tweak docstrings; simplify tests

pypocketfft.cc

@@ -597,11 +597,18 @@ axes : list of integers
 inorm : int
     Normalization type
       0 : no normalization
-      1 : divide by sqrt(N)
+      1 : make transform orthogonal and divide by sqrt(N)
       2 : divide by N
     where N is the product of n_i for every transformed axis i.
     n_i is 2*(<axis_length>-1 for type 1 and 2*<axis length>
     for types 2, 3, 4.
+    Making the transform orthogonal involves the following additional steps
+    for every 1D sub-transform:
+      Type 1 : multiply first and last input value by sqrt(2)
+               divide first and last output value by sqrt(2)
+      Type 2 : divide first output value by sqrt(2)
+      Type 3 : multiply first input value by sqrt(2)
+      Type 4 : nothing
 out : numpy.ndarray (same shape and data type as `a`)
     May be identical to `a`, but if it isn't, it must not overlap with `a`.
     If None, a new array is allocated to store the output.
@@ -629,11 +636,17 @@ axes : list of integers
 inorm : int
     Normalization type
       0 : no normalization
-      1 : divide by sqrt(N)
+      1 : make transform orthogonal and divide by sqrt(N)
       2 : divide by N
     where N is the product of n_i for every transformed axis i.
     n_i is 2*(<axis_length>+1 for type 1 and 2*<axis length>
     for types 2, 3, 4.
+    Making the transform orthogonal involves the following additional steps
+    for every 1D sub-transform:
+      Type 1 : nothing
+      Type 2 : divide first output value by sqrt(2)
+      Type 3 : multiply first input value by sqrt(2)
+      Type 4 : nothing
 out : numpy.ndarray (same shape and data type as `a`)
     May be identical to `a`, but if it isn't, it must not overlap with `a`.
     If None, a new array is allocated to store the output.

test.py

@@ -55,36 +55,27 @@ def irfft_scipy(a, axis, inorm=0, out=None, nthreads=1):
                                    forward=False, inorm=inorm, out=out,
                                    nthreads=nthreads)
 
+tol = {np.float32: 6e-7, np.float64: 1.5e-15, np.longfloat: 1e-18}
+ctype = {np.float32: np.complex64, np.float64: np.complex128, np.longfloat: np.longcomplex}
 
 @pmp("len", len1D)
 @pmp("inorm", [0, 1, 2])
-def test1D(len, inorm):
+@pmp("dtype", [np.float32, np.float64, np.longfloat])
+def test1D(len, inorm, dtype):
     a = np.random.rand(len)-0.5 + 1j*np.random.rand(len)-0.5j
-    b = a.astype(np.complex64)
-    c = a.astype(np.complex256)
-    _assert_close(a, ifftn(fftn(c, inorm=inorm), inorm=2-inorm), 1e-18)
-    assert_(_l2error(a, ifftn(fftn(a, inorm=inorm), inorm=2-inorm)) < 1.5e-15)
+    a = a.astype(ctype[dtype])
+    eps = tol[dtype]
+    assert_(_l2error(a, ifftn(fftn(a, inorm=inorm), inorm=2-inorm)) < eps)
     assert_(_l2error(a.real, ifftn(fftn(a.real, inorm=inorm), inorm=2-inorm))
-            < 1.5e-15)
+            < eps)
     assert_(_l2error(a.real, fftn(ifftn(a.real, inorm=inorm), inorm=2-inorm))
-            < 1.5e-15)
+            < eps)
     assert_(_l2error(a.real, irfftn(rfftn(a.real, inorm=inorm),
-                                    inorm=2-inorm, lastsize=len)) < 1.5e-15)
+                                    inorm=2-inorm, lastsize=len)) < eps)
     tmp = a.copy()
     assert_(ifftn(fftn(tmp, out=tmp, inorm=inorm), out=tmp, inorm=2-inorm)
             is tmp)
-    assert_(_l2error(tmp, a) < 1.5e-15)
-    assert_(_l2error(b, ifftn(fftn(b, inorm=inorm), inorm=2-inorm)) < 6e-7)
-    assert_(_l2error(b.real, ifftn(fftn(b.real, inorm=inorm), inorm=2-inorm))
-            < 6e-7)
-    assert_(_l2error(b.real, fftn(ifftn(b.real, inorm=inorm), inorm=2-inorm))
-            < 6e-7)
-    assert_(_l2error(b.real, irfftn(rfftn(b.real, inorm=inorm), lastsize=len,
-                                    inorm=2-inorm)) < 6e-7)
-    tmp = b.copy()
-    assert_(ifftn(fftn(tmp, out=tmp, inorm=inorm), out=tmp, inorm=2-inorm)
-            is tmp)
-    assert_(_l2error(tmp, b) < 6e-7)
+    assert_(_l2error(tmp, a) < eps)
 
