[Scipy-svn] r7141 - in trunk: doc/source/tutorial scipy/signal scipy/signal/tests
scipy-svn at scipy.org
scipy-svn at scipy.org
Sat Feb 12 23:48:41 EST 2011
Author: rgommers
Date: 2011-02-12 22:48:40 -0600 (Sat, 12 Feb 2011)
New Revision: 7141
Added:
trunk/scipy/signal/spectral.c
trunk/scipy/signal/spectral.pyx
trunk/scipy/signal/tests/test_spectral.py
Modified:
trunk/doc/source/tutorial/signal.rst
trunk/scipy/signal/SConscript
trunk/scipy/signal/__init__.py
trunk/scipy/signal/setup.py
Log:
ENH: Add Lomb-Scargle periodogram in new signal.spectral module.
Thanks to Pim Schellart for this contribution.
Modified: trunk/doc/source/tutorial/signal.rst
===================================================================
--- trunk/doc/source/tutorial/signal.rst 2011-02-12 10:58:52 UTC (rev 7140)
+++ trunk/doc/source/tutorial/signal.rst 2011-02-13 04:48:40 UTC (rev 7141)
@@ -3,6 +3,10 @@
.. sectionauthor:: Travis E. Oliphant
+.. sectionauthor:: Pim Schellart
+
+.. currentmodule:: scipy.signal
+
The signal processing toolbox currently contains some filtering
functions, a limited set of filter design tools, and a few B-spline
interpolation algorithms for one- and two-dimensional data. While the
@@ -19,25 +23,29 @@
A B-spline is an approximation of a continuous function over a finite-
domain in terms of B-spline coefficients and knot points. If the knot-
-points are equally spaced with spacing :math:`\Delta x` , then the B-spline approximation to a 1-dimensional function is the
-finite-basis expansion.
+points are equally spaced with spacing :math:`\Delta x` , then the B-spline
+approximation to a 1-dimensional function is the finite-basis expansion.
.. math::
:nowrap:
\[ y\left(x\right)\approx\sum_{j}c_{j}\beta^{o}\left(\frac{x}{\Delta x}-j\right).\]
-In two dimensions with knot-spacing :math:`\Delta x` and :math:`\Delta y` , the function representation is
+In two dimensions with knot-spacing :math:`\Delta x` and :math:`\Delta y` , the
+function representation is
.. math::
:nowrap:
\[ z\left(x,y\right)\approx\sum_{j}\sum_{k}c_{jk}\beta^{o}\left(\frac{x}{\Delta x}-j\right)\beta^{o}\left(\frac{y}{\Delta y}-k\right).\]
-In these expressions, :math:`\beta^{o}\left(\cdot\right)` is the space-limited B-spline basis function of order, :math:`o` . The requirement of equally-spaced knot-points and equally-spaced
-data points, allows the development of fast (inverse-filtering)
-algorithms for determining the coefficients, :math:`c_{j}` , from sample-values, :math:`y_{n}` . Unlike the general spline interpolation algorithms, these algorithms
-can quickly find the spline coefficients for large images.
+In these expressions, :math:`\beta^{o}\left(\cdot\right)` is the space-limited
+B-spline basis function of order, :math:`o` . The requirement of equally-spaced
+knot-points and equally-spaced data points, allows the development of fast
+(inverse-filtering) algorithms for determining the coefficients, :math:`c_{j}`
+, from sample-values, :math:`y_{n}` . Unlike the general spline interpolation
+algorithms, these algorithms can quickly find the spline coefficients for large
+images.
The advantage of representing a set of samples via B-spline basis
functions is that continuous-domain operators (derivatives, re-
@@ -179,7 +187,9 @@
In this case, the matrix multiplication can be accomplished using
Fourier transforms.
-Let :math:`x\left[n\right]` define a one-dimensional signal indexed by the integer :math:`n.` Full convolution of two one-dimensional signals can be expressed as
+Let :math:`x\left[n\right]` define a one-dimensional signal indexed by the
+integer :math:`n.` Full convolution of two one-dimensional signals can be
+expressed as
.. math::
:nowrap:
@@ -199,14 +209,17 @@
\[ y\left[n\right]=\sum_{k=\max\left(n-M,0\right)}^{\min\left(n,K\right)}x\left[k\right]h\left[n-k\right].\]
-For convenience assume :math:`K\geq M.` Then, more explicitly the output of this operation is
+For convenience assume :math:`K\geq M.` Then, more explicitly the output of
+this operation is
.. math::
:nowrap:
\begin{eqnarray*} y\left[0\right] & = & x\left[0\right]h\left[0\right]\\ y\left[1\right] & = & x\left[0\right]h\left[1\right]+x\left[1\right]h\left[0\right]\\ y\left[2\right] & = & x\left[0\right]h\left[2\right]+x\left[1\right]h\left[1\right]+x\left[2\right]h\left[0\right]\\ \vdots & \vdots & \vdots\\ y\left[M\right] & = & x\left[0\right]h\left[M\right]+x\left[1\right]h\left[M-1\right]+\cdots+x\left[M\right]h\left[0\right]\\ y\left[M+1\right] & = & x\left[1\right]h\left[M\right]+x\left[2\right]h\left[M-1\right]+\cdots+x\left[M+1\right]h\left[0\right]\\ \vdots & \vdots & \vdots\\ y\left[K\right] & = & x\left[K-M\right]h\left[M\right]+\cdots+x\left[K\right]h\left[0\right]\\ y\left[K+1\right] & = & x\left[K+1-M\right]h\left[M\right]+\cdots+x\left[K\right]h\left[1\right]\\ \vdots & \vdots & \vdots\\ y\left[K+M-1\right] & = & x\left[K-1\right]h\left[M\right]+x\left[K\right]h\left[M-1\right]\\ y\left[K+M\right] & = & x\left[K\right]h\left[M\right].\end{eqnarray*}
-Thus, the full discrete convolution of two finite sequences of lengths :math:`K+1` and :math:`M+1` respectively results in a finite sequence of length :math:`K+M+1=\left(K+1\right)+\left(M+1\right)-1.`
+Thus, the full discrete convolution of two finite sequences of lengths
+:math:`K+1` and :math:`M+1` respectively results in a finite sequence of length
+:math:`K+M+1=\left(K+1\right)+\left(M+1\right)-1.`
One dimensional convolution is implemented in SciPy with the function
``signal.convolve`` . This function takes as inputs the signals
@@ -237,7 +250,10 @@
\[ w\left[n\right]=\sum_{k=-\infty}^{\infty}y\left[k\right]x\left[n+k\right]\]
-is the (cross) correlation of the signals :math:`y` and :math:`x.` For finite-length signals with :math:`y\left[n\right]=0` outside of the range :math:`\left[0,K\right]` and :math:`x\left[n\right]=0` outside of the range :math:`\left[0,M\right],` the summation can simplify to
+is the (cross) correlation of the signals :math:`y` and :math:`x.` For
+finite-length signals with :math:`y\left[n\right]=0` outside of the range
+:math:`\left[0,K\right]` and :math:`x\left[n\right]=0` outside of the range
+:math:`\left[0,M\right],` the summation can simplify to
.. math::
:nowrap:
@@ -299,7 +315,8 @@
:math:`y\left[n\right]` for :math:`n<0` resulting in a filter that
cannot be expressed using convolution.
-The difference equation filter can be thought of as finding :math:`y\left[n\right]` recursively in terms of it's previous values
+The difference equation filter can be thought of as finding
+:math:`y\left[n\right]` recursively in terms of it's previous values
.. math::
:nowrap:
@@ -352,7 +369,10 @@
\[ z_{m}\left[n\right]=\sum_{p=0}^{K-m-1}\left(b_{m+p+1}x\left[n-p\right]-a_{m+p+1}y\left[n-p\right]\right).\]
-Using this formula we can find the intial condition vector :math:`z_{0}\left[-1\right]` to :math:`z_{K-1}\left[-1\right]` given initial conditions on :math:`y` (and :math:`x` ). The command :obj:`signal.lfiltic` performs this function.
+Using this formula we can find the intial condition vector
+:math:`z_{0}\left[-1\right]` to :math:`z_{K-1}\left[-1\right]` given initial
+conditions on :math:`y` (and :math:`x` ). The command :obj:`signal.lfiltic`
+performs this function.
Other filters
@@ -433,8 +453,83 @@
\[ Y=X\cdot H\]
-where :math:`H` is 2 for positive frequencies, :math:`0` for negative frequencies and :math:`1` for zero-frequencies.
+where :math:`H` is 2 for positive frequencies, :math:`0` for negative
+frequencies and :math:`1` for zero-frequencies.
+
+Least-Squares Spectral Analysis (:mod:`spectral`)
+-------------------------------------------------
+
+Least-squares spectral analysis (LSSA) is a method of estimating a frequency
+spectrum, based on a least squares fit of sinusoids to data samples, similar to
+Fourier analysis. Fourier analysis, the most used spectral method in science,
+generally boosts long-periodic noise in long gapped records; LSSA mitigates
+such problems.
+
+
+Lomb-Scargle Periodograms (:func:`spectral.lombscargle`)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The Lomb-Scargle method performs spectral analysis on unevenly sampled data and
+is known to be a powerful way to find, and test the significance of, weak
+periodic signals.
+
+For a time series comprising :math:`N_{t}` measurements
+:math:`X_{j}\equiv X(t_{j})` sampled at times :math:`t_{j}` where
+:math:`(j = 1, \ldots, N_{t})`, assumed to have been scaled and shifted
+such that its mean is zero and its variance is unity, the normalized
+Lomb-Scargle periodogram at frequency :math:`f` is
+
+.. math::
+
+ P_{n}(f) \frac{1}{2}\left\{\frac{\left[\sum_{j}^{N_{t}}X_{j}\cos\omega(t_{j}-\tau)\right]^{2}}{\sum_{j}^{N_{t}}\cos^{2}\omega(t_{j}-\tau)}+\frac{\left[\sum_{j}^{N_{t}}X_{j}\sin\omega(t_{j}-\tau)\right]^{2}}{\sum_{j}^{N_{t}}\sin^{2}\omega(t_{j}-\tau)}\right\}.
