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J.S. Oishi committed 45e6b30

added some things. might need to unadd later...

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Files changed (8)

dedalus/data_objects/test_alltoall.py

+import numpy as na
+import pylab as P
+from mpi4py import MPI
+
+comm = MPI.COMM_WORLD
+nproc = comm.Get_size()
+myproc = comm.Get_rank()
+x = na.linspace(0,10,100)
+xx,yy = na.meshgrid(x,x)
+nz_local = 100/nproc
+data = yy[myproc*nz_local:(myproc+1)*nz_local,:]
+incoming = na.empty((100,nz_local))
+
+size = []
+soffset = []
+roffset = []
+for i in range(nproc):
+    size.append(data.size/nproc)
+    soffset.append(i*size[i])
+    roffset.append(i*size[i])
+print size, soffset
+send = data
+comm.Alltoallv((send.ravel('F'), (size, soffset), MPI.DOUBLE), 
+               (incoming, (size,roffset), MPI.DOUBLE))
+
+
+P.subplot(121)
+P.imshow(incoming,vmin=0, vmax=10)
+P.title("Proc %i" % myproc)
+P.colorbar()
+P.subplot(122)
+P.imshow(send,vmin=0,vmax=10)
+#P.plot(incoming[:,0])
+P.colorbar()
+P.show()

dedalus/data_objects/test_mpi_rep.py

+from fourier_data import ParallelFourierRepresentation
+from mpi4py import MPI
+from numpy import pi
+comm = MPI.COMM_WORLD
+
+nproc = comm.Get_size()
+print nproc
+fr = ParallelFourierRepresentation(None, [16/nproc,16,16], [2*pi/nproc,2*pi,2*pi])
+
+outfile = open("data_%s" % comm.Get_rank(),'w')
+outfile.write(str(fr.k['z']))
+outfile.close()

