PEP8 code cleanups.

gprMax/fields_outputs.py

@@ -67,7 +67,7 @@ __global__ void store_outputs(int NRX, int iteration, const int* __restrict__ rx
     //      NRX: Total number of receivers in the model
     //      rxs: Array to store field components for receivers - rows are field components; columns are iterations; pages are receivers
     //      E, H: Access to field component arrays
-    
+
     // Obtain the linear index corresponding to the current thread and use for each receiver
     int rx = blockIdx.x * blockDim.x + threadIdx.x;
 

gprMax/fields_updates_gpu.py

@@ -29,7 +29,7 @@ kernels_template_fields = Template("""
 #define INDEX4D_ID(p, i, j, k) (p)*($NX_ID)*($NY_ID)*($NZ_ID)+(i)*($NY_ID)*($NZ_ID)+(j)*($NZ_ID)+(k)
 #define INDEX4D_T(p, i, j, k) (p)*($NX_T)*($NY_T)*($NZ_T)+(i)*($NY_T)*($NZ_T)+(j)*($NZ_T)+(k)
 
-// Material coefficients (read-only) in constant memory (64KB) 
+// Material coefficients (read-only) in constant memory (64KB)_
 __device__ __constant__ $REAL updatecoeffsE[$N_updatecoeffsE];
 __device__ __constant__ $REAL updatecoeffsH[$N_updatecoeffsH];
 
@@ -44,7 +44,7 @@ __global__ void update_e(int NX, int NY, int NZ, const unsigned int* __restrict_
     //  Args:
     //      NX, NY, NZ: Number of cells of the model domain
     //      ID, E, H: Access to ID and field component arrays
-    
+
     // Obtain the linear index corresponding to the current thread
     int idx = blockIdx.x * blockDim.x + threadIdx.x;
 
@@ -63,13 +63,13 @@ __global__ void update_e(int NX, int NY, int NZ, const unsigned int* __restrict_
         int materialEx = ID[INDEX4D_ID(0,i_ID,j_ID,k_ID)];
         Ex[INDEX3D_FIELDS(i,j,k)] = updatecoeffsE[INDEX2D_MAT(materialEx,0)] * Ex[INDEX3D_FIELDS(i,j,k)] + updatecoeffsE[INDEX2D_MAT(materialEx,2)] * (Hz[INDEX3D_FIELDS(i,j,k)] - Hz[INDEX3D_FIELDS(i,j-1,k)]) - updatecoeffsE[INDEX2D_MAT(materialEx,3)] * (Hy[INDEX3D_FIELDS(i,j,k)] - Hy[INDEX3D_FIELDS(i,j,k-1)]);
     }
-    
+
     // Ey component
     if ((NX != 1 || NZ != 1) && i > 0 && i < NX && j >= 0 && j < NY && k > 0 && k < NZ) {
         int materialEy = ID[INDEX4D_ID(1,i_ID,j_ID,k_ID)];
         Ey[INDEX3D_FIELDS(i,j,k)] = updatecoeffsE[INDEX2D_MAT(materialEy,0)] * Ey[INDEX3D_FIELDS(i,j,k)] + updatecoeffsE[INDEX2D_MAT(materialEy,3)] * (Hx[INDEX3D_FIELDS(i,j,k)] - Hx[INDEX3D_FIELDS(i,j,k-1)]) - updatecoeffsE[INDEX2D_MAT(materialEy,1)] * (Hz[INDEX3D_FIELDS(i,j,k)] - Hz[INDEX3D_FIELDS(i-1,j,k)]);
     }
-    
+
     // Ez component
     if ((NX != 1 || NY != 1) && i > 0 && i < NX && j > 0 && j < NY && k >= 0 && k < NZ) {
         int materialEz = ID[INDEX4D_ID(2,i_ID,j_ID,k_ID)];
@@ -89,7 +89,7 @@ __global__ void update_e_dispersive_A(int NX, int NY, int NZ, int MAXPOLES, cons
     //      NX, NY, NZ: Number of cells of the model domain
     //      MAXPOLES: Maximum number of dispersive material poles present in model
     //      updatedispersivecoeffs, T, ID, E, H: Access to update coefficients, dispersive, ID and field component arrays
-    
+
     // Obtain the linear index corresponding to the current thread
     int idx = blockIdx.x * blockDim.x + threadIdx.x;
 