+
+Here, :math:`\omega \equiv 2\pi f` is the angular frequency.
+The frequency dependent time offset :math:`\tau` is given by
+
+.. math::
+
+ \tan 2\omega\tau = \frac{\sum_{j}^{N_{t}}\sin 2\omega t_{j}}{\sum_{j}^{N_{t}}\cos 2\omega t_{j}}.
+
+The :func:`~scipy.signal.spectral.lombscargle` function
+calculates the periodogram using a slightly
+modified algorithm due to Townsend [3]_ which allows the
+periodogram to be calculated using only a single pass through
+the input arrays for each frequency.
+
+The equation is refactored as:
+
+.. math::
+
+ P_{n}(f) = \frac{1}{2}\left[\frac{(c_{\tau}XC + s_{\tau}XS)^{2}}{c_{\tau}^{2}CC + 2c_{\tau}s_{\tau}CS + s_{\tau}^{2}SS} + \frac{(c_{\tau}XS - s_{\tau}XC)^{2}}{c_{\tau}^{2}SS - 2c_{\tau}s_{\tau}CS + s_{\tau}^{2}CC}\right]
+
+and
+
+.. math::
+
+ \tan 2\omega\tau = \frac{2CS}{CC-SS}.
+
+Here,
+
+.. math::
+
+ c_{\tau} = \cos\omega\tau,\qquad s_{\tau} = \sin\omega\tau
+
+while the sums are
+
+.. math::
+
+ XC &= \sum_{j}^{N_{t}} X_{j}\cos\omega t_{j}\\
+ XS &= \sum_{j}^{N_{t}} X_{j}\sin\omega t_{j}\\
+ CC &= \sum_{j}^{N_{t}} \cos^{2}\omega t_{j}\\
+ SS &= \sum_{j}^{N_{t}} \sin^{2}\omega t_{j}\\
+ CS &= \sum_{j}^{N_{t}} \cos\omega t_{j}\sin\omega t_{j}.
+
+This requires :math:`N_{f}(2N_{t}+3)` trigonometric function
+evaluations giving a factor of :math:`\sim 2` speed increase over the
+straightforward implementation.
+
+
.. XXX: TODO
..
.. Detrend
@@ -542,3 +637,20 @@
..
.. Tilbert transform
.. -----------------
+
+
+.. rubric:: References
+
+Some further reading and related software:
+
+.. [1] N.R. Lomb "Least-squares frequency analysis of unequally spaced
+data", Astrophysics and Space Science, vol 39, pp. 447-462, 1976
+
+.. [2] J.D. Scargle "Studies in astronomical time series analysis. II -
+Statistical aspects of spectral analysis of unevenly spaced data",
+The Astrophysical Journal, vol 263, pp. 835-853, 1982
+
+.. [3] R.H.D. Townsend, "Fast calculation of the Lomb-Scargle
+periodogram using graphics processing units.", The Astrophysical
+Journal Supplement Series, vol 191, pp. 247-253, 2010
+
Modified: trunk/scipy/signal/SConscript
===================================================================
--- trunk/scipy/signal/SConscript 2011-02-12 10:58:52 UTC (rev 7140)
+++ trunk/scipy/signal/SConscript 2011-02-13 04:48:40 UTC (rev 7141)
@@ -13,6 +13,8 @@
'firfilter.c', \
'medianfilter.c'])
+env.NumpyPythonExtension('spectral', source='spectral.c')
+
env.NumpyPythonExtension('spline',
source = ['splinemodule.c', 'S_bspline_util.c',
'D_bspline_util.c', 'C_bspline_util.c',
Modified: trunk/scipy/signal/__init__.py
===================================================================
--- trunk/scipy/signal/__init__.py 2011-02-12 10:58:52 UTC (rev 7140)
+++ trunk/scipy/signal/__init__.py 2011-02-13 04:48:40 UTC (rev 7141)
@@ -12,6 +12,7 @@
from ltisys import *
from windows import *
from signaltools import *
+from spectral import *
from wavelets import *
__all__ = filter(lambda s:not s.startswith('_'),dir())
Modified: trunk/scipy/signal/setup.py
===================================================================
--- trunk/scipy/signal/setup.py 2011-02-12 10:58:52 UTC (rev 7140)
+++ trunk/scipy/signal/setup.py 2011-02-13 04:48:40 UTC (rev 7141)
@@ -15,6 +15,8 @@
include_dirs=['.']
)
+ config.add_extension('spectral', sources=['spectral.c'])
+
config.add_extension('spline',
sources = ['splinemodule.c','S_bspline_util.c','D_bspline_util.c',
'C_bspline_util.c','Z_bspline_util.c','bspline_util.c'],
Added: trunk/scipy/signal/spectral.c
===================================================================
--- trunk/scipy/signal/spectral.c (rev 0)
+++ trunk/scipy/signal/spectral.c 2011-02-13 04:48:40 UTC (rev 7141)
@@ -0,0 +1,5108 @@
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+#else
+#define T_SIZET \
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+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
+static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject*);
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+#if __GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))
+#define likely(x) __builtin_expect(!!(x), 1)
+#define unlikely(x) __builtin_expect(!!(x), 0)
+#else /* __GNUC__ > 2 ... */
+#define likely(x) (x)
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+#endif /* __GNUC__ > 2 ... */
+#else /* __GNUC__ */
+#define likely(x) (x)
+#define unlikely(x) (x)
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+static PyObject *__pyx_b;
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+static PyObject *__pyx_empty_bytes;
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+ #define CYTHON_CCOMPLEX 0
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+
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+ #include <complex.h>
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+#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
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+typedef npy_int16 __pyx_t_5numpy_int16_t;
+
+typedef npy_int32 __pyx_t_5numpy_int32_t;
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+typedef npy_int64 __pyx_t_5numpy_int64_t;
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+typedef npy_uint8 __pyx_t_5numpy_uint8_t;
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+typedef npy_uint16 __pyx_t_5numpy_uint16_t;
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+typedef npy_uint32 __pyx_t_5numpy_uint32_t;
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+typedef npy_uint64 __pyx_t_5numpy_uint64_t;
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+typedef npy_float32 __pyx_t_5numpy_float32_t;
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+typedef npy_float64 __pyx_t_5numpy_float64_t;
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+typedef npy_long __pyx_t_5numpy_int_t;
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+typedef npy_longlong __pyx_t_5numpy_long_t;
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+typedef npy_intp __pyx_t_5numpy_intp_t;
+
+typedef npy_uintp __pyx_t_5numpy_uintp_t;
+
+typedef npy_ulong __pyx_t_5numpy_uint_t;
+
+typedef npy_ulonglong __pyx_t_5numpy_ulong_t;
+
+typedef npy_double __pyx_t_5numpy_float_t;
+
+typedef npy_double __pyx_t_5numpy_double_t;
+
+typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
+
+#if CYTHON_CCOMPLEX
+ #ifdef __cplusplus
+ typedef ::std::complex< float > __pyx_t_float_complex;
+ #else
+ typedef float _Complex __pyx_t_float_complex;
+ #endif
+#else
+ typedef struct { float real, imag; } __pyx_t_float_complex;
+#endif
+
+#if CYTHON_CCOMPLEX
+ #ifdef __cplusplus
+ typedef ::std::complex< double > __pyx_t_double_complex;
+ #else
+ typedef double _Complex __pyx_t_double_complex;
+ #endif
+#else
+ typedef struct { double real, imag; } __pyx_t_double_complex;
+#endif
+
+/* Type declarations */
+
+typedef npy_cfloat __pyx_t_5numpy_cfloat_t;
+
+typedef npy_cdouble __pyx_t_5numpy_cdouble_t;
+
+typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;
+
+typedef npy_cdouble __pyx_t_5numpy_complex_t;
+
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+ #define __Pyx_GIVEREF(r)
+ #define __Pyx_XDECREF(r) Py_XDECREF(r)
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+#define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);} } while(0)
+#define __Pyx_XGOTREF(r) do { if((r) != NULL) {__Pyx_GOTREF(r);} } while(0)
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+static void __Pyx_RaiseDoubleKeywordsError(
+ const char* func_name, PyObject* kw_name); /*proto*/
+
+static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
+ Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found); /*proto*/
+
+static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[], PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args, const char* function_name); /*proto*/
+
+/* Run-time type information about structs used with buffers */
+struct __Pyx_StructField_;
+
+typedef struct {
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+ struct __Pyx_StructField_* fields;
+ size_t size; /* sizeof(type) */
+ char typegroup; /* _R_eal, _C_omplex, Signed _I_nt, _U_nsigned int, _S_truct, _P_ointer, _O_bject */
+} __Pyx_TypeInfo;
+
+typedef struct __Pyx_StructField_ {
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+} __Pyx_StructField;
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+typedef struct {
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+} __Pyx_BufFmt_StackElem;
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+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
+static int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
+#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
+
+#define __Pyx_SetItemInt(o, i, v, size, to_py_func) ((size <= sizeof(Py_ssize_t)) ? \
+ __Pyx_SetItemInt_Fast(o, i, v, size <= sizeof(long)) : \
+ __Pyx_SetItemInt_Generic(o, to_py_func(i), v))
+
+static CYTHON_INLINE int __Pyx_SetItemInt_Generic(PyObject *o, PyObject *j, PyObject *v) {
+ int r;
+ if (!j) return -1;
+ r = PyObject_SetItem(o, j, v);
+ Py_DECREF(j);
+ return r;
+}
+
+static CYTHON_INLINE int __Pyx_SetItemInt_Fast(PyObject *o, Py_ssize_t i, PyObject *v, int fits_long) {
+ if (PyList_CheckExact(o) && ((0 <= i) & (i < PyList_GET_SIZE(o)))) {