dedalus/utils/fftw/_fftw.pxi

+

dedalus/utils/fftw/fftw3.h

+/*
+ * Copyright (c) 2003, 2007-8 Matteo Frigo
+ * Copyright (c) 2003, 2007-8 Massachusetts Institute of Technology
+ *
+ * The following statement of license applies *only* to this header file,
+ * and *not* to the other files distributed with FFTW or derived therefrom:
+ * 
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
+ * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
+ * GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+ * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/***************************** NOTE TO USERS *********************************
+ *
+ *                 THIS IS A HEADER FILE, NOT A MANUAL
+ *
+ *    If you want to know how to use FFTW, please read the manual,
+ *    online at http://www.fftw.org/doc/ and also included with FFTW.
+ *    For a quick start, see the manual's tutorial section.
+ *
+ *   (Reading header files to learn how to use a library is a habit
+ *    stemming from code lacking a proper manual.  Arguably, it's a
+ *    *bad* habit in most cases, because header files can contain
+ *    interfaces that are not part of the public, stable API.)
+ *
+ ****************************************************************************/
+
+#ifndef FFTW3_H
+#define FFTW3_H
+
+#include <stdio.h>
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif /* __cplusplus */
+
+/* If <complex.h> is included, use the C99 complex type.  Otherwise
+   define a type bit-compatible with C99 complex */
+#if !defined(FFTW_NO_Complex) && defined(_Complex_I) && defined(complex) && defined(I)
+#  define FFTW_DEFINE_COMPLEX(R, C) typedef R _Complex C
+#else
+#  define FFTW_DEFINE_COMPLEX(R, C) typedef R C[2]
+#endif
+
+#define FFTW_CONCAT(prefix, name) prefix ## name
+#define FFTW_MANGLE_DOUBLE(name) FFTW_CONCAT(fftw_, name)
+#define FFTW_MANGLE_FLOAT(name) FFTW_CONCAT(fftwf_, name)
+#define FFTW_MANGLE_LONG_DOUBLE(name) FFTW_CONCAT(fftwl_, name)
+
+/* IMPORTANT: for Windows compilers, you should add a line
+        #define FFTW_DLL
+   here and in kernel/ifftw.h if you are compiling/using FFTW as a
+   DLL, in order to do the proper importing/exporting, or
+   alternatively compile with -DFFTW_DLL or the equivalent
+   command-line flag.  This is not necessary under MinGW/Cygwin, where
+   libtool does the imports/exports automatically. */
+#if defined(FFTW_DLL) && (defined(_WIN32) || defined(__WIN32__))
+   /* annoying Windows syntax for shared-library declarations */
+#  if defined(COMPILING_FFTW) /* defined in api.h when compiling FFTW */
+#    define FFTW_EXTERN extern __declspec(dllexport) 
+#  else /* user is calling FFTW; import symbol */
+#    define FFTW_EXTERN extern __declspec(dllimport) 
+#  endif
+#else
+#  define FFTW_EXTERN extern
+#endif
+
+enum fftw_r2r_kind_do_not_use_me {
+     FFTW_R2HC=0, FFTW_HC2R=1, FFTW_DHT=2,
+     FFTW_REDFT00=3, FFTW_REDFT01=4, FFTW_REDFT10=5, FFTW_REDFT11=6,
+     FFTW_RODFT00=7, FFTW_RODFT01=8, FFTW_RODFT10=9, FFTW_RODFT11=10
+};
+
+struct fftw_iodim_do_not_use_me {
+     int n;                     /* dimension size */
+     int is;			/* input stride */
+     int os;			/* output stride */
+};
+
+#include <stddef.h> /* for ptrdiff_t */
+struct fftw_iodim64_do_not_use_me {
+     ptrdiff_t n;                     /* dimension size */
+     ptrdiff_t is;			/* input stride */
+     ptrdiff_t os;			/* output stride */
+};
+
+/*
+  huge second-order macro that defines prototypes for all API
+  functions.  We expand this macro for each supported precision
+ 
+  X: name-mangling macro
+  R: real data type
+  C: complex data type
+*/
+
+#define FFTW_DEFINE_API(X, R, C)					   \
+									   \
+FFTW_DEFINE_COMPLEX(R, C);						   \
+									   \
+typedef struct X(plan_s) *X(plan);					   \
+									   \
+typedef struct fftw_iodim_do_not_use_me X(iodim);			   \
+typedef struct fftw_iodim64_do_not_use_me X(iodim64);			   \
+									   \
+typedef enum fftw_r2r_kind_do_not_use_me X(r2r_kind);			   \
+									   \
+FFTW_EXTERN void X(execute)(const X(plan) p);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft)(int rank, const int *n,			   \
+		    C *in, C *out, int sign, unsigned flags);		   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft_1d)(int n, C *in, C *out, int sign,	   \
+		       unsigned flags);					   \
+FFTW_EXTERN X(plan) X(plan_dft_2d)(int n0, int n1,			   \
+		       C *in, C *out, int sign, unsigned flags);	   \
+FFTW_EXTERN X(plan) X(plan_dft_3d)(int n0, int n1, int n2,		   \
+		       C *in, C *out, int sign, unsigned flags);	   \
+									   \
+FFTW_EXTERN X(plan) X(plan_many_dft)(int rank, const int *n,		   \
+                         int howmany,					   \
+                         C *in, const int *inembed,			   \
+                         int istride, int idist,			   \
+                         C *out, const int *onembed,			   \
+                         int ostride, int odist,			   \
+                         int sign, unsigned flags);			   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru_dft)(int rank, const X(iodim) *dims,	   \
+			 int howmany_rank,				   \
+			 const X(iodim) *howmany_dims,			   \