@@ -118,7 +118,7 @@ __global__ void update_e_dispersive_A(int NX, int NY, int NZ, int MAXPOLES, cons
         }
         Ex[INDEX3D_FIELDS(i,j,k)] = updatecoeffsE[INDEX2D_MAT(materialEx,0)] * Ex[INDEX3D_FIELDS(i,j,k)] + updatecoeffsE[INDEX2D_MAT(materialEx,2)] * (Hz[INDEX3D_FIELDS(i,j,k)] - Hz[INDEX3D_FIELDS(i,j-1,k)]) - updatecoeffsE[INDEX2D_MAT(materialEx,3)] * (Hy[INDEX3D_FIELDS(i,j,k)] - Hy[INDEX3D_FIELDS(i,j,k-1)]) - updatecoeffsE[INDEX2D_MAT(materialEx,4)] * phi;
     }
-    
+
     // Ey component
     if ((NX != 1 || NZ != 1) && i > 0 && i < NX && j >= 0 && j < NY && k > 0 && k < NZ) {
         int materialEy = ID[INDEX4D_ID(1,i_ID,j_ID,k_ID)];
@@ -129,7 +129,7 @@ __global__ void update_e_dispersive_A(int NX, int NY, int NZ, int MAXPOLES, cons
         }
         Ey[INDEX3D_FIELDS(i,j,k)] = updatecoeffsE[INDEX2D_MAT(materialEy,0)] * Ey[INDEX3D_FIELDS(i,j,k)] + updatecoeffsE[INDEX2D_MAT(materialEy,3)] * (Hx[INDEX3D_FIELDS(i,j,k)] - Hx[INDEX3D_FIELDS(i,j,k-1)]) - updatecoeffsE[INDEX2D_MAT(materialEy,1)] * (Hz[INDEX3D_FIELDS(i,j,k)] - Hz[INDEX3D_FIELDS(i-1,j,k)]) - updatecoeffsE[INDEX2D_MAT(materialEy,4)] * phi;
     }
-    
+
     // Ez component
     if ((NX != 1 || NY != 1) && i > 0 && i < NX && j > 0 && j < NY && k >= 0 && k < NZ) {
         int materialEz = ID[INDEX4D_ID(2,i_ID,j_ID,k_ID)];
@@ -150,7 +150,7 @@ __global__ void update_e_dispersive_B(int NX, int NY, int NZ, int MAXPOLES, cons
     //      NX, NY, NZ: Number of cells of the model domain
     //      MAXPOLES: Maximum number of dispersive material poles present in model
     //      updatedispersivecoeffs, T, ID, E, H: Access to update coefficients, dispersive, ID and field component arrays
-    
+
     // Obtain the linear index corresponding to the current thread
     int idx = blockIdx.x * blockDim.x + threadIdx.x;
 
@@ -176,7 +176,7 @@ __global__ void update_e_dispersive_B(int NX, int NY, int NZ, int MAXPOLES, cons
             Tx[INDEX4D_T(pole,i_T,j_T,k_T)] = Tx[INDEX4D_T(pole,i_T,j_T,k_T)] - updatecoeffsdispersive[INDEX2D_MATDISP(materialEx,2+(pole*3))] * Ex[INDEX3D_FIELDS(i,j,k)];
         }
     }
-    
+
     // Ey component
     if ((NX != 1 || NZ != 1) && i > 0 && i < NX && j >= 0 && j < NY && k > 0 && k < NZ) {
         int materialEy = ID[INDEX4D_ID(1,i_ID,j_ID,k_ID)];
@@ -184,7 +184,7 @@ __global__ void update_e_dispersive_B(int NX, int NY, int NZ, int MAXPOLES, cons
             Ty[INDEX4D_T(pole,i_T,j_T,k_T)] = Ty[INDEX4D_T(pole,i_T,j_T,k_T)] - updatecoeffsdispersive[INDEX2D_MATDISP(materialEy,2+(pole*3))] * Ey[INDEX3D_FIELDS(i,j,k)];
         }
     }
-    
+
     // Ez component
     if ((NX != 1 || NY != 1) && i > 0 && i < NX && j > 0 && j < NY && k >= 0 && k < NZ) {
         int materialEz = ID[INDEX4D_ID(2,i_ID,j_ID,k_ID)];
@@ -206,7 +206,7 @@ __global__ void update_h(int NX, int NY, int NZ, const unsigned int* __restrict_
     //  Args:
     //      NX, NY, NZ: Number of cells of the model domain
     //      ID, E, H: Access to ID and field component arrays
-    
+
     // Obtain the linear index corresponding to the current thread
     int idx = blockIdx.x * blockDim.x + threadIdx.x;
 