+ Py_INCREF(v);
+ Py_DECREF(PyList_GET_ITEM(o, i));
+ PyList_SET_ITEM(o, i, v);
+ return 1;
+ }
+ else if (Py_TYPE(o)->tp_as_sequence && Py_TYPE(o)->tp_as_sequence->sq_ass_item && (likely(i >= 0)))
+ return PySequence_SetItem(o, i, v);
+ else {
+ PyObject *j = fits_long ? PyInt_FromLong(i) : PyLong_FromLongLong(i);
+ return __Pyx_SetItemInt_Generic(o, j, v);
+ }
+}
+
+static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb); /*proto*/
+static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb); /*proto*/
+
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);
+
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(void);
+
+static PyObject *__Pyx_UnpackItem(PyObject *, Py_ssize_t index); /*proto*/
+static int __Pyx_EndUnpack(PyObject *); /*proto*/
+
+static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); /*proto*/
+
+static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);
+
+static void __Pyx_UnpackTupleError(PyObject *, Py_ssize_t index); /*proto*/
+
+static int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
+ const char *name, int exact); /*proto*/
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
+static void __Pyx_ReleaseBuffer(Py_buffer *view);
+#else
+#define __Pyx_GetBuffer PyObject_GetBuffer
+#define __Pyx_ReleaseBuffer PyBuffer_Release
+#endif
+
+Py_ssize_t __Pyx_zeros[] = {0};
+Py_ssize_t __Pyx_minusones[] = {-1};
+
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list); /*proto*/
+
+static PyObject *__Pyx_GetName(PyObject *dict, PyObject *name); /*proto*/
+
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb); /*proto*/
+
+static CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_npy_intp(npy_intp);
+
+#if CYTHON_CCOMPLEX
+ #ifdef __cplusplus
+ #define __Pyx_CREAL(z) ((z).real())
+ #define __Pyx_CIMAG(z) ((z).imag())
+ #else
+ #define __Pyx_CREAL(z) (__real__(z))
+ #define __Pyx_CIMAG(z) (__imag__(z))
+ #endif
+#else
+ #define __Pyx_CREAL(z) ((z).real)
+ #define __Pyx_CIMAG(z) ((z).imag)
+#endif
+
+#if defined(_WIN32) && defined(__cplusplus) && CYTHON_CCOMPLEX
+ #define __Pyx_SET_CREAL(z,x) ((z).real(x))
+ #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
+#else
+ #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
+ #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
+#endif
+
+static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);
+
+#if CYTHON_CCOMPLEX
+ #define __Pyx_c_eqf(a, b) ((a)==(b))
+ #define __Pyx_c_sumf(a, b) ((a)+(b))
+ #define __Pyx_c_difff(a, b) ((a)-(b))
+ #define __Pyx_c_prodf(a, b) ((a)*(b))
+ #define __Pyx_c_quotf(a, b) ((a)/(b))
+ #define __Pyx_c_negf(a) (-(a))
+ #ifdef __cplusplus
+ #define __Pyx_c_is_zerof(z) ((z)==(float)0)
+ #define __Pyx_c_conjf(z) (::std::conj(z))
+ /*#define __Pyx_c_absf(z) (::std::abs(z))*/
+ #else
+ #define __Pyx_c_is_zerof(z) ((z)==0)
+ #define __Pyx_c_conjf(z) (conjf(z))
+ /*#define __Pyx_c_absf(z) (cabsf(z))*/
+ #endif
+#else
+ static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex, __pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex, __pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex, __pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex, __pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex, __pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex);
+ static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex);
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex);
+ /*static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex);*/
+#endif
+
+static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);
+
+#if CYTHON_CCOMPLEX
+ #define __Pyx_c_eq(a, b) ((a)==(b))
+ #define __Pyx_c_sum(a, b) ((a)+(b))
+ #define __Pyx_c_diff(a, b) ((a)-(b))
+ #define __Pyx_c_prod(a, b) ((a)*(b))
+ #define __Pyx_c_quot(a, b) ((a)/(b))
+ #define __Pyx_c_neg(a) (-(a))
+ #ifdef __cplusplus
+ #define __Pyx_c_is_zero(z) ((z)==(double)0)
+ #define __Pyx_c_conj(z) (::std::conj(z))
+ /*#define __Pyx_c_abs(z) (::std::abs(z))*/
+ #else
+ #define __Pyx_c_is_zero(z) ((z)==0)
+ #define __Pyx_c_conj(z) (conj(z))
+ /*#define __Pyx_c_abs(z) (cabs(z))*/
+ #endif
+#else
+ static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex, __pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex, __pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex, __pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex, __pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex, __pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex);
+ static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex);
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex);
+ /*static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex);*/
+#endif
+
+static CYTHON_INLINE unsigned char __Pyx_PyInt_AsUnsignedChar(PyObject *);
+
+static CYTHON_INLINE unsigned short __Pyx_PyInt_AsUnsignedShort(PyObject *);
+
+static CYTHON_INLINE unsigned int __Pyx_PyInt_AsUnsignedInt(PyObject *);
+
+static CYTHON_INLINE char __Pyx_PyInt_AsChar(PyObject *);
+
+static CYTHON_INLINE short __Pyx_PyInt_AsShort(PyObject *);
+
+static CYTHON_INLINE int __Pyx_PyInt_AsInt(PyObject *);
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+static CYTHON_INLINE signed char __Pyx_PyInt_AsSignedChar(PyObject *);
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+static CYTHON_INLINE signed short __Pyx_PyInt_AsSignedShort(PyObject *);
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+static CYTHON_INLINE signed int __Pyx_PyInt_AsSignedInt(PyObject *);
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+static CYTHON_INLINE unsigned long __Pyx_PyInt_AsUnsignedLong(PyObject *);
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+static CYTHON_INLINE unsigned PY_LONG_LONG __Pyx_PyInt_AsUnsignedLongLong(PyObject *);
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+static CYTHON_INLINE long __Pyx_PyInt_AsLong(PyObject *);
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+static CYTHON_INLINE PY_LONG_LONG __Pyx_PyInt_AsLongLong(PyObject *);
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+static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject *);
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+static CYTHON_INLINE signed PY_LONG_LONG __Pyx_PyInt_AsSignedLongLong(PyObject *);
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+static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, long size, int strict); /*proto*/
+
+static PyObject *__Pyx_ImportModule(const char *name); /*proto*/
+
+static void __Pyx_AddTraceback(const char *funcname); /*proto*/
+
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); /*proto*/
+/* Module declarations from python_buffer */
+
+/* Module declarations from python_ref */
+
+/* Module declarations from stdlib */
+
+/* Module declarations from stdio */
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+
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+static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
+static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
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+static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew1(PyObject *); /*proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew2(PyObject *, PyObject *); /*proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew3(PyObject *, PyObject *, PyObject *); /*proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew4(PyObject *, PyObject *, PyObject *, PyObject *); /*proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew5(PyObject *, PyObject *, PyObject *, PyObject *, PyObject *); /*proto*/
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+static CYTHON_INLINE void __pyx_f_5numpy_set_array_base(PyArrayObject *, PyObject *); /*proto*/
+static CYTHON_INLINE PyObject *__pyx_f_5numpy_get_array_base(PyArrayObject *); /*proto*/
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+static char __pyx_k__ndim[] = "ndim";
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+static char __pyx_k__dtype[] = "dtype";
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+static char __pyx_k__freqs[] = "freqs";
+static char __pyx_k__names[] = "names";
+static char __pyx_k__numpy[] = "numpy";
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+/* "/Users/rgommers/Code/scipy/scipy/signal/spectral.pyx":16