+			 C *in, C *out,					   \
+			 int sign, unsigned flags);			   \
+FFTW_EXTERN X(plan) X(plan_guru_split_dft)(int rank, const X(iodim) *dims, \
+			 int howmany_rank,				   \
+			 const X(iodim) *howmany_dims,			   \
+			 R *ri, R *ii, R *ro, R *io,			   \
+			 unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru64_dft)(int rank,			   \
+                         const X(iodim64) *dims,			   \
+			 int howmany_rank,				   \
+			 const X(iodim64) *howmany_dims,		   \
+			 C *in, C *out,					   \
+			 int sign, unsigned flags);			   \
+FFTW_EXTERN X(plan) X(plan_guru64_split_dft)(int rank,			   \
+                         const X(iodim64) *dims,			   \
+			 int howmany_rank,				   \
+			 const X(iodim64) *howmany_dims,		   \
+			 R *ri, R *ii, R *ro, R *io,			   \
+			 unsigned flags);				   \
+									   \
+FFTW_EXTERN void X(execute_dft)(const X(plan) p, C *in, C *out);	   \
+FFTW_EXTERN void X(execute_split_dft)(const X(plan) p, R *ri, R *ii,	   \
+                                      R *ro, R *io);			   \
+									   \
+FFTW_EXTERN X(plan) X(plan_many_dft_r2c)(int rank, const int *n,	   \
+                             int howmany,				   \
+                             R *in, const int *inembed,			   \
+                             int istride, int idist,			   \
+                             C *out, const int *onembed,		   \
+                             int ostride, int odist,			   \
+                             unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft_r2c)(int rank, const int *n,		   \
+                        R *in, C *out, unsigned flags);			   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft_r2c_1d)(int n,R *in,C *out,unsigned flags); \
+FFTW_EXTERN X(plan) X(plan_dft_r2c_2d)(int n0, int n1,			   \
+			   R *in, C *out, unsigned flags);		   \
+FFTW_EXTERN X(plan) X(plan_dft_r2c_3d)(int n0, int n1,			   \
+			   int n2,					   \
+			   R *in, C *out, unsigned flags);		   \
+									   \
+									   \
+FFTW_EXTERN X(plan) X(plan_many_dft_c2r)(int rank, const int *n,	   \
+			     int howmany,				   \
+			     C *in, const int *inembed,			   \
+			     int istride, int idist,			   \
+			     R *out, const int *onembed,		   \
+			     int ostride, int odist,			   \
+			     unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft_c2r)(int rank, const int *n,		   \
+                        C *in, R *out, unsigned flags);			   \
+									   \
+FFTW_EXTERN X(plan) X(plan_dft_c2r_1d)(int n,C *in,R *out,unsigned flags); \
+FFTW_EXTERN X(plan) X(plan_dft_c2r_2d)(int n0, int n1,			   \
+			   C *in, R *out, unsigned flags);		   \
+FFTW_EXTERN X(plan) X(plan_dft_c2r_3d)(int n0, int n1,			   \
+			   int n2,					   \
+			   C *in, R *out, unsigned flags);		   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru_dft_r2c)(int rank, const X(iodim) *dims,   \
+			     int howmany_rank,				   \
+			     const X(iodim) *howmany_dims,		   \
+			     R *in, C *out,				   \
+			     unsigned flags);				   \
+FFTW_EXTERN X(plan) X(plan_guru_dft_c2r)(int rank, const X(iodim) *dims,   \
+			     int howmany_rank,				   \
+			     const X(iodim) *howmany_dims,		   \
+			     C *in, R *out,				   \
+			     unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru_split_dft_r2c)(				   \
+                             int rank, const X(iodim) *dims,		   \
+			     int howmany_rank,				   \
+			     const X(iodim) *howmany_dims,		   \
+			     R *in, R *ro, R *io,			   \
+			     unsigned flags);				   \
+FFTW_EXTERN X(plan) X(plan_guru_split_dft_c2r)(				   \
+                             int rank, const X(iodim) *dims,		   \
+			     int howmany_rank,				   \
+			     const X(iodim) *howmany_dims,		   \
+			     R *ri, R *ii, R *out,			   \
+			     unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru64_dft_r2c)(int rank,			   \
+                             const X(iodim64) *dims,			   \
+			     int howmany_rank,				   \
+			     const X(iodim64) *howmany_dims,		   \
+			     R *in, C *out,				   \
+			     unsigned flags);				   \
+FFTW_EXTERN X(plan) X(plan_guru64_dft_c2r)(int rank,			   \
+                             const X(iodim64) *dims,			   \
+			     int howmany_rank,				   \
+			     const X(iodim64) *howmany_dims,		   \
+			     C *in, R *out,				   \
+			     unsigned flags);				   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru64_split_dft_r2c)(			   \
+                             int rank, const X(iodim64) *dims,		   \
+			     int howmany_rank,				   \
+			     const X(iodim64) *howmany_dims,		   \
+			     R *in, R *ro, R *io,			   \
+			     unsigned flags);				   \
+FFTW_EXTERN X(plan) X(plan_guru64_split_dft_c2r)(			   \
+                             int rank, const X(iodim64) *dims,		   \
+			     int howmany_rank,				   \
+			     const X(iodim64) *howmany_dims,		   \
+			     R *ri, R *ii, R *out,			   \
+			     unsigned flags);				   \
+									   \
+FFTW_EXTERN void X(execute_dft_r2c)(const X(plan) p, R *in, C *out);	   \
+FFTW_EXTERN void X(execute_dft_c2r)(const X(plan) p, C *in, R *out);	   \
+									   \
+FFTW_EXTERN void X(execute_split_dft_r2c)(const X(plan) p,		   \