@@ -225,13 +225,13 @@ __global__ void update_h(int NX, int NY, int NZ, const unsigned int* __restrict_
         int materialHx = ID[INDEX4D_ID(3,i_ID,j_ID,k_ID)];
         Hx[INDEX3D_FIELDS(i,j,k)] = updatecoeffsH[INDEX2D_MAT(materialHx,0)] * Hx[INDEX3D_FIELDS(i,j,k)] - updatecoeffsH[INDEX2D_MAT(materialHx,2)] * (Ez[INDEX3D_FIELDS(i,j+1,k)] - Ez[INDEX3D_FIELDS(i,j,k)]) + updatecoeffsH[INDEX2D_MAT(materialHx,3)] * (Ey[INDEX3D_FIELDS(i,j,k+1)] - Ey[INDEX3D_FIELDS(i,j,k)]);
     }
-    
+
     // Hy component
     if (NY != 1 && i >= 0 && i < NX && j > 0 && j < NY && k >= 0 && k < NZ) {
         int materialHy = ID[INDEX4D_ID(4,i_ID,j_ID,k_ID)];
         Hy[INDEX3D_FIELDS(i,j,k)] = updatecoeffsH[INDEX2D_MAT(materialHy,0)] * Hy[INDEX3D_FIELDS(i,j,k)] - updatecoeffsH[INDEX2D_MAT(materialHy,3)] * (Ex[INDEX3D_FIELDS(i,j,k+1)] - Ex[INDEX3D_FIELDS(i,j,k)]) + updatecoeffsH[INDEX2D_MAT(materialHy,1)] * (Ez[INDEX3D_FIELDS(i+1,j,k)] - Ez[INDEX3D_FIELDS(i,j,k)]);
     }
-    
+
     // Hz component
     if (NZ != 1 && i >= 0 && i < NX && j >= 0 && j < NY && k > 0 && k < NZ) {
         int materialHz = ID[INDEX4D_ID(5,i_ID,j_ID,k_ID)];

gprMax/fractals.py

@@ -100,7 +100,7 @@ class FractalSurface(object):
         fractalmax = np.amax(self.fractalsurface)
         fractalrange = fractalmax - fractalmin
         self.fractalsurface = self.fractalsurface * ((self.fractalrange[1] - self.fractalrange[0]) / fractalrange) \
-                + self.fractalrange[0] - ((self.fractalrange[1] - self.fractalrange[0]) / fractalrange) * fractalmin
+            + self.fractalrange[0] - ((self.fractalrange[1] - self.fractalrange[0]) / fractalrange) * fractalmin
 
 
 class FractalVolume(object):

gprMax/geometry_outputs.py

@@ -218,25 +218,25 @@ class GeometryView(object):
                 z_materials = np.zeros((n_z_lines), dtype=np.uint32)
 
                 define_fine_geometry(self.nx,
-                    self.ny,
+                                     self.ny,
-                    self.nz,
+                                     self.nz,
-                    self.xs,
+                                     self.xs,
-                    self.xf,
+                                     self.xf,
-                    self.ys,
+                                     self.ys,
-                    self.yf,
+                                     self.yf,
-                    self.zs,
+                                     self.zs,
-                    self.zf,
+                                     self.zf,
-                    G.dx,
+                                     G.dx,
-                    G.dy,
+                                     G.dy,
-                    G.dz,
+                                     G.dz,
-                    G.ID,
+                                     G.ID,
-                    points,
+                                     points,
-                    x_lines,
+                                     x_lines,
-                    x_materials,
+                                     x_materials,
-                    y_lines,
+                                     y_lines,
-                    y_materials,
+                                     y_materials,
-                    z_lines,
+                                     z_lines,
-                    z_materials)
+                                     z_materials)
 
                 # Write point data
                 datasize = points.nbytes

gprMax/gprMax.py

@@ -70,18 +70,18 @@ def main():
 
 
 def api(
-            inputfile,
+    inputfile,
-            n=1,
+    n=1,
-            task=None,
+    task=None,
-            restart=None,
+    restart=None,
-            mpi=False,
+    mpi=False,
-            gpu=None,
+    gpu=None,
-            benchmark=False,
+    benchmark=False,
-            geometry_only=False,
+    geometry_only=False,
-            geometry_fixed=False,
+    geometry_fixed=False,
-            write_processed=False,
+    write_processed=False,
-            opt_taguchi=False
+    opt_taguchi=False
-        ):
+):
     """If installed as a module this is the entry point."""
 