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+static char __pyx_doc_5scipy_6signal_8spectral_lombscargle[] = "Computes the Lomb-Scargle periodogram.\n"" \n"" The Lomb-Scargle periodogram was developed by Lomb [1]_ and further\n"" extended by Scargle [2]_ to find, and test the significance of weak\n"" periodic signals with uneven temporal sampling.\n""\n"" The computed periodogram is unnormalized, it takes the value\n"" ``(A**2) * N/4`` for a harmonic signal with amplitude A for sufficiently\n"" large N.\n""\n"" Parameters\n"" ----------\n"" x : array_like\n"" Sample times.\n"" y : array_like\n"" Measurement values.\n"" freqs : array_like\n"" Angular frequencies for output periodogram.\n""\n"" Returns\n"" -------\n"" pgram : array_like\n"" Lomb-Scargle periodogram.\n""\n"" Raises\n"" ------\n"" ValueError\n"" If the input arrays `x` and `y` do not have the same shape.\n""\n"" Notes\n"" -----\n"" This subroutine calculates the periodogram using a slightly\n"" modified algorithm due to Townsend [3]_ which allows the\n"" periodogram to be calculated using only a single pass through\n"" the input arrays for each frequency.\n""\n"" The algorithm running time scales roughly as O(x * freqs) or O(N^2)\n"" for a large number of samples and frequencies.\n""\n"" References\n"" ----------\n"" .. [1] N.R. Lomb \"Least-squares frequency analysis of unequally spaced\n"" data\", Astrophysics and Space Science, vol 39, pp. 447-462, 1976\n""\n"" .. [2] J.D. Scargle \"Studies in astronomical time series analysis. II - \n"" Statistical aspects of spectral analysis of unevenly spaced data\",\n"" The Astrophysical Journal, vol 263, pp. 835-853, 1982\n""\n"" .. [3] R.H.D. Townsend, \"Fast calculation of the Lomb-Scargle\n"" periodogram using graphics processing units.\", The Astrophysical\n"" Journal Supplement Series, vol 191, pp. 247-253, 2010\n""\n"" Examples\n"" --------\n"" >>> import scipy.signal\n""\n"" First define some input parameters for the signal:\n""\n"" >>> A = 2.\n"" >>> w = 1.\n"" >>> phi = 0.5 * np.pi\n"" >>> nin = 1000\n"" >>> nout = 100000\n"" >>> frac_points = 0.9 # Fraction of points to select\n"" \n"" Randomly select a fraction of an array with timesteps:\n""\n"" >>> r = np.random.rand(nin)\n"" >>> x = np.linspace(0.01, 10*np.pi, nin)\n"" >>> x = x[r >= frac_points]\n"" >>> normval = x.shape[0] # For normalization of the periodogram\n"" \n"" Plot a sine wave for the selected times:\n""\n"" >>> y = A * np.sin(w*x+phi)\n""\n"" Define the array of frequencies for which to compute the periodogram:\n"" \n"" >>> f = np.linspace(0.01, 10, nout)\n"" \n"" Calculate Lomb-Scargle periodogram:\n""\n"" >>> pgram = sp.signal.lombscargle(x, y, f)\n""\n"" Now make a plot of the input data:\n""\n"" >>> plt.subplot(2, 1, 1)\n"" <matplotlib.axes.AxesSubplot object at 0x102154f50>\n"" >>> plt.plot(x, y, 'b+')\n"" [<matplotlib.lines.Line2D object at 0x102154a10>]\n""\n"" Then plot the normalized periodogram:\n""\n"" >>> plt.subplot(2, 1, 2)\n"" <matplotlib.axes.AxesSubplot object at 0x104b0a990>\n"" >>> plt.plot(f, np.sqrt(4*(pgram/normval)))\n"" [<matplotlib.lines.Line2D object at 0x104b2f910>]\n"" >>> plt.show()\n"" \n"" ";
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+}
+
+static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
+ switch (ch) {
+ case 'c': case 'b': case 'B': return 1;
+ case 'h': case 'H': return sizeof(short);
+ case 'i': case 'I': return sizeof(int);
+ case 'l': case 'L': return sizeof(long);
+ #ifdef HAVE_LONG_LONG
+ case 'q': case 'Q': return sizeof(PY_LONG_LONG);
+ #endif
+ case 'f': return sizeof(float) * (is_complex ? 2 : 1);
+ case 'd': return sizeof(double) * (is_complex ? 2 : 1);
+ case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
+ case 'O': case 'P': return sizeof(void*);
+ default: {
+ __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+ return 0;
+ }
+ }
+}
+
+typedef struct { char c; short x; } __Pyx_st_short;
+typedef struct { char c; int x; } __Pyx_st_int;
+typedef struct { char c; long x; } __Pyx_st_long;
+typedef struct { char c; float x; } __Pyx_st_float;
+typedef struct { char c; double x; } __Pyx_st_double;
+typedef struct { char c; long double x; } __Pyx_st_longdouble;
+typedef struct { char c; void *x; } __Pyx_st_void_p;
+#ifdef HAVE_LONG_LONG
+typedef struct { char c; PY_LONG_LONG x; } __Pyx_s_long_long;
+#endif
+
+static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, int is_complex) {
+ switch (ch) {
+ case '?': case 'c': case 'b': case 'B': return 1;
+ case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
+ case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
+ case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
+#ifdef HAVE_LONG_LONG
+ case 'q': case 'Q': return sizeof(__Pyx_s_long_long) - sizeof(PY_LONG_LONG);
+#endif
+ case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
+ case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
+ case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
+ case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
+ default:
+ __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+ return 0;
+ }
+}
+
+static size_t __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
+ switch (ch) {
+ case 'c': case 'b': case 'h': case 'i': case 'l': case 'q': return 'I';
+ case 'B': case 'H': case 'I': case 'L': case 'Q': return 'U';
+ case 'f': case 'd': case 'g': return (is_complex ? 'C' : 'R');
+ case 'O': return 'O';
+ case 'P': return 'P';
+ default: {
+ __Pyx_BufFmt_RaiseUnexpectedChar(ch);
+ return 0;
+ }
+ }
+}
+
+static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
+ if (ctx->head == NULL || ctx->head->field == &ctx->root) {
+ const char* expected;
+ const char* quote;
+ if (ctx->head == NULL) {
+ expected = "end";
+ quote = "";
+ } else {
+ expected = ctx->head->field->type->name;
+ quote = "'";
+ }
+ PyErr_Format(PyExc_ValueError,
+ "Buffer dtype mismatch, expected %s%s%s but got %s",
+ quote, expected, quote,
+ __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
+ } else {
+ __Pyx_StructField* field = ctx->head->field;
+ __Pyx_StructField* parent = (ctx->head - 1)->field;
+ PyErr_Format(PyExc_ValueError,
+ "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
+ field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
+ parent->type->name, field->name);
+ }
+}
+
+static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
+ char group;
+ size_t size, offset;
+ if (ctx->enc_type == 0) return 0;
+ group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
+ do {
+ __Pyx_StructField* field = ctx->head->field;
+ __Pyx_TypeInfo* type = field->type;
+
+ if (ctx->packmode == '@' || ctx->packmode == '^') {
+ size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
+ } else {
+ size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
+ }
+ if (ctx->packmode == '@') {
+ int align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
+ int align_mod_offset;
+ if (align_at == 0) return -1;
+ align_mod_offset = ctx->fmt_offset % align_at;
+ if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
+ }
+
+ if (type->size != size || type->typegroup != group) {
+ if (type->typegroup == 'C' && type->fields != NULL) {
+ /* special case -- treat as struct rather than complex number */
+ size_t parent_offset = ctx->head->parent_offset + field->offset;
+ ++ctx->head;
+ ctx->head->field = type->fields;
+ ctx->head->parent_offset = parent_offset;
+ continue;
+ }
+
+ __Pyx_BufFmt_RaiseExpected(ctx);
+ return -1;
+ }
+
+ offset = ctx->head->parent_offset + field->offset;
+ if (ctx->fmt_offset != offset) {
+ PyErr_Format(PyExc_ValueError,
+ "Buffer dtype mismatch; next field is at offset %"PY_FORMAT_SIZE_T"d "
+ "but %"PY_FORMAT_SIZE_T"d expected", ctx->fmt_offset, offset);
+ return -1;
+ }
+
+ ctx->fmt_offset += size;
+
+ --ctx->enc_count; /* Consume from buffer string */
+
+ /* Done checking, move to next field, pushing or popping struct stack if needed */
+ while (1) {
+ if (field == &ctx->root) {
+ ctx->head = NULL;
+ if (ctx->enc_count != 0) {
+ __Pyx_BufFmt_RaiseExpected(ctx);
+ return -1;
+ }
+ break; /* breaks both loops as ctx->enc_count == 0 */
+ }
+ ctx->head->field = ++field;
+ if (field->type == NULL) {
+ --ctx->head;
+ field = ctx->head->field;
+ continue;
+ } else if (field->type->typegroup == 'S') {
+ size_t parent_offset = ctx->head->parent_offset + field->offset;
+ if (field->type->fields->type == NULL) continue; /* empty struct */
+ field = field->type->fields;
+ ++ctx->head;
+ ctx->head->field = field;
+ ctx->head->parent_offset = parent_offset;
+ break;
+ } else {
+ break;
+ }
+ }
+ } while (ctx->enc_count);
+ ctx->enc_type = 0;
+ ctx->is_complex = 0;
+ return 0;
+}
+
+static int __Pyx_BufFmt_FirstPack(__Pyx_BufFmt_Context* ctx) {
+ if (ctx->enc_type != 0 || ctx->packmode != '@') {
+ PyErr_SetString(PyExc_ValueError, "Buffer packing mode currently only allowed at beginning of format string (this is a defect)");
+ return -1;
+ }
+ return 0;
+}
+
+static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
+ int got_Z = 0;
+ while (1) {
+ switch(*ts) {
+ case 0:
+ if (ctx->enc_type != 0 && ctx->head == NULL) {
+ __Pyx_BufFmt_RaiseExpected(ctx);
+ return NULL;
+ }
+ if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+ if (ctx->head != NULL) {
+ __Pyx_BufFmt_RaiseExpected(ctx);
+ return NULL;
+ }
+ return ts;
+ case ' ':
+ case 10:
+ case 13:
+ ++ts;
+ break;
+ case '<':
+ if (!__Pyx_IsLittleEndian()) {
+ PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
+ return NULL;
+ }
+ if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
+ ctx->packmode = '=';
+ ++ts;
+ break;
+ case '>':
+ case '!':
+ if (__Pyx_IsLittleEndian()) {
+ PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
+ return NULL;
+ }
+ if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
+ ctx->packmode = '=';
+ ++ts;
+ break;
+ case '=':
+ case '@':
+ case '^':
+ if (__Pyx_BufFmt_FirstPack(ctx) == -1) return NULL;
+ ctx->packmode = *ts++;
+ break;
+ case 'T': /* substruct */
+ {
+ int i;
+ const char* ts_after_sub;
+ int struct_count = ctx->new_count;
+ ctx->new_count = 1;
+ ++ts;
+ if (*ts != '{') {
+ PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
+ return NULL;
+ }
+ ++ts;
+ ts_after_sub = ts;
