from __future__ import division, print_function, absolute_import

import os
import warnings

import numpy as np
from numpy.testing import assert_equal, assert_allclose, assert_, \
    TestCase, assert_raises
from numpy import array, asarray, pi, sin, cos, arange, dot, ravel, sqrt, round
from scipy.interpolate.fitpack import splrep, splev, bisplrep, bisplev, \
     sproot, splprep, splint, spalde, splder, splantider, insert


def data_file(basename):
    return os.path.join(os.path.abspath(os.path.dirname(__file__)),
                        'data', basename)


def norm2(x):
    return sqrt(dot(x.T,x))


def f1(x,d=0):
    if d is None:
        return "sin"
    if x is None:
        return "sin(x)"
    if d % 4 == 0:
        return sin(x)
    if d % 4 == 1:
        return cos(x)
    if d % 4 == 2:
        return -sin(x)
    if d % 4 == 3:
        return -cos(x)


def f2(x,y=0,dx=0,dy=0):
    if x is None:
        return "sin(x+y)"
    d = dx+dy
    if d % 4 == 0:
        return sin(x+y)
    if d % 4 == 1:
        return cos(x+y)
    if d % 4 == 2:
        return -sin(x+y)
    if d % 4 == 3:
        return -cos(x+y)


def makepairs(x, y):
    """Helper function to create an array of pairs of x and y."""
    # Or itertools.product (>= python 2.6)
    xy = array([[a, b] for a in asarray(x) for b in asarray(y)])
    return xy.T


def put(*a):
    """Produce some output if file run directly"""
    import sys
    if hasattr(sys.modules['__main__'], '__put_prints'):
        sys.stderr.write("".join(map(str, a)) + "\n")


class TestSmokeTests(TestCase):
    """
    Smoke tests (with a few asserts) for fitpack routines -- mostly
    check that they are runnable
    """

    def check_1(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,at=0,xb=None,xe=None):
        if xb is None:
            xb = a
        if xe is None:
            xe = b
        x = a+(b-a)*arange(N+1,dtype=float)/float(N)    # nodes
        x1 = a+(b-a)*arange(1,N,dtype=float)/float(N-1)  # middle points of the nodes
        v,v1 = f(x),f(x1)
        nk = []

        def err_est(k, d):
            # Assume f has all derivatives < 1
            h = 1.0/float(N)
            tol = 5 * h**(.75*(k-d))
            if s > 0:
                tol += 1e5*s
            return tol

        for k in range(1,6):
            tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
            if at:
                t = tck[0][k:-k]
            else:
                t = x1
            nd = []
            for d in range(k+1):
                tol = err_est(k, d)
                err = norm2(f(t,d)-splev(t,tck,d)) / norm2(f(t,d))
                assert_(err < tol, (k, d, err, tol))
                nd.append((err, tol))
            nk.append(nd)
        put("\nf = %s  s=S_k(x;t,c)  x in [%s, %s] > [%s, %s]" % (f(None),
                                                        repr(round(xb,3)),repr(round(xe,3)),
                                                          repr(round(a,3)),repr(round(b,3))))
        if at:
            str = "at knots"
        else:
            str = "at the middle of nodes"
        put(" per=%d s=%s Evaluation %s" % (per,repr(s),str))
        put(" k :  |f-s|^2  |f'-s'| |f''-.. |f'''-. |f''''- |f'''''")
        k = 1
        for l in nk:
            put(' %d : ' % k)
            for r in l:
                put(' %.1e  %.1e' % r)
            put('\n')
            k = k+1

    def check_2(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
              ia=0,ib=2*pi,dx=0.2*pi):
        if xb is None:
            xb = a
        if xe is None:
            xe = b
        x = a+(b-a)*arange(N+1,dtype=float)/float(N)    # nodes
        v = f(x)

        def err_est(k, d):
            # Assume f has all derivatives < 1
            h = 1.0/float(N)
            tol = 5 * h**(.75*(k-d))
            if s > 0:
                tol += 1e5*s
            return tol

