BUG: fix DCT normalisation

dctdlt.c

@@ -44,11 +44,11 @@ void dctdlt(unsigned int n, unsigned int stride_in, const double* dct,
     double a, b;
     unsigned int i, j;
 
-    a = 0.5;
-    b = 1.;
+    a = 1.;
+    b = 2.;
     if(n > 0)
     {
-        *dlt = b*dct[0];
+        *dlt = dct[0];
         for(j = 2; j < n; j += 2)
         {
             b *= (j-3.)/(j+1.);
@@ -93,11 +93,11 @@ void dltdct(unsigned int n, unsigned int stride_in, const double* dlt,
     double a, b;
     unsigned int i, j;
 
-    a = 2.;
+    a = 1.;
     b = 1.;
     if(n > 0)
     {
-        *dct = b*dlt[0];
+        *dct = dlt[0];
         for(j = 2; j < n; j += 2)
         {
             b *= ((j-1.)*(j-1.))/(j*j);

flt.pyx

@@ -130,7 +130,11 @@ def dlt(a, closed=False):
         dcttype = 3
 
     # compute the DCT coefficients
-    b = idct(a, type=dcttype, axis=-1, norm=None)
+    b = idct(a, type=dcttype, axis=-1, norm='backward')
+
+    # fix last coefficient for DCT-I
+    if closed:
+        b[-1] /= 2
 
     # memview for C interop
     cdef double[::1] b_ = b
@@ -222,8 +226,12 @@ def idlt(b, closed=False):
     # transform DLT coefficients to DCT coefficients using C function
     dltdct(n, 1, &b_[0], 1, &a_[0])
 
+    # fix last coefficient for DCT-I
+    if closed:
+        a[-1] *= 2
+
     # perform the DCT
-    return dct(a, type=dcttype, axis=-1, norm=None, overwrite_x=True)
+    return dct(a, type=dcttype, axis=-1, norm='backward', overwrite_x=True)
 
 
 def dltmtx(n, closed=False):

setup.cfg

@@ -1,6 +1,6 @@
 [metadata]
 name = flt
-version = 2022.7.27
+version = 2022.7.27.1
 maintainer = Nicolas Tessore
 maintainer_email = n.tessore@ucl.ac.uk
 description = fast Legendre transform

test_flt.py

@@ -0,0 +1,30 @@
+import numpy as np
+import pytest
+
+from flt import dlt, idlt, theta
+
+
+@pytest.mark.parametrize('n', [2, 5, 10, 11, 100, 101, 1000, 1001])
+@pytest.mark.parametrize('closed', [False, True])
+def test_dlt(n, closed):
+    t = theta(n, closed=closed)
+    for i in range(n):
+        a = np.zeros(n)
+        a[i] = 1
+
+        f = np.polynomial.legendre.legval(np.cos(t), a)
+
+        np.testing.assert_allclose(dlt(f, closed=closed), a, rtol=0, atol=1e-12)
+
+
+@pytest.mark.parametrize('n', [2, 5, 10, 11, 100, 101, 1000, 1001])
+@pytest.mark.parametrize('closed', [False, True])
+def test_idlt(n, closed):
+    t = theta(n, closed=closed)
+    for i in range(n):
+        a = np.zeros(n)
+        a[i] = 1
+
+        f = np.polynomial.legendre.legval(np.cos(t), a)
+
+        np.testing.assert_allclose(idlt(a, closed=closed), f, rtol=0, atol=1e-10)