+ for (i = 0; i != struct_count; ++i) {
+ ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
+ if (!ts_after_sub) return NULL;
+ }
+ ts = ts_after_sub;
+ }
+ break;
+ case '}': /* end of substruct; either repeat or move on */
+ ++ts;
+ return ts;
+ case 'x':
+ if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+ ctx->fmt_offset += ctx->new_count;
+ ctx->new_count = 1;
+ ctx->enc_count = 0;
+ ctx->enc_type = 0;
+ ++ts;
+ break;
+ case 'Z':
+ got_Z = 1;
+ ++ts;
+ if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
+ __Pyx_BufFmt_RaiseUnexpectedChar('Z');
+ return NULL;
+ } /* fall through */
+ case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
+ case 'l': case 'L': case 'q': case 'Q':
+ case 'f': case 'd': case 'g':
+ case 'O':
+ if (ctx->enc_type == *ts && got_Z == ctx->is_complex) {
+ /* Continue pooling same type */
+ ctx->enc_count += ctx->new_count;
+ } else {
+ /* New type */
+ if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
+ ctx->enc_count = ctx->new_count;
+ ctx->enc_type = *ts;
+ ctx->is_complex = got_Z;
+ }
+ ++ts;
+ ctx->new_count = 1;
+ got_Z = 0;
+ break;
+ default:
+ {
+ ctx->new_count = __Pyx_BufFmt_ParseNumber(&ts);
+ if (ctx->new_count == -1) { /* First char was not a digit */
+ char msg[2] = { *ts, 0 };
+ PyErr_Format(PyExc_ValueError,
+ "Does not understand character buffer dtype format string ('%s')", msg);
+ return NULL;
+ }
+ }
+
+ }
+ }
+}
+
+static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
+ buf->buf = NULL;
+ buf->obj = NULL;
+ buf->strides = __Pyx_zeros;
+ buf->shape = __Pyx_zeros;
+ buf->suboffsets = __Pyx_minusones;
+}
+
+static int __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj, __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack) {
+ if (obj == Py_None) {
+ __Pyx_ZeroBuffer(buf);
+ return 0;
+ }
+ buf->buf = NULL;
+ if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
+ if (buf->ndim != nd) {
+ PyErr_Format(PyExc_ValueError,
+ "Buffer has wrong number of dimensions (expected %d, got %d)",
+ nd, buf->ndim);
+ goto fail;
+ }
+ if (!cast) {
+ __Pyx_BufFmt_Context ctx;
+ __Pyx_BufFmt_Init(&ctx, stack, dtype);
+ if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
+ }
+ if ((unsigned)buf->itemsize != dtype->size) {
+ PyErr_Format(PyExc_ValueError,
+ "Item size of buffer (%"PY_FORMAT_SIZE_T"d byte%s) does not match size of '%s' (%"PY_FORMAT_SIZE_T"d byte%s)",
+ buf->itemsize, (buf->itemsize > 1) ? "s" : "",
+ dtype->name,
+ dtype->size, (dtype->size > 1) ? "s" : "");
+ goto fail;
+ }
+ if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
+ return 0;
+fail:;
+ __Pyx_ZeroBuffer(buf);
+ return -1;
+}
+
+static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
+ if (info->buf == NULL) return;
+ if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
+ __Pyx_ReleaseBuffer(info);
+}
+
+
+static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb) {
+ PyObject *tmp_type, *tmp_value, *tmp_tb;
+ PyThreadState *tstate = PyThreadState_GET();
+
+ tmp_type = tstate->curexc_type;
+ tmp_value = tstate->curexc_value;
+ tmp_tb = tstate->curexc_traceback;
+ tstate->curexc_type = type;
+ tstate->curexc_value = value;
+ tstate->curexc_traceback = tb;
+ Py_XDECREF(tmp_type);
+ Py_XDECREF(tmp_value);
+ Py_XDECREF(tmp_tb);
+}
+
+static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb) {
+ PyThreadState *tstate = PyThreadState_GET();
+ *type = tstate->curexc_type;
+ *value = tstate->curexc_value;
+ *tb = tstate->curexc_traceback;
+
+ tstate->curexc_type = 0;
+ tstate->curexc_value = 0;
+ tstate->curexc_traceback = 0;
+}
+
+
+static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
+ PyErr_Format(PyExc_ValueError,
+ #if PY_VERSION_HEX < 0x02050000
+ "need more than %d value%s to unpack", (int)index,
+ #else
+ "need more than %zd value%s to unpack", index,
+ #endif
+ (index == 1) ? "" : "s");
+}
+
+static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(void) {
+ PyErr_SetString(PyExc_ValueError, "too many values to unpack");
+}
+
+static PyObject *__Pyx_UnpackItem(PyObject *iter, Py_ssize_t index) {
+ PyObject *item;
+ if (!(item = PyIter_Next(iter))) {
+ if (!PyErr_Occurred()) {
+ __Pyx_RaiseNeedMoreValuesError(index);
+ }
+ }
+ return item;
+}
+
+static int __Pyx_EndUnpack(PyObject *iter) {
+ PyObject *item;
+ if ((item = PyIter_Next(iter))) {
+ Py_DECREF(item);
+ __Pyx_RaiseTooManyValuesError();
+ return -1;
+ }
+ else if (!PyErr_Occurred())
+ return 0;
+ else
+ return -1;
+}
+
+static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
+ if (unlikely(!type)) {
+ PyErr_Format(PyExc_SystemError, "Missing type object");
+ return 0;
+ }
+ if (likely(PyObject_TypeCheck(obj, type)))
+ return 1;
+ PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
+ Py_TYPE(obj)->tp_name, type->tp_name);
+ return 0;
+}
+
+static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
+ PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
+}
+
+static void __Pyx_UnpackTupleError(PyObject *t, Py_ssize_t index) {
+ if (t == Py_None) {
+ __Pyx_RaiseNoneNotIterableError();
+ } else if (PyTuple_GET_SIZE(t) < index) {
+ __Pyx_RaiseNeedMoreValuesError(PyTuple_GET_SIZE(t));
+ } else {
+ __Pyx_RaiseTooManyValuesError();
+ }
+}
+
+static int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
+ const char *name, int exact)
+{
+ if (!type) {
+ PyErr_Format(PyExc_SystemError, "Missing type object");
+ return 0;
+ }
+ if (none_allowed && obj == Py_None) return 1;
+ else if (exact) {
+ if (Py_TYPE(obj) == type) return 1;
+ }
+ else {
+ if (PyObject_TypeCheck(obj, type)) return 1;
+ }
+ PyErr_Format(PyExc_TypeError,
+ "Argument '%s' has incorrect type (expected %s, got %s)",
+ name, type->tp_name, Py_TYPE(obj)->tp_name);
+ return 0;
+}
+
+#if PY_MAJOR_VERSION < 3
+static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
+ #if PY_VERSION_HEX >= 0x02060000
+ if (Py_TYPE(obj)->tp_flags & Py_TPFLAGS_HAVE_NEWBUFFER)
+ return PyObject_GetBuffer(obj, view, flags);
+ #endif
+ if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pf_5numpy_7ndarray___getbuffer__(obj, view, flags);
+ else {
+ PyErr_Format(PyExc_TypeError, "'%100s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
+ return -1;
+ }
+}
+
+static void __Pyx_ReleaseBuffer(Py_buffer *view) {
+ PyObject* obj = view->obj;
+ if (obj) {
+if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pf_5numpy_7ndarray___releasebuffer__(obj, view);
+ Py_DECREF(obj);
+ view->obj = NULL;
+ }
+}
+
+#endif
+
+static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list) {
+ PyObject *__import__ = 0;
+ PyObject *empty_list = 0;
+ PyObject *module = 0;
+ PyObject *global_dict = 0;
+ PyObject *empty_dict = 0;
+ PyObject *list;
+ __import__ = __Pyx_GetAttrString(__pyx_b, "__import__");
+ if (!__import__)
+ goto bad;
+ if (from_list)
+ list = from_list;
+ else {
+ empty_list = PyList_New(0);
+ if (!empty_list)
+ goto bad;
+ list = empty_list;
+ }
+ global_dict = PyModule_GetDict(__pyx_m);
+ if (!global_dict)
+ goto bad;
+ empty_dict = PyDict_New();
+ if (!empty_dict)
+ goto bad;
+ module = PyObject_CallFunctionObjArgs(__import__,
+ name, global_dict, empty_dict, list, NULL);
+bad:
+ Py_XDECREF(empty_list);
+ Py_XDECREF(__import__);
+ Py_XDECREF(empty_dict);
+ return module;
+}
+
+static PyObject *__Pyx_GetName(PyObject *dict, PyObject *name) {
+ PyObject *result;
+ result = PyObject_GetAttr(dict, name);
+ if (!result)
+ PyErr_SetObject(PyExc_NameError, name);
+ return result;
+}
+
+#if PY_MAJOR_VERSION < 3
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
+ Py_XINCREF(type);
+ Py_XINCREF(value);
+ Py_XINCREF(tb);
+ /* First, check the traceback argument, replacing None with NULL. */
+ if (tb == Py_None) {
+ Py_DECREF(tb);
+ tb = 0;
+ }
+ else if (tb != NULL && !PyTraceBack_Check(tb)) {
+ PyErr_SetString(PyExc_TypeError,
+ "raise: arg 3 must be a traceback or None");
+ goto raise_error;
+ }
+ /* Next, replace a missing value with None */
+ if (value == NULL) {
+ value = Py_None;
+ Py_INCREF(value);
+ }
+ #if PY_VERSION_HEX < 0x02050000
+ if (!PyClass_Check(type))
+ #else
+ if (!PyType_Check(type))
+ #endif
+ {
+ /* Raising an instance. The value should be a dummy. */
+ if (value != Py_None) {
+ PyErr_SetString(PyExc_TypeError,
+ "instance exception may not have a separate value");
+ goto raise_error;
+ }
+ /* Normalize to raise <class>, <instance> */
+ Py_DECREF(value);
+ value = type;
+ #if PY_VERSION_HEX < 0x02050000
+ if (PyInstance_Check(type)) {
+ type = (PyObject*) ((PyInstanceObject*)type)->in_class;
+ Py_INCREF(type);
+ }
+ else {
+ type = 0;
+ PyErr_SetString(PyExc_TypeError,
+ "raise: exception must be an old-style class or instance");
+ goto raise_error;
+ }
+ #else
+ type = (PyObject*) Py_TYPE(type);
+ Py_INCREF(type);
+ if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
+ PyErr_SetString(PyExc_TypeError,
+ "raise: exception class must be a subclass of BaseException");
+ goto raise_error;
+ }
+ #endif
+ }
+
+ __Pyx_ErrRestore(type, value, tb);
+ return;
+raise_error:
+ Py_XDECREF(value);
+ Py_XDECREF(type);
+ Py_XDECREF(tb);
+ return;
+}
+
+#else /* Python 3+ */
+
+static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb) {
+ if (tb == Py_None) {
+ tb = 0;
+ } else if (tb && !PyTraceBack_Check(tb)) {
+ PyErr_SetString(PyExc_TypeError,