        nk = []
        for k in range(1,6):
            tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
            nk.append([splint(ia,ib,tck),spalde(dx,tck)])
        put("\nf = %s  s=S_k(x;t,c)  x in [%s, %s] > [%s, %s]" % (f(None),
                                                   repr(round(xb,3)),repr(round(xe,3)),
                                                    repr(round(a,3)),repr(round(b,3))))
        put(" per=%d s=%s N=%d [a, b] = [%s, %s]  dx=%s" % (per,repr(s),N,repr(round(ia,3)),repr(round(ib,3)),repr(round(dx,3))))
        put(" k :  int(s,[a,b]) Int.Error   Rel. error of s^(d)(dx) d = 0, .., k")
        k = 1
        for r in nk:
            if r[0] < 0:
                sr = '-'
            else:
                sr = ' '
            put(" %d   %s%.8f   %.1e " % (k,sr,abs(r[0]),
                                         abs(r[0]-(f(ib,-1)-f(ia,-1)))))
            d = 0
            for dr in r[1]:
                err = abs(1-dr/f(dx,d))
                tol = err_est(k, d)
                assert_(err < tol, (k, d))
                put(" %.1e %.1e" % (err, tol))
                d = d+1
            put("\n")
            k = k+1

    def check_3(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
              ia=0,ib=2*pi,dx=0.2*pi):
        if xb is None:
            xb = a
        if xe is None:
            xe = b
        x = a+(b-a)*arange(N+1,dtype=float)/float(N)    # nodes
        v = f(x)
        put("  k  :     Roots of s(x) approx %s  x in [%s,%s]:" %
              (f(None),repr(round(a,3)),repr(round(b,3))))
        for k in range(1,6):
            tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
            if k == 3:
                roots = sproot(tck)
                assert_allclose(splev(roots, tck), 0, atol=1e-10, rtol=1e-10)
                assert_allclose(roots, pi*array([1, 2, 3, 4]), rtol=1e-3)
                put('  %d  : %s' % (k, repr(roots.tolist())))
            else:
                assert_raises(ValueError, sproot, tck)

    def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
              ia=0,ib=2*pi,dx=0.2*pi):
        if xb is None:
            xb = a
        if xe is None:
            xe = b
        x = a+(b-a)*arange(N+1,dtype=float)/float(N)    # nodes
        x1 = a + (b-a)*arange(1,N,dtype=float)/float(N-1)  # middle points of the nodes
        v,v1 = f(x),f(x1)
        put(" u = %s   N = %d" % (repr(round(dx,3)),N))
        put("  k  :  [x(u), %s(x(u))]  Error of splprep  Error of splrep " % (f(0,None)))
        for k in range(1,6):
            tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
            tck = splrep(x,v,s=s,per=per,k=k)
            uv = splev(dx,tckp)
            err1 = abs(uv[1]-f(uv[0]))
            err2 = abs(splev(uv[0],tck)-f(uv[0]))
            assert_(err1 < 1e-2)
            assert_(err2 < 1e-2)
            put("  %d  :  %s    %.1e           %.1e" %
                  (k,repr([round(z,3) for z in uv]),
                   err1,
                   err2))
        put("Derivatives of parametric cubic spline at u (first function):")
        k = 3
        tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
        for d in range(1,k+1):
            uv = splev(dx,tckp,d)
            put(" %s " % (repr(uv[0])))

    def check_5(self,f=f2,kx=3,ky=3,xb=0,xe=2*pi,yb=0,ye=2*pi,Nx=20,Ny=20,s=0):
        x = xb+(xe-xb)*arange(Nx+1,dtype=float)/float(Nx)
        y = yb+(ye-yb)*arange(Ny+1,dtype=float)/float(Ny)
        xy = makepairs(x,y)
        tck = bisplrep(xy[0],xy[1],f(xy[0],xy[1]),s=s,kx=kx,ky=ky)
        tt = [tck[0][kx:-kx],tck[1][ky:-ky]]
        t2 = makepairs(tt[0],tt[1])
        v1 = bisplev(tt[0],tt[1],tck)
        v2 = f2(t2[0],t2[1])
        v2.shape = len(tt[0]),len(tt[1])
        err = norm2(ravel(v1-v2))
        assert_(err < 1e-2, err)
        put(err)