+                                          R *in, R *ro, R *io);		   \
+FFTW_EXTERN void X(execute_split_dft_c2r)(const X(plan) p,		   \
+                                          R *ri, R *ii, R *out);	   \
+									   \
+FFTW_EXTERN X(plan) X(plan_many_r2r)(int rank, const int *n,		   \
+                         int howmany,					   \
+                         R *in, const int *inembed,			   \
+                         int istride, int idist,			   \
+                         R *out, const int *onembed,			   \
+                         int ostride, int odist,			   \
+                         const X(r2r_kind) *kind, unsigned flags);	   \
+									   \
+FFTW_EXTERN X(plan) X(plan_r2r)(int rank, const int *n, R *in, R *out,	   \
+                    const X(r2r_kind) *kind, unsigned flags);		   \
+									   \
+FFTW_EXTERN X(plan) X(plan_r2r_1d)(int n, R *in, R *out,		   \
+                       X(r2r_kind) kind, unsigned flags);		   \
+FFTW_EXTERN X(plan) X(plan_r2r_2d)(int n0, int n1, R *in, R *out,	   \
+                       X(r2r_kind) kind0, X(r2r_kind) kind1,		   \
+                       unsigned flags);					   \
+FFTW_EXTERN X(plan) X(plan_r2r_3d)(int n0, int n1, int n2,		   \
+                       R *in, R *out, X(r2r_kind) kind0,		   \
+                       X(r2r_kind) kind1, X(r2r_kind) kind2,		   \
+                       unsigned flags);					   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru_r2r)(int rank, const X(iodim) *dims,	   \
+                         int howmany_rank,				   \
+                         const X(iodim) *howmany_dims,			   \
+                         R *in, R *out,					   \
+                         const X(r2r_kind) *kind, unsigned flags);	   \
+									   \
+FFTW_EXTERN X(plan) X(plan_guru64_r2r)(int rank, const X(iodim64) *dims,   \
+                         int howmany_rank,				   \
+                         const X(iodim64) *howmany_dims,		   \
+                         R *in, R *out,					   \
+                         const X(r2r_kind) *kind, unsigned flags);	   \
+									   \
+FFTW_EXTERN void X(execute_r2r)(const X(plan) p, R *in, R *out);	   \
+									   \
+FFTW_EXTERN void X(destroy_plan)(X(plan) p);				   \
+FFTW_EXTERN void X(forget_wisdom)(void);				   \
+FFTW_EXTERN void X(cleanup)(void);					   \
+									   \
+FFTW_EXTERN void X(set_timelimit)(double);				   \
+									   \
+FFTW_EXTERN void X(plan_with_nthreads)(int nthreads);			   \
+FFTW_EXTERN int X(init_threads)(void);					   \
+FFTW_EXTERN void X(cleanup_threads)(void);				   \
+									   \
+FFTW_EXTERN void X(export_wisdom_to_file)(FILE *output_file);		   \
+FFTW_EXTERN char *X(export_wisdom_to_string)(void);			   \
+FFTW_EXTERN void X(export_wisdom)(void (*write_char)(char c, void *),	   \
+                                  void *data);				   \
+FFTW_EXTERN int X(import_system_wisdom)(void);				   \
+FFTW_EXTERN int X(import_wisdom_from_file)(FILE *input_file);		   \
+FFTW_EXTERN int X(import_wisdom_from_string)(const char *input_string);	   \
+FFTW_EXTERN int X(import_wisdom)(int (*read_char)(void *), void *data);	   \
+									   \
+FFTW_EXTERN void X(fprint_plan)(const X(plan) p, FILE *output_file);	   \
+FFTW_EXTERN void X(print_plan)(const X(plan) p);			   \
+									   \
+FFTW_EXTERN void *X(malloc)(size_t n);					   \
+FFTW_EXTERN void X(free)(void *p);					   \
+									   \
+FFTW_EXTERN void X(flops)(const X(plan) p,				   \
+                          double *add, double *mul, double *fmas);	   \
+FFTW_EXTERN double X(estimate_cost)(const X(plan) p);			   \
+									   \
+FFTW_EXTERN const char X(version)[];					   \
+FFTW_EXTERN const char X(cc)[];						   \
+FFTW_EXTERN const char X(codelet_optim)[];
+
+
+/* end of FFTW_DEFINE_API macro */
+
+FFTW_DEFINE_API(FFTW_MANGLE_DOUBLE, double, fftw_complex)
+FFTW_DEFINE_API(FFTW_MANGLE_FLOAT, float, fftwf_complex)
+FFTW_DEFINE_API(FFTW_MANGLE_LONG_DOUBLE, long double, fftwl_complex)
+
+#define FFTW_FORWARD (-1)
+#define FFTW_BACKWARD (+1)
+
+#define FFTW_NO_TIMELIMIT (-1.0)
+
+/* documented flags */
+#define FFTW_MEASURE (0U)
+#define FFTW_DESTROY_INPUT (1U << 0)
+#define FFTW_UNALIGNED (1U << 1)
+#define FFTW_CONSERVE_MEMORY (1U << 2)
+#define FFTW_EXHAUSTIVE (1U << 3) /* NO_EXHAUSTIVE is default */
+#define FFTW_PRESERVE_INPUT (1U << 4) /* cancels FFTW_DESTROY_INPUT */
+#define FFTW_PATIENT (1U << 5) /* IMPATIENT is default */
+#define FFTW_ESTIMATE (1U << 6)
+
+/* undocumented beyond-guru flags */
+#define FFTW_ESTIMATE_PATIENT (1U << 7)
+#define FFTW_BELIEVE_PCOST (1U << 8)
+#define FFTW_NO_DFT_R2HC (1U << 9)
+#define FFTW_NO_NONTHREADED (1U << 10)
+#define FFTW_NO_BUFFERING (1U << 11)
+#define FFTW_NO_INDIRECT_OP (1U << 12)
+#define FFTW_ALLOW_LARGE_GENERIC (1U << 13) /* NO_LARGE_GENERIC is default */
+#define FFTW_NO_RANK_SPLITS (1U << 14)
+#define FFTW_NO_VRANK_SPLITS (1U << 15)
+#define FFTW_NO_VRECURSE (1U << 16)
+#define FFTW_NO_SIMD (1U << 17)
+#define FFTW_NO_SLOW (1U << 18)
+#define FFTW_NO_FIXED_RADIX_LARGE_N (1U << 19)
+#define FFTW_ALLOW_PRUNING (1U << 20)
+#define FFTW_WISDOM_ONLY (1U << 21)
+
+#ifdef __cplusplus
+}  /* extern "C" */
+#endif /* __cplusplus */
+
+#endif /* FFTW3_H */