+ "raise: arg 3 must be a traceback or None");
+ goto bad;
+ }
+ if (value == Py_None)
+ value = 0;
+
+ if (PyExceptionInstance_Check(type)) {
+ if (value) {
+ PyErr_SetString(PyExc_TypeError,
+ "instance exception may not have a separate value");
+ goto bad;
+ }
+ value = type;
+ type = (PyObject*) Py_TYPE(value);
+ } else if (!PyExceptionClass_Check(type)) {
+ PyErr_SetString(PyExc_TypeError,
+ "raise: exception class must be a subclass of BaseException");
+ goto bad;
+ }
+
+ PyErr_SetObject(type, value);
+
+ if (tb) {
+ PyThreadState *tstate = PyThreadState_GET();
+ PyObject* tmp_tb = tstate->curexc_traceback;
+ if (tb != tmp_tb) {
+ Py_INCREF(tb);
+ tstate->curexc_traceback = tb;
+ Py_XDECREF(tmp_tb);
+ }
+ }
+
+bad:
+ return;
+}
+#endif
+
+static CYTHON_INLINE PyObject *__Pyx_PyInt_to_py_npy_intp(npy_intp val) {
+ const npy_intp neg_one = (npy_intp)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(npy_intp) < sizeof(long)) {
+ return PyInt_FromLong((long)val);
+ } else if (sizeof(npy_intp) == sizeof(long)) {
+ if (is_unsigned)
+ return PyLong_FromUnsignedLong((unsigned long)val);
+ else
+ return PyInt_FromLong((long)val);
+ } else { /* (sizeof(npy_intp) > sizeof(long)) */
+ if (is_unsigned)
+ return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)val);
+ else
+ return PyLong_FromLongLong((PY_LONG_LONG)val);
+ }
+}
+
+#if CYTHON_CCOMPLEX
+ #ifdef __cplusplus
+ static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+ return ::std::complex< float >(x, y);
+ }
+ #else
+ static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+ return x + y*(__pyx_t_float_complex)_Complex_I;
+ }
+ #endif
+#else
+ static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
+ __pyx_t_float_complex z;
+ z.real = x;
+ z.imag = y;
+ return z;
+ }
+#endif
+
+#if CYTHON_CCOMPLEX
+#else
+ static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+ return (a.real == b.real) && (a.imag == b.imag);
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+ __pyx_t_float_complex z;
+ z.real = a.real + b.real;
+ z.imag = a.imag + b.imag;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+ __pyx_t_float_complex z;
+ z.real = a.real - b.real;
+ z.imag = a.imag - b.imag;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+ __pyx_t_float_complex z;
+ z.real = a.real * b.real - a.imag * b.imag;
+ z.imag = a.real * b.imag + a.imag * b.real;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
+ __pyx_t_float_complex z;
+ float denom = b.real * b.real + b.imag * b.imag;
+ z.real = (a.real * b.real + a.imag * b.imag) / denom;
+ z.imag = (a.imag * b.real - a.real * b.imag) / denom;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex a) {
+ __pyx_t_float_complex z;
+ z.real = -a.real;
+ z.imag = -a.imag;
+ return z;
+ }
+ static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex a) {
+ return (a.real == 0) && (a.imag == 0);
+ }
+ static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex a) {
+ __pyx_t_float_complex z;
+ z.real = a.real;
+ z.imag = -a.imag;
+ return z;
+ }
+/*
+ static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
+#if HAVE_HYPOT
+ return hypotf(z.real, z.imag);
+#else
+ return sqrtf(z.real*z.real + z.imag*z.imag);
+#endif
+ }
+*/
+#endif
+
+#if CYTHON_CCOMPLEX
+ #ifdef __cplusplus
+ static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+ return ::std::complex< double >(x, y);
+ }
+ #else
+ static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+ return x + y*(__pyx_t_double_complex)_Complex_I;
+ }
+ #endif
+#else
+ static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
+ __pyx_t_double_complex z;
+ z.real = x;
+ z.imag = y;
+ return z;
+ }
+#endif
+
+#if CYTHON_CCOMPLEX
+#else
+ static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+ return (a.real == b.real) && (a.imag == b.imag);
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+ __pyx_t_double_complex z;
+ z.real = a.real + b.real;
+ z.imag = a.imag + b.imag;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+ __pyx_t_double_complex z;
+ z.real = a.real - b.real;
+ z.imag = a.imag - b.imag;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+ __pyx_t_double_complex z;
+ z.real = a.real * b.real - a.imag * b.imag;
+ z.imag = a.real * b.imag + a.imag * b.real;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
+ __pyx_t_double_complex z;
+ double denom = b.real * b.real + b.imag * b.imag;
+ z.real = (a.real * b.real + a.imag * b.imag) / denom;
+ z.imag = (a.imag * b.real - a.real * b.imag) / denom;
+ return z;
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
+ __pyx_t_double_complex z;
+ z.real = -a.real;
+ z.imag = -a.imag;
+ return z;
+ }
+ static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
+ return (a.real == 0) && (a.imag == 0);
+ }
+ static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
+ __pyx_t_double_complex z;
+ z.real = a.real;
+ z.imag = -a.imag;
+ return z;
+ }
+/*
+ static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
+#if HAVE_HYPOT
+ return hypot(z.real, z.imag);
+#else
+ return sqrt(z.real*z.real + z.imag*z.imag);
+#endif
+ }
+*/
+#endif
+
+static CYTHON_INLINE unsigned char __Pyx_PyInt_AsUnsignedChar(PyObject* x) {
+ const unsigned char neg_one = (unsigned char)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(unsigned char) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(unsigned char)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to unsigned char" :
+ "value too large to convert to unsigned char");
+ }
+ return (unsigned char)-1;
+ }
+ return (unsigned char)val;
+ }
+ return (unsigned char)__Pyx_PyInt_AsUnsignedLong(x);
+}
+
+static CYTHON_INLINE unsigned short __Pyx_PyInt_AsUnsignedShort(PyObject* x) {
+ const unsigned short neg_one = (unsigned short)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(unsigned short) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(unsigned short)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to unsigned short" :
+ "value too large to convert to unsigned short");
+ }
+ return (unsigned short)-1;
+ }
+ return (unsigned short)val;
+ }
+ return (unsigned short)__Pyx_PyInt_AsUnsignedLong(x);
+}
+
+static CYTHON_INLINE unsigned int __Pyx_PyInt_AsUnsignedInt(PyObject* x) {
+ const unsigned int neg_one = (unsigned int)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(unsigned int) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(unsigned int)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to unsigned int" :
+ "value too large to convert to unsigned int");
+ }
+ return (unsigned int)-1;
+ }
+ return (unsigned int)val;
+ }
+ return (unsigned int)__Pyx_PyInt_AsUnsignedLong(x);
+}
+
+static CYTHON_INLINE char __Pyx_PyInt_AsChar(PyObject* x) {
+ const char neg_one = (char)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(char) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(char)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to char" :
+ "value too large to convert to char");
+ }
+ return (char)-1;
+ }
+ return (char)val;
+ }
+ return (char)__Pyx_PyInt_AsLong(x);
+}
+
+static CYTHON_INLINE short __Pyx_PyInt_AsShort(PyObject* x) {
+ const short neg_one = (short)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(short) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(short)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to short" :
+ "value too large to convert to short");
+ }
+ return (short)-1;
+ }
+ return (short)val;
+ }
+ return (short)__Pyx_PyInt_AsLong(x);
+}
+
+static CYTHON_INLINE int __Pyx_PyInt_AsInt(PyObject* x) {
+ const int neg_one = (int)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(int) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(int)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to int" :
+ "value too large to convert to int");
+ }
+ return (int)-1;
+ }
+ return (int)val;
+ }
+ return (int)__Pyx_PyInt_AsLong(x);
+}
+
+static CYTHON_INLINE signed char __Pyx_PyInt_AsSignedChar(PyObject* x) {
+ const signed char neg_one = (signed char)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(signed char) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(signed char)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to signed char" :
+ "value too large to convert to signed char");
+ }
+ return (signed char)-1;
+ }
+ return (signed char)val;
+ }
+ return (signed char)__Pyx_PyInt_AsSignedLong(x);
+}
+
+static CYTHON_INLINE signed short __Pyx_PyInt_AsSignedShort(PyObject* x) {
+ const signed short neg_one = (signed short)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(signed short) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(signed short)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to signed short" :
+ "value too large to convert to signed short");
+ }
+ return (signed short)-1;
+ }
+ return (signed short)val;
+ }
+ return (signed short)__Pyx_PyInt_AsSignedLong(x);
+}
+
+static CYTHON_INLINE signed int __Pyx_PyInt_AsSignedInt(PyObject* x) {
+ const signed int neg_one = (signed int)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+ if (sizeof(signed int) < sizeof(long)) {
+ long val = __Pyx_PyInt_AsLong(x);
+ if (unlikely(val != (long)(signed int)val)) {
+ if (!unlikely(val == -1 && PyErr_Occurred())) {
+ PyErr_SetString(PyExc_OverflowError,
+ (is_unsigned && unlikely(val < 0)) ?
