515244, -0.00025094711499193845, -0.067632829059523988, -0.030725681478322865, 0.14854074933476008, 0.096840783220879037, -0.29327378327258685, -0.13319738582208895, 0.65728807803663891, -0.6048231236767786, 0.24383467463766728, -0.038077947363167282)
    ),
    "db10" : (
        (-1.3264203002354869e-005, 9.3588670001089845e-005, -0.0001164668549943862, -0.00068585669500468248, 0.0019924052949908499, 0.0013953517469940798, -0.010733175482979604, 0.0036065535669883944, 0.033212674058933238, -0.029457536821945671, -0.071394147165860775, 0.093057364603806592, 0.12736934033574265, -0.19594627437659665, -0.24984642432648865, 0.28117234366042648, 0.68845903945259213, 0.52720118893091983, 0.18817680007762133, 0.026670057900950818),
        (-0.026670057900950818, 0.18817680007762133, -0.52720118893091983, 0.68845903945259213, -0.28117234366042648, -0.24984642432648865, 0.19594627437659665, 0.12736934033574265, -0.093057364603806592, -0.071394147165860775, 0.029457536821945671, 0.033212674058933238, -0.0036065535669883944, -0.010733175482979604, -0.0013953517469940798, 0.0019924052949908499, 0.00068585669500468248, -0.0001164668549943862, -9.3588670001089845e-005, -1.3264203002354869e-005),
        (0.026670057900950818, 0.18817680007762133, 0.52720118893091983, 0.68845903945259213, 0.28117234366042648, -0.24984642432648865, -0.19594627437659665, 0.12736934033574265, 0.093057364603806592, -0.071394147165860775, -0.029457536821945671, 0.033212674058933238, 0.0036065535669883944, -0.010733175482979604, 0.0013953517469940798, 0.0019924052949908499, -0.00068585669500468248, -0.0001164668549943862, 9.3588670001089845e-005, -1.3264203002354869e-005),
        (-1.3264203002354869e-005, -9.3588670001089845e-005, -0.0001164668549943862, 0.00068585669500468248, 0.0019924052949908499, -0.0013953517469940798, -0.010733175482979604, -0.0036065535669883944, 0.033212674058933238, 0.029457536821945671, -0.071394147165860775, -0.093057364603806592, 0.12736934033574265, 0.19594627437659665, -0.24984642432648865, -0.28117234366042648, 0.68845903945259213, -0.52720118893091983, 0.18817680007762133, -0.026670057900950818)
    ),
    "db11" : (
        (4.4942742772363519e-006, -3.4634984186983789e-005, 5.4439074699366381e-005, 0.00024915252355281426, -0.00089302325066623663, -0.00030859285881515924, 0.0049284176560587777, -0.0033408588730145018, -0.015364820906201324, 0.020840904360180039, 0.031335090219045313, -0.066438785695020222, -0.04647995511667613, 0.14981201246638268, 0.066043588196690886, -0.27423084681792875, -0.16227524502747828, 0.41196436894789695, 0.68568677491617847, 0.44989976435603013, 0.14406702115061959, 0.018694297761470441),
        (-0.018694297761470441, 0.14406702115061959, -0.44989976435603013, 0.68568677491617847, -0.41196436894789695, -0.16227524502747828, 0.27423084681792875, 0.066043588196690886, -0.14981201246638268, -0.04647995511667613, 0.066438785695020222, 0.031335090219045313, -0.020840904360180039, -0.015364820906201324, 0.0033408588730145018, 0.0049284176560587777, 0.00030859285881515924, -0.00089302325066623663, -0.00024915252355281426, 5.4439074699366381e-005, 3.4634984186983789e-005, 4.4942742772363519e-006),