 
 @pmp("shp", shapes)
@@ -206,54 +197,17 @@ def test_genuine_hartley_2D(shp, axes):
 
 
 @pmp("len", len1D)
-@pmp("inorm", [0, 1, 2])
-@pmp("type", [1, 2, 3])
-def testdcst1D(len, inorm, type):
-    a = np.random.rand(len)-0.5
-    b = a.astype(np.float32)
-    c = a.astype(np.float128)
-    itp = (0, 1, 3, 2, 4)
-    itype = itp[type]
-    if type != 1 or len > 1:
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-18)
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-15)
-        _assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-7)
-    _assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-18)
-    _assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-15)
-    _assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-7)
-
-@pmp("len", len1D)
-@pmp("type", [1, 2, 3])
-def testdcst1Dortho(len, type):
-    a = np.random.rand(len)-0.5
-    b = a.astype(np.float32)
-    c = a.astype(np.float128)
-    itp = (0, 1, 3, 2, 4)
-    itype = itp[type]
-    if type != 1 or len > 1:
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=1, type=type), inorm=1, type=itype), 2e-18)
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=1, type=type), inorm=1, type=itype), 1.5e-15)
-        _assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=1, type=type), inorm=1, type=itype), 6e-7)
-    if type != 1:
-        _assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=1, type=type), inorm=1, type=itype), 2e-18)
-        _assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=1, type=type), inorm=1, type=itype), 1.5e-15)
-        _assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=1, type=type), inorm=1, type=itype), 6e-7)
-
-
-# TEMPORARY: separate test for DCT/DST IV, since they are less accurate
-@pmp("len", len1D)
-@pmp("inorm", [0, 1, 2])
-@pmp("type", [4])
-def testdcst1D4(len, inorm, type):
-    a = np.random.rand(len)-0.5
-    b = a.astype(np.float32)
-    c = a.astype(np.float128)
+@pmp("inorm", [0, 1])  # inorm==2 not needed, tested via inverse
+@pmp("type", [1, 2, 3, 4])
+@pmp("dtype", [np.float32, np.float64, np.longfloat])
+def testdcst1D(len, inorm, type, dtype):
+    a = (np.random.rand(len)-0.5).astype(dtype)
+    eps = tol[dtype]
     itp = (0, 1, 3, 2, 4)
+    if type==4 and len%2 == 1:  # relaxed accuracies for odd-length type 4 transforms
+        special_tol = {np.float32: 4e-5, np.float64: 6e-14, np.longfloat: 4e-17}
+        eps = special_tol[dtype]
     itype = itp[type]
-    if type != 1 or len > 1:
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
-        _assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
-        _assert_close(b, pypocketfft.dct(pypocketfft.dct(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)
-    _assert_close(a, pypocketfft.dst(pypocketfft.dst(c, inorm=inorm, type=type), inorm=2-inorm, type=itype), 2e-16)
-    _assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), 1.5e-13)
-    _assert_close(b, pypocketfft.dst(pypocketfft.dst(b, inorm=inorm, type=type), inorm=2-inorm, type=itype), 6e-5)
+    if type != 1 or len > 1:  # there are no length-1 type 1 DCTs
+        _assert_close(a, pypocketfft.dct(pypocketfft.dct(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), eps)
+    _assert_close(a, pypocketfft.dst(pypocketfft.dst(a, inorm=inorm, type=type), inorm=2-inorm, type=itype), eps)