+ "can't convert negative value to signed int" :
+ "value too large to convert to signed int");
+ }
+ return (signed int)-1;
+ }
+ return (signed int)val;
+ }
+ return (signed int)__Pyx_PyInt_AsSignedLong(x);
+}
+
+static CYTHON_INLINE unsigned long __Pyx_PyInt_AsUnsignedLong(PyObject* x) {
+ const unsigned long neg_one = (unsigned long)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to unsigned long");
+ return (unsigned long)-1;
+ }
+ return (unsigned long)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to unsigned long");
+ return (unsigned long)-1;
+ }
+ return PyLong_AsUnsignedLong(x);
+ } else {
+ return PyLong_AsLong(x);
+ }
+ } else {
+ unsigned long val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (unsigned long)-1;
+ val = __Pyx_PyInt_AsUnsignedLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+static CYTHON_INLINE unsigned PY_LONG_LONG __Pyx_PyInt_AsUnsignedLongLong(PyObject* x) {
+ const unsigned PY_LONG_LONG neg_one = (unsigned PY_LONG_LONG)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to unsigned PY_LONG_LONG");
+ return (unsigned PY_LONG_LONG)-1;
+ }
+ return (unsigned PY_LONG_LONG)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to unsigned PY_LONG_LONG");
+ return (unsigned PY_LONG_LONG)-1;
+ }
+ return PyLong_AsUnsignedLongLong(x);
+ } else {
+ return PyLong_AsLongLong(x);
+ }
+ } else {
+ unsigned PY_LONG_LONG val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (unsigned PY_LONG_LONG)-1;
+ val = __Pyx_PyInt_AsUnsignedLongLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+static CYTHON_INLINE long __Pyx_PyInt_AsLong(PyObject* x) {
+ const long neg_one = (long)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to long");
+ return (long)-1;
+ }
+ return (long)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to long");
+ return (long)-1;
+ }
+ return PyLong_AsUnsignedLong(x);
+ } else {
+ return PyLong_AsLong(x);
+ }
+ } else {
+ long val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (long)-1;
+ val = __Pyx_PyInt_AsLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+static CYTHON_INLINE PY_LONG_LONG __Pyx_PyInt_AsLongLong(PyObject* x) {
+ const PY_LONG_LONG neg_one = (PY_LONG_LONG)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to PY_LONG_LONG");
+ return (PY_LONG_LONG)-1;
+ }
+ return (PY_LONG_LONG)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to PY_LONG_LONG");
+ return (PY_LONG_LONG)-1;
+ }
+ return PyLong_AsUnsignedLongLong(x);
+ } else {
+ return PyLong_AsLongLong(x);
+ }
+ } else {
+ PY_LONG_LONG val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (PY_LONG_LONG)-1;
+ val = __Pyx_PyInt_AsLongLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+static CYTHON_INLINE signed long __Pyx_PyInt_AsSignedLong(PyObject* x) {
+ const signed long neg_one = (signed long)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to signed long");
+ return (signed long)-1;
+ }
+ return (signed long)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to signed long");
+ return (signed long)-1;
+ }
+ return PyLong_AsUnsignedLong(x);
+ } else {
+ return PyLong_AsLong(x);
+ }
+ } else {
+ signed long val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (signed long)-1;
+ val = __Pyx_PyInt_AsSignedLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+static CYTHON_INLINE signed PY_LONG_LONG __Pyx_PyInt_AsSignedLongLong(PyObject* x) {
+ const signed PY_LONG_LONG neg_one = (signed PY_LONG_LONG)-1, const_zero = 0;
+ const int is_unsigned = neg_one > const_zero;
+#if PY_VERSION_HEX < 0x03000000
+ if (likely(PyInt_Check(x))) {
+ long val = PyInt_AS_LONG(x);
+ if (is_unsigned && unlikely(val < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to signed PY_LONG_LONG");
+ return (signed PY_LONG_LONG)-1;
+ }
+ return (signed PY_LONG_LONG)val;
+ } else
+#endif
+ if (likely(PyLong_Check(x))) {
+ if (is_unsigned) {
+ if (unlikely(Py_SIZE(x) < 0)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "can't convert negative value to signed PY_LONG_LONG");
+ return (signed PY_LONG_LONG)-1;
+ }
+ return PyLong_AsUnsignedLongLong(x);
+ } else {
+ return PyLong_AsLongLong(x);
+ }
+ } else {
+ signed PY_LONG_LONG val;
+ PyObject *tmp = __Pyx_PyNumber_Int(x);
+ if (!tmp) return (signed PY_LONG_LONG)-1;
+ val = __Pyx_PyInt_AsSignedLongLong(tmp);
+ Py_DECREF(tmp);
+ return val;
+ }
+}
+
+#ifndef __PYX_HAVE_RT_ImportType
+#define __PYX_HAVE_RT_ImportType
+static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
+ long size, int strict)
+{
+ PyObject *py_module = 0;
+ PyObject *result = 0;
+ PyObject *py_name = 0;
+ char warning[200];
+
+ py_module = __Pyx_ImportModule(module_name);
+ if (!py_module)
+ goto bad;
+ #if PY_MAJOR_VERSION < 3
+ py_name = PyString_FromString(class_name);
+ #else
+ py_name = PyUnicode_FromString(class_name);
+ #endif
+ if (!py_name)
+ goto bad;
+ result = PyObject_GetAttr(py_module, py_name);
+ Py_DECREF(py_name);
+ py_name = 0;
+ Py_DECREF(py_module);
+ py_module = 0;
+ if (!result)
+ goto bad;
+ if (!PyType_Check(result)) {
+ PyErr_Format(PyExc_TypeError,
+ "%s.%s is not a type object",
+ module_name, class_name);
+ goto bad;
+ }
+ if (!strict && ((PyTypeObject *)result)->tp_basicsize > size) {
+ PyOS_snprintf(warning, sizeof(warning),
+ "%s.%s size changed, may indicate binary incompatibility",
+ module_name, class_name);
+ PyErr_WarnEx(NULL, warning, 0);
+ }
+ else if (((PyTypeObject *)result)->tp_basicsize != size) {
+ PyErr_Format(PyExc_ValueError,
+ "%s.%s has the wrong size, try recompiling",
+ module_name, class_name);
+ goto bad;
+ }
+ return (PyTypeObject *)result;
+bad:
+ Py_XDECREF(py_module);
+ Py_XDECREF(result);
+ return 0;
+}
+#endif
+
+#ifndef __PYX_HAVE_RT_ImportModule
+#define __PYX_HAVE_RT_ImportModule
+static PyObject *__Pyx_ImportModule(const char *name) {
+ PyObject *py_name = 0;
+ PyObject *py_module = 0;
+
+ #if PY_MAJOR_VERSION < 3
+ py_name = PyString_FromString(name);
+ #else
+ py_name = PyUnicode_FromString(name);
+ #endif
+ if (!py_name)
+ goto bad;
+ py_module = PyImport_Import(py_name);
+ Py_DECREF(py_name);
+ return py_module;
+bad:
+ Py_XDECREF(py_name);
+ return 0;
+}
+#endif
+
+#include "compile.h"
+#include "frameobject.h"
+#include "traceback.h"
+
+static void __Pyx_AddTraceback(const char *funcname) {
+ PyObject *py_srcfile = 0;
+ PyObject *py_funcname = 0;
+ PyObject *py_globals = 0;
+ PyCodeObject *py_code = 0;
+ PyFrameObject *py_frame = 0;
+
+ #if PY_MAJOR_VERSION < 3
+ py_srcfile = PyString_FromString(__pyx_filename);
+ #else
+ py_srcfile = PyUnicode_FromString(__pyx_filename);
+ #endif
+ if (!py_srcfile) goto bad;
+ if (__pyx_clineno) {
+ #if PY_MAJOR_VERSION < 3
+ py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
+ #else
+ py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, __pyx_clineno);
+ #endif
+ }
+ else {
+ #if PY_MAJOR_VERSION < 3
+ py_funcname = PyString_FromString(funcname);
+ #else
+ py_funcname = PyUnicode_FromString(funcname);
+ #endif
+ }
+ if (!py_funcname) goto bad;
+ py_globals = PyModule_GetDict(__pyx_m);
+ if (!py_globals) goto bad;
+ py_code = PyCode_New(
+ 0, /*int argcount,*/
+ #if PY_MAJOR_VERSION >= 3
+ 0, /*int kwonlyargcount,*/
+ #endif
+ 0, /*int nlocals,*/
+ 0, /*int stacksize,*/
+ 0, /*int flags,*/
+ __pyx_empty_bytes, /*PyObject *code,*/
+ __pyx_empty_tuple, /*PyObject *consts,*/
+ __pyx_empty_tuple, /*PyObject *names,*/
+ __pyx_empty_tuple, /*PyObject *varnames,*/
+ __pyx_empty_tuple, /*PyObject *freevars,*/
+ __pyx_empty_tuple, /*PyObject *cellvars,*/
+ py_srcfile, /*PyObject *filename,*/
+ py_funcname, /*PyObject *name,*/
+ __pyx_lineno, /*int firstlineno,*/
+ __pyx_empty_bytes /*PyObject *lnotab*/
+ );
+ if (!py_code) goto bad;
+ py_frame = PyFrame_New(
+ PyThreadState_GET(), /*PyThreadState *tstate,*/
+ py_code, /*PyCodeObject *code,*/
+ py_globals, /*PyObject *globals,*/
+ 0 /*PyObject *locals*/
+ );
+ if (!py_frame) goto bad;
+ py_frame->f_lineno = __pyx_lineno;
+ PyTraceBack_Here(py_frame);
+bad:
+ Py_XDECREF(py_srcfile);
+ Py_XDECREF(py_funcname);
+ Py_XDECREF(py_code);
+ Py_XDECREF(py_frame);
+}
+
+static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
+ while (t->p) {
+ #if PY_MAJOR_VERSION < 3
+ if (t->is_unicode) {
+ *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
+ } else if (t->intern) {
+ *t->p = PyString_InternFromString(t->s);
+ } else {
+ *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
+ }
+ #else /* Python 3+ has unicode identifiers */
+ if (t->is_unicode | t->is_str) {
+ if (t->intern) {
+ *t->p = PyUnicode_InternFromString(t->s);
+ } else if (t->encoding) {
+ *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
+ } else {
+ *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
+ }
+ } else {
+ *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
+ }
+ #endif
+ if (!*t->p)
+ return -1;
+ ++t;
+ }
+ return 0;
+}
+
+/* Type Conversion Functions */
+
+static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
+ if (x == Py_True) return 1;
+ else if ((x == Py_False) | (x == Py_None)) return 0;
+ else return PyObject_IsTrue(x);
+}
+
+static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
+ PyNumberMethods *m;
+ const char *name = NULL;
+ PyObject *res = NULL;
+#if PY_VERSION_HEX < 0x03000000
+ if (PyInt_Check(x) || PyLong_Check(x))
+#else
+ if (PyLong_Check(x))
+#endif
+ return Py_INCREF(x), x;
+ m = Py_TYPE(x)->tp_as_number;
+#if PY_VERSION_HEX < 0x03000000
+ if (m && m->nb_int) {
+ name = "int";
+ res = PyNumber_Int(x);
+ }
+ else if (m && m->nb_long) {
+ name = "long";
+ res = PyNumber_Long(x);
+ }
+#else
+ if (m && m->nb_int) {
+ name = "int";
+ res = PyNumber_Long(x);
+ }
+#endif
+ if (res) {
+#if PY_VERSION_HEX < 0x03000000
+ if (!PyInt_Check(res) && !PyLong_Check(res)) {
+#else
+ if (!PyLong_Check(res)) {
+#endif
+ PyErr_Format(PyExc_TypeError,
+ "__%s__ returned non-%s (type %.200s)",
+ name, name, Py_TYPE(res)->tp_name);
+ Py_DECREF(res);
+ return NULL;
+ }
+ }
+ else if (!PyErr_Occurred()) {
+ PyErr_SetString(PyExc_TypeError,
+ "an integer is required");
+ }
+ return res;
+}
+
+static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
+ Py_ssize_t ival;
+ PyObject* x = PyNumber_Index(b);
+ if (!x) return -1;
+ ival = PyInt_AsSsize_t(x);
+ Py_DECREF(x);
+ return ival;
+}
+
+static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
+#if PY_VERSION_HEX < 0x02050000
+ if (ival <= LONG_MAX)
+ return PyInt_FromLong((long)ival);
+ else {
+ unsigned char *bytes = (unsigned char *) &ival;
+ int one = 1; int little = (int)*(unsigned char*)&one;
+ return _PyLong_FromByteArray(bytes, sizeof(size_t), little, 0);
+ }
+#else
+ return PyInt_FromSize_t(ival);
+#endif
+}
+
+static CYTHON_INLINE size_t __Pyx_PyInt_AsSize_t(PyObject* x) {
+ unsigned PY_LONG_LONG val = __Pyx_PyInt_AsUnsignedLongLong(x);
+ if (unlikely(val == (unsigned PY_LONG_LONG)-1 && PyErr_Occurred())) {
+ return (size_t)-1;
+ } else if (unlikely(val != (unsigned PY_LONG_LONG)(size_t)val)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "value too large to convert to size_t");
+ return (size_t)-1;
+ }
+ return (size_t)val;
+}
+
+
+#endif /* Py_PYTHON_H */
Added: trunk/scipy/signal/spectral.pyx
===================================================================
--- trunk/scipy/signal/spectral.pyx (rev 0)
+++ trunk/scipy/signal/spectral.pyx 2011-02-13 04:48:40 UTC (rev 7141)
@@ -0,0 +1,164 @@
+# Author: Pim Schellart
+# 2010 - 2011
+
+"""Tools for spectral analysis of unequally sampled signals."""