    def test_smoke_splrep_splev(self):
        put("***************** splrep/splev")
        self.check_1(s=1e-6)
        self.check_1()
        self.check_1(at=1)
        self.check_1(per=1)
        self.check_1(per=1,at=1)
        self.check_1(b=1.5*pi)
        self.check_1(b=1.5*pi,xe=2*pi,per=1,s=1e-1)

    def test_smoke_splint_spalde(self):
        put("***************** splint/spalde")
        self.check_2()
        self.check_2(per=1)
        self.check_2(ia=0.2*pi,ib=pi)
        self.check_2(ia=0.2*pi,ib=pi,N=50)

    def test_smoke_sproot(self):
        put("***************** sproot")
        self.check_3(a=0.1,b=15)

    def test_smoke_splprep_splrep_splev(self):
        put("***************** splprep/splrep/splev")
        self.check_4()
        self.check_4(N=50)

    def test_smoke_bisplrep_bisplev(self):
        put("***************** bisplev")
        self.check_5()


class TestSplev(TestCase):
    def test_1d_shape(self):
        x = [1,2,3,4,5]
        y = [4,5,6,7,8]
        tck = splrep(x, y)
        z = splev([1], tck)
        assert_equal(z.shape, (1,))
        z = splev(1, tck)
        assert_equal(z.shape, ())


class TestSplder(object):
    def __init__(self):
        # non-uniform grid, just to make it sure
        x = np.linspace(0, 1, 100)**3
        y = np.sin(20 * x)
        self.spl = splrep(x, y)

        # double check that knots are non-uniform
        assert_(np.diff(self.spl[0]).ptp() > 0)

    def test_inverse(self):
        # Check that antiderivative + derivative is identity.
        for n in range(5):
            spl2 = splantider(self.spl, n)
            spl3 = splder(spl2, n)
            assert_allclose(self.spl[0], spl3[0])
            assert_allclose(self.spl[1], spl3[1])
            assert_equal(self.spl[2], spl3[2])

    def test_splder_vs_splev(self):
        # Check derivative vs. FITPACK

        for n in range(3+1):
            # Also extrapolation!
            xx = np.linspace(-1, 2, 2000)
            if n == 3:
                # ... except that FITPACK extrapolates strangely for
                # order 0, so let's not check that.
                xx = xx[(xx >= 0) & (xx <= 1)]

            dy = splev(xx, self.spl, n)
            spl2 = splder(self.spl, n)
            dy2 = splev(xx, spl2)
            if n == 1:
                assert_allclose(dy, dy2, rtol=2e-6)
            else:
                assert_allclose(dy, dy2)

    def test_splantider_vs_splint(self):
        # Check antiderivative vs. FITPACK
        spl2 = splantider(self.spl)

        # no extrapolation, splint assumes function is zero outside
        # range
        xx = np.linspace(0, 1, 20)

        for x1 in xx:
            for x2 in xx:
                y1 = splint(x1, x2, self.spl)
                y2 = splev(x2, spl2) - splev(x1, spl2)
                assert_allclose(y1, y2)

    def test_order0_diff(self):
        assert_raises(ValueError, splder, self.spl, 4)

    def test_kink(self):
        # Should refuse to differentiate splines with kinks

        spl2 = insert(0.5, self.spl, m=2)
        splder(spl2, 2)  # Should work
        assert_raises(ValueError, splder, spl2, 3)

        spl2 = insert(0.5, self.spl, m=3)
        splder(spl2, 1)  # Should work
        assert_raises(ValueError, splder, spl2, 2)

        spl2 = insert(0.5, self.spl, m=4)
        assert_raises(ValueError, splder, spl2, 1)


class TestBisplrep(object):
    def test_overflow(self):
        a = np.linspace(0, 1, 620)