dedalus/utils/fftw/test.py

+import time
+import numpy as np
+import pylab as P
+from fftw import Plan
+
+size = 128
+data = np.zeros((size,size,size), dtype='complex')
+
+fp = Plan(data)
+rp = Plan(data, direction='FFTW_BACKWARD', flags=['FFTW_MEASURE'])
+x = np.linspace(0,2*np.pi,size, endpoint=False)
+y = np.linspace(0,2*np.pi,size, endpoint=False)
+xx, yy = np.meshgrid(x,y)
+data[:] = (np.sin(xx) + np.sin(yy) + 0j) * np.ones((1,1,size))
+data_blah = data.copy()
+
+start = time.time()
+fp()
+rp()
+end = time.time()
+print "ratio = %10.5f" % (data[10,10,10].real/data_blah[10,10,10].real)
+print "128**3 = %10.5f" % 128**3
+
+# P.subplot(121)
+# P.imshow(data_blah[:,:,0].real)
+# P.subplot(122)
+# P.imshow(data[:,:,0].real)
+# P.show()
+
+print "time = %10.5f" % (end-start)

dedalus/utils/fftw/test2.py

+import time
+import numpy as np
+import pylab as P
+from fftw import PlanAxes
+
+size = 128
+data = np.zeros((size,size,size), dtype='complex')
+
+p = PlanAxes(data)
+
+

dedalus/utils/fftw/test_pencils.py

+import time
+import numpy as np
+import pylab as P
+from fftw import PlanPencil
+
+size = 128
+data = np.zeros((size,size,size), dtype='complex')
+
+p_start = time.time()
+p = PlanPencil(data)
+p_stop = time.time()
+
+data[:] = np.random.rand(size, size, size) + 0j
+data2 = data.copy()
+
+fw_start = time.time()
+p()
+fw_stop = time.time()
+
+np_start = time.time()
+npdata = np.fft.fft(data2,axis=2)
+np_stop = time.time()
+
+
+np.testing.assert_almost_equal(data, npdata)
+
+print "numpy time = %10.5f sec" % (np_stop-np_start)
+print "fftw time = %10.5f sec" % (fw_stop-fw_start)
+print "plan time = %10.5f sec" % (p_stop-p_start)

dedalus/utils/fftw/test_planes.py

+import time
+import numpy as np
+import pylab as P
+from fftw import PlanPlanes
+
+size = 128
+data = np.zeros((size,size,size), dtype='complex')
+
+p_start = time.time()
+p = PlanPlanes(data)
+p_stop = time.time()
+
+data[:] = np.random.rand(size, size, size) + 0j
+data2 = data.copy()
+
+fw_start = time.time()
+p()
+fw_stop = time.time()
+
+np_start = time.time()
+npdata = np.fft.fftn(data2,axes=(0,1))
+np_stop = time.time()
+
+
+np.testing.assert_almost_equal(data, npdata)
+
+print "numpy time = %10.5f sec" % (np_stop-np_start)
+print "fftw time = %10.5f sec" % (fw_stop-fw_start)
+print "plan time = %10.5f sec" % (p_stop-p_start)