+
+import numpy as np
+cimport numpy as np
+cimport cython
+
+cdef extern from "math.h":
+ double cos(double)
+ double sin(double)
+ double atan(double)
+
+ at cython.boundscheck(False)
+def lombscargle(np.ndarray[np.float64_t, ndim=1] x,
+ np.ndarray[np.float64_t, ndim=1] y,
+ np.ndarray[np.float64_t, ndim=1] freqs):
+ """Computes the Lomb-Scargle periodogram.
+
+ The Lomb-Scargle periodogram was developed by Lomb [1]_ and further
+ extended by Scargle [2]_ to find, and test the significance of weak
+ periodic signals with uneven temporal sampling.
+
+ The computed periodogram is unnormalized, it takes the value
+ ``(A**2) * N/4`` for a harmonic signal with amplitude A for sufficiently
+ large N.
+
+ Parameters
+ ----------
+ x : array_like
+ Sample times.
+ y : array_like
+ Measurement values.
+ freqs : array_like
+ Angular frequencies for output periodogram.
+
+ Returns
+ -------
+ pgram : array_like
+ Lomb-Scargle periodogram.
+
+ Raises
+ ------
+ ValueError
+ If the input arrays `x` and `y` do not have the same shape.
+
+ Notes
+ -----
+ This subroutine calculates the periodogram using a slightly
+ modified algorithm due to Townsend [3]_ which allows the
+ periodogram to be calculated using only a single pass through
+ the input arrays for each frequency.
+
+ The algorithm running time scales roughly as O(x * freqs) or O(N^2)
+ for a large number of samples and frequencies.
+
+ References
+ ----------
+ .. [1] N.R. Lomb "Least-squares frequency analysis of unequally spaced
+ data", Astrophysics and Space Science, vol 39, pp. 447-462, 1976
+
+ .. [2] J.D. Scargle "Studies in astronomical time series analysis. II -
+ Statistical aspects of spectral analysis of unevenly spaced data",
+ The Astrophysical Journal, vol 263, pp. 835-853, 1982
+
+ .. [3] R.H.D. Townsend, "Fast calculation of the Lomb-Scargle
+ periodogram using graphics processing units.", The Astrophysical
+ Journal Supplement Series, vol 191, pp. 247-253, 2010
+
+ Examples
+ --------
+ >>> import scipy.signal
+
+ First define some input parameters for the signal:
+
+ >>> A = 2.
+ >>> w = 1.
+ >>> phi = 0.5 * np.pi
+ >>> nin = 1000
+ >>> nout = 100000
+ >>> frac_points = 0.9 # Fraction of points to select
+
+ Randomly select a fraction of an array with timesteps:
+
+ >>> r = np.random.rand(nin)
+ >>> x = np.linspace(0.01, 10*np.pi, nin)
+ >>> x = x[r >= frac_points]
+ >>> normval = x.shape[0] # For normalization of the periodogram
+
+ Plot a sine wave for the selected times:
+
+ >>> y = A * np.sin(w*x+phi)
+
+ Define the array of frequencies for which to compute the periodogram:
+
+ >>> f = np.linspace(0.01, 10, nout)
+
+ Calculate Lomb-Scargle periodogram:
+
+ >>> pgram = sp.signal.lombscargle(x, y, f)
+
+ Now make a plot of the input data:
+
+ >>> plt.subplot(2, 1, 1)
+ <matplotlib.axes.AxesSubplot object at 0x102154f50>
+ >>> plt.plot(x, y, 'b+')
+ [<matplotlib.lines.Line2D object at 0x102154a10>]
+
+ Then plot the normalized periodogram:
+
+ >>> plt.subplot(2, 1, 2)
+ <matplotlib.axes.AxesSubplot object at 0x104b0a990>
+ >>> plt.plot(f, np.sqrt(4*(pgram/normval)))
+ [<matplotlib.lines.Line2D object at 0x104b2f910>]
+ >>> plt.show()
+
+ """
+
+ # Check input sizes
+ if x.shape[0] != y.shape[0]:
+ raise ValueError("Input arrays do not have the same size.")
+
+ # Create empty array for output periodogram
+ pgram = np.empty(freqs.shape[0], dtype=np.float64)
+
+ # Local variables
+ cdef Py_ssize_t i, j
+ cdef double c, s, xc, xs, cc, ss, cs
+ cdef double tau, c_tau, s_tau, c_tau2, s_tau2, cs_tau
+
+ for i in range(freqs.shape[0]):
+
+ xc = 0.
+ xs = 0.
+ cc = 0.
+ ss = 0.
+ cs = 0.
+
+ for j in range(x.shape[0]):
+
+ c = cos(freqs[i] * x[j])
+ s = sin(freqs[i] * x[j])
+
+ xc += y[j] * c
+ xs += y[j] * s
+ cc += c * c
+ ss += s * s
+ cs += c * s
+
+ tau = atan(2 * cs / (cc - ss)) / (2 * freqs[i])
+ c_tau = cos(freqs[i] * tau)
+ s_tau = sin(freqs[i] * tau)
+ c_tau2 = c_tau * c_tau
+ s_tau2 = s_tau * s_tau
+ cs_tau = 2 * c_tau * s_tau
+
+ pgram[i] = 0.5 * (((c_tau * xc + s_tau * xs)**2 / \
+ (c_tau2 * cc + cs_tau * cs + s_tau2 * ss)) + \
+ ((c_tau * xs - s_tau * xc)**2 / \
+ (c_tau2 * ss - cs_tau * cs + s_tau2 * cc)))
+
+ return pgram
+
Added: trunk/scipy/signal/tests/test_spectral.py
===================================================================
--- trunk/scipy/signal/tests/test_spectral.py (rev 0)
+++ trunk/scipy/signal/tests/test_spectral.py 2011-02-13 04:48:40 UTC (rev 7141)
@@ -0,0 +1,95 @@
+"""Unit tests for Lomb Scargle routines.
+"""
+
+import numpy as np
+from numpy.testing import dec, assert_raises, assert_equal, \
+ assert_almost_equal, assert_array_equal, \
+ assert_array_almost_equal, assert_approx_equal, \
+ assert_, run_module_suite
+
+from scipy.signal.spectral import lombscargle
+
+
+class TestLombscargle:
+ def test_frequency(self):
+ """Test if frequency location of peak corresponds to frequency of
+ generated input signal.
+ """
+
+ # Input parameters
+ ampl = 2.
+ w = 1.
+ phi = 0.5 * np.pi
+ nin = 100
+ nout = 1000
+ p = 0.7 # Fraction of points to select
+
+ # Randomly select a fraction of an array with timesteps
+ np.random.seed(2353425)
+ r = np.random.rand(nin)
+ t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+ # Plot a sine wave for the selected times
+ x = ampl * np.sin(w*t + phi)
+
+ # Define the array of frequencies for which to compute the periodogram
+ f = np.linspace(0.01, 10., nout)
+
+ # Calculate Lomb-Scargle periodogram
+ P = lombscargle(t, x, f)
+
+ # Check if difference between found frequency maximum and input
+ # frequency is less than accuracy
+ delta = f[1] - f[0]
+ assert_(w - f[np.argmax(P)] < (delta/2.))
+
+ def test_amplitude(self):
+ """Test if height of peak in normalized Lomb-Scargle periodogram
+ corresponds to amplitude of the generated input signal.
+ """
+
+ # Input parameters
+ ampl = 2.
+ w = 1.
+ phi = 0.5 * np.pi
+ nin = 100
+ nout = 1000
+ p = 0.7 # Fraction of points to select
+
+ # Randomly select a fraction of an array with timesteps
+ np.random.seed(2353425)
+ r = np.random.rand(nin)
+ t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
+
+ # Plot a sine wave for the selected times
+ x = ampl * np.sin(w*t + phi)
+
+ # Define the array of frequencies for which to compute the periodogram
+ f = np.linspace(0.01, 10., nout)
+
+ # Calculate Lomb-Scargle periodogram
+ pgram = lombscargle(t, x, f)
+
+ # Normalize
+ pgram = np.sqrt(4 * pgram / t.shape[0])
+
+ # Check if difference between found frequency maximum and input
+ # frequency is less than accuracy
+ assert_approx_equal(np.max(pgram), ampl, significant=2)
+
+ def test_wrong_shape(self):
+ t = np.linspace(0, 1, 1)
+ x = np.linspace(0, 1, 2)
+ f = np.linspace(0, 1, 3)
+ assert_raises(ValueError, lombscargle, t, x, f)
+
+ def test_zero_division(self):
+ t = np.zeros(1)
+ x = np.zeros(1)
+ f = np.zeros(1)
+ assert_raises(ZeroDivisionError, lombscargle, t, x, f)
+
+
+if __name__ == "__main__":
+ run_module_suite()
+
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