        (0.018694297761470441, 0.14406702115061959, 0.44989976435603013, 0.68568677491617847, 0.41196436894789695, -0.16227524502747828, -0.27423084681792875, 0.066043588196690886, 0.14981201246638268, -0.04647995511667613, -0.066438785695020222, 0.031335090219045313, 0.020840904360180039, -0.015364820906201324, -0.0033408588730145018, 0.0049284176560587777, -0.00030859285881515924, -0.00089302325066623663, 0.00024915252355281426, 5.4439074699366381e-005, -3.4634984186983789e-005, 4.4942742772363519e-006),
        (4.4942742772363519e-006, 3.4634984186983789e-005, 5.4439074699366381e-005, -0.00024915252355281426, -0.00089302325066623663, 0.00030859285881515924, 0.0049284176560587777, 0.0033408588730145018, -0.015364820906201324, -0.020840904360180039, 0.031335090219045313, 0.066438785695020222, -0.04647995511667613, -0.14981201246638268, 0.066043588196690886, 0.27423084681792875, -0.16227524502747828, -0.41196436894789695, 0.68568677491617847, -0.44989976435603013, 0.14406702115061959, -0.018694297761470441)
    ),
    "db12" : (
        (-1.5290717580684923e-006, 1.2776952219379579e-005, -2.4241545757030318e-005, -8.8504109208203182e-005, 0.00038865306282092672, 6.5451282125215034e-006, -0.0021795036186277044, 0.0022486072409952287, 0.0067114990087955486, -0.012840825198299882, -0.01221864906974642, 0.041546277495087637, 0.010849130255828966, -0.09643212009649671, 0.0053595696743599965, 0.18247860592758275, -0.023779257256064865, -0.31617845375277914, -0.044763885653777619, 0.51588647842780067, 0.65719872257929113, 0.37735513521420411, 0.10956627282118277, 0.013112257957229239),
        (-0.013112257957229239, 0.10956627282118277, -0.37735513521420411, 0.65719872257929113, -0.51588647842780067, -0.044763885653777619, 0.31617845375277914, -0.023779257256064865, -0.18247860592758275, 0.0053595696743599965, 0.09643212009649671, 0.010849130255828966, -0.041546277495087637, -0.01221864906974642, 0.012840825198299882, 0.0067114990087955486, -0.0022486072409952287, -0.0021795036186277044, -6.5451282125215034e-006, 0.00038865306282092672, 8.8504109208203182e-005, -2.4241545757030318e-005, -1.2776952219379579e-005, -1.5290717580684923e-006),
        (0.013112257957229239, 0.10956627282118277, 0.37735513521420411, 0.65719872257929113, 0.51588647842780067, -0.044763885653777619, -0.31617845375277914, -0.023779257256064865, 0.18247860592758275, 0.0053595696743599965, -0.09643212009649671, 0.010849130255828966, 0.041546277495087637, -0.01221864906974642, -0.012840825198299882, 0.0067114990087955486, 0.0022486072409952287, -0.0021795036186277044, 6.5451282125215034e-006, 0.00038865306282092672, -8.8504109208203182e-005, -2.4241545757030318e-005, 1.2776952219379579e-005, -1.5290717580684923e-006),
        (-1.5290717580684923e-006, -1.2776952219379579e-005, -2.4241545757030318e-005, 8.8504109208203182e-005, 0.00038865306282092672, -6.5451282125215034e-006, -0.0021795036186277044, -0.0022486072409952287, 0.0067114990087955486, 0.012840825198299882, -0.01221864906974642, -0.041546277495087637, 0.010849130255828966, 0.09643212009649671, 0.0053595696743599965, -0.18247860592758275, -0.023779257256064865, 0.31617845375277914, -0.044763885653777619, -0.51588647842780067, 0.65719872257929113, -0.37735513521420411, 0.10956627282118277, -0.013112257957229239)
    ),
    "db13" : (
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        (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.35355339059327379, 0.70710678118654757, 0.35355339059327379, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),
        (0.0, -0.0015105430506304422, -0.0030210861012608843, 0.012947511862546647, 0.028916109826354178, -0.052998481890690945, -0.13491307360773608, 0.16382918343409025, 0.46257144047591658, -0.95164212189717856, 0.46257144047591658, 0.16382918343409025, -0.13491307360773608, -0.052998481890690945, 0.028916109826354178, 0.012947511862546647, -0.0030210861012608843, -0.0015105430506304422)
    ),
    "bior3.1" : (
        (-0.35355339059327379, 1.0606601717798214, 1.0606601717798214, -0.35355339059327379),
        (-0.17677669529663689, 0.53033008588991071, -0.53033008588991071, 0.17677669529663689),
        (0.17677669529663689, 0.53033008588991071, 0.53033008588991071, 0.17677669529663689),
        (-0.35355339059327379, -1.0606601717798214, 1.0606601717798214, 0.35355339059327379)
    ),
    "bior3.3" : (
        (0.066291260736238838, -0.19887378220871652, -0.15467960838455727, 0.99436891104358249, 0.99436891104358249, -0.15467960838455727, -0.19887378220871652, 0.066291260736238838),
        (0.0, 0.0, -0.17677669529663689, 0.53033008588991071, -0.53033008588991071, 0.17677669529663689, 0.0, 0.0),
        (0.0, 0.0, 0.17677669529663689, 0.53033008588991071, 0.53033008588991071, 0.17677669529663689, 0.0, 0.0),
        (0.066291260736238838, 0.19887378220871652, -0.15467960838455727, -0.99436891104358249, 0.99436891104358249, 0.15467960838455727, -0.19887378220871652, -0.066291260736238838)
    ),
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        (-0.013810679320049757, 0.041432037960149271, 0.052480581416189075, -0.26792717880896527, -0.071815532464258744, 0.96674755240348298, 0.96674755240348298, -0.071815532464258744, -0.26792717880896527, 0.052480581416189075, 0.041432037960149271, -0.013810679320049757),
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        (-0.013810679320049757, -0.041432037960149271, 0.052480581416189075, 0.26792717880896527, -0.071815532464258744, -0.96674755240348298, 0.96674755240348298, 0.071815532464258744, -0.26792717880896527, -0.052480581416189075, 0.041432037960149271, 0.013810679320049757)
    ),
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        (0.0030210861012608843, -0.0090632583037826529, -0.016831765421310641, 0.074663985074019001, 0.031332978707362888, -0.301159125922835, -0.026499240945345472, 0.95164212189717856, 0.95164212189717856, -0.026499240945345472, -0.301159125922835, 0.031332978707362888, 0.074663985074019001, -0.016831765421310641, -0.0090632583037826529, 0.0030210861012608843),
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    ),
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    ),
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        (0.0, 0.0, 0.03968708834740544, 0.0079481086372403219, -0.054463788468236907, 0.34560528195603346, 0.73666018142821055, 0.34560528195603346, -0.054463788468236907, 0.0079481086372403219, 0.03968708834740544, 0.0),
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        (0.013456709459118716, -0.0026949668801115071, -0.13670658466432914, -0.093504697400938863, 0.47680326579848425, 0.89950610974864842, 0.47680326579848425, -0.093504697400938863, -0.13670658466432914, -0.0026949668801115071, 0.013456709459118716, 0.0),
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    ),
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    ),
    "dmey" : (
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    )
}


def daubcqf(N, TYPE='min'):
    """
    Computes the Daubechies' scaling and wavelet filters (normalized to sqrt(2)).

    Parameters
    ----------
    N : int
        Length of filter (must be even)
    TYPE : ['min', 'max', 'mid'], optional (default='min')
        Distinguishes the minimum phase, maximum phase and mid-phase solutions
        ('min', 'max', or 'mid').

    Returns
    -------
    h_0 : array-like, shape = [N]
        Daubechies' scaling filter 
    h_1 : array-like, shape = [N]
        Daubechies' wavelet filter 

    Examples
    --------
    >>> from rwt.wavelets import daubcqf
    >>> h_0, h_1 = daubcqf(N=4, TYPE='min')
    >>> print h_0, h_1
    [[0.4830, 0.8365, 0.2241, -0.1294]] [[0.1294, 0.2241, -0.8365, 0.4830]]
    """

    assert N%2==0, 'No Daubechies filter exists for odd length'

    K = int(N/2)
    a = 1
    p = 1
    q = 1

    h_0 = np.array([1.0, 1.0])
    for j in range(1, K):
        a = -a * 0.25 * (j + K - 1)/j
        h_0 = np.hstack((0, h_0)) + np.hstack((h_0, 0))
        p = np.hstack((0, -p)) + np.hstack((p, 0))
        p = np.hstack((0, -p)) + np.hstack((p, 0))
        q = np.hstack((0, q, 0)) + a * p

    q = np.sort(np.roots(q))

    qt = q[:K-1]

    if TYPE == 'mid':
        if K%2==1:
            ind = np.hstack((np.arange(0, N-2, 4), np.arange(1, N-2, 4)))
        else:
            ind = np.hstack(
                (
                    1,
                    np.arange(3, K-1, 4),
                    np.arange(4, K-1, 4),
                    np.arange(N-3, K, -4),
                    np.arange(N-4, K, -4)
                )
            )
        qt = q[ind]

    h_0 = np.convolve(h_0, np.real(np.poly(qt)))
    h_0 = np.sqrt(2) * h_0 / np.sum(h_0)

    h_0.shape = (1, -1)

    if TYPE=='max':
        h_0 = sp.fliplr(h_0);

    assert np.abs(np.sum(h_0 ** 2))-1 < 1e-4, 'Numerically unstable for this value of "N".'

    h_1 = sp.rot90(h_0, 2).copy()
    h_1[0, :N:2] = -h_1[0, :N:2]

    return (h_0, h_1)


def waveletlist():
    """
    Return the list of supported wavelets.

    Parameters
    ----------

    Returns
    -------
    wavelet_list : list of strings
        The names of supported wavelets. This names can be used in :py:func:`waveletCoeffs`.
        
    .. note:: 
        The wavelet coefficients are taken from the `PyWavelets - Discrete Wavelet Transform in Python <http://www.pybytes.com/pywavelets/>`_ pacakge,
        copyright (c) 2006-2010 `Filip Wasilewski <http://filipwasilewski.pl/>`_.
    """
    
    wavelet_names = ['haar'] + WAVELETS_DICT.keys()
    return wavelet_names

    
def waveletCoeffs(name):
    """
    Return the wavelet coefficients according to the wavelet name.

    Parameters
    ----------
    name : str
        Name of wavelet. Supported values:
            * '**haar**' : Haar wavelet
            * '**db1**'-'**db20**' : Daubechie wavelets with different support size
            * '**sym1**'-'**sym20**' : Symlets wavelets with different support size
            * '**coif1**'-'**coif5**' : Coiflets wavelets with different support size
            * '**bior1.{1,3,5}**', '**bior2.{2,4,6,8}**', '**bior3.{1,3,5,7}**', '**bior4.4**', '**bior5.5**', '**bior6.8**': Biorthogonal wavelets with different support size
            * '**dmey**' : Discrete Meyer wavelet
            
    Returns
    -------
    dec_lo : array
        Decoding coefficients of the scaling function
    dec_hi : array
        Decoding coefficients of the wavelet function
    rec_lo : array
        Reconstruction coefficients of the scaling function
    rec_hi : array
        Reconstruction coefficients of the wavelet function

    Examples
    --------
    >>> from rwt.wavelets import waveletCoeffs
    >>> dl, dh, rl, rh = waveletCoeffs("db1")
    
    .. note:: 
        The wavelet coefficients are taken from the `PyWavelets - Discrete Wavelet Transform in Python <http://www.pybytes.com/pywavelets/>`_ pacakge,
        copyright (c) 2006-2010 `Filip Wasilewski <http://filipwasilewski.pl/>`_.
    """
    
    if name == 'haar':
        name = 'db1'
        
    if name not in WAVELETS_DICT.keys():
        raise NameError("Unkown wavelet name. Available wavelets: %s", str(WAVELETS_DICT.keys()))
    
    dec_lo, dec_hi, rec_lo, rec_hi = WAVELETS_DICT[name]
    
    return np.array(dec_lo), np.array(dec_hi), np.array(rec_lo), np.array(rec_hi)


if __name__ == '__main__':

    N = 4
    TYPE = 'min'
    h_0, h_1 = daubcqf(N, TYPE)
    print h_0
    print h_1