     # Print gprMax logo, version, and licencing/copyright information
@@ -165,7 +165,7 @@ def run_main(args):
         # Process for simulation with Taguchi optimisation #
         ####################################################
         elif args.opt_taguchi:
-            if args.mpi_worker: # Special case for MPI spawned workers - they do not need to enter the Taguchi optimisation mode
+            if args.mpi_worker:  # Special case for MPI spawned workers - they do not need to enter the Taguchi optimisation mode
                 run_mpi_sim(args, inputfile, usernamespace)
             else:
                 from gprMax.optimisation_taguchi import run_opt_sim
@@ -396,9 +396,9 @@ def run_mpi_sim(args, inputfile, usernamespace, optparams=None):
 
         # Connect to parent
         try:
-            comm = MPI.Comm.Get_parent() # get MPI communicator object
+            comm = MPI.Comm.Get_parent()  # get MPI communicator object
             rank = comm.Get_rank()  # rank of this process
-        except:
+        except ValueError:
             raise ValueError('Could not connect to parent')
 
         # Ask for work until stop sentinel

gprMax/grid.py

@@ -50,10 +50,10 @@ class Grid(object):
         self.grid = grid
 
     def n_edges(self):
-        l = self.nx
+        i = self.nx
-        m = self.ny
+        j = self.ny
-        n = self.nz
+        k = self.nz
-        e = (l * m * (n - 1)) + (m * n * (l - 1)) + (l * n * (m - 1))
+        e = (i * j * (k - 1)) + (j * k * (i - 1)) + (i * k * (j - 1))
         return e
 
     def n_nodes(self):
@@ -239,8 +239,8 @@ def dispersion_analysis(G):
 
                 # Built-in waveform
                 else:
-                # Time to analyse waveform - 4*pulse_width as using entire
+                    # Time to analyse waveform - 4*pulse_width as using entire
-                # time window can result in demanding FFT
+                    # time window can result in demanding FFT
                     waveform.calculate_coefficients()
                     iterations = round_value(4 * waveform.chi / G.dt)
                     if iterations > G.iterations:
@@ -261,7 +261,7 @@ def dispersion_analysis(G):
                     try:
                         freqthres = np.where(power[freqmaxpower:] < -G.highestfreqthres)[0][0] + freqmaxpower
                         results['maxfreq'].append(freqs[freqthres])
-                    except:
+                    except ValueError:
                         results['error'] = 'unable to calculate maximum power from waveform, most likely due to undersampling.'
 
                 # If waveform is truncated don't do any further analysis

gprMax/input_cmd_funcs.py

@@ -413,7 +413,7 @@ def cylinder(x1, y1, z1, x2, y2, z2, radius, material, averaging='', rotate90ori
 
 
 def cylindrical_sector(axis, ctr1, ctr2, t1, t2, radius,
-                startingangle, sweptangle, material, averaging=''):
+                       startingangle, sweptangle, material, averaging=''):
     """Prints the gprMax #cylindrical_sector command.
 
     Args:
@@ -471,7 +471,7 @@ def waveform(shape, amplitude, frequency, identifier):
 
 
 def hertzian_dipole(polarisation, f1, f2, f3, identifier,
-                t0=None, t_remove=None, dxdy=None, rotate90origin=()):
+                    t0=None, t_remove=None, dxdy=None, rotate90origin=()):
     """Prints the #hertzian_dipole: polarisation, f1, f2, f3, identifier, [t0, t_remove]
 
     Args:
@@ -545,7 +545,7 @@ def magnetic_dipole(polarisation, f1, f2, f3, identifier,
 
 
 def voltage_source(polarisation, f1, f2, f3, resistance, identifier,
-                    t0=None, t_remove=None, dxdy=None, rotate90origin=()):
+                   t0=None, t_remove=None, dxdy=None, rotate90origin=()):
     """Prints the #voltage_source: polarisation, f1, f2, f3, resistance, identifier, [t0, t_remove]
 
     Args:
@@ -583,7 +583,7 @@ def voltage_source(polarisation, f1, f2, f3, resistance, identifier,
 
 
 def transmission_line(polarisation, f1, f2, f3, resistance, identifier,
-                    t0=None, t_remove=None, dxdy=None, rotate90origin=()):
+                      t0=None, t_remove=None, dxdy=None, rotate90origin=()):
     """Prints the #transmission_line: polarisation, f1, f2, f3, resistance, identifier, [t0, t_remove]
 
     Args:

gprMax/input_cmds_geometry.py

@@ -877,10 +877,7 @@ def process_geometrycmds(geometry, G):
             volume.nbins = nbins
             volume.seed = seed
             volume.weighting = np.array([float(tmp[8]), float(tmp[9]), float(tmp[10])])
-            try:
+            volume.averaging = averagefractalbox
-                volume.averaging = averagefractalbox
-            except:
-                pass
 
             if G.messages:
                 if volume.averaging:

gprMax/input_cmds_multiuse.py

@@ -499,7 +499,7 @@ def process_multicmds(multicmds, G):
             try:
                 time = int(tmp[9])
             # If real floating point value given
-            except:
+            except ValueError:
                 time = float(tmp[9])
                 if time > 0:
                     time = round_value((time / G.dt)) + 1
@@ -587,13 +587,8 @@ def process_multicmds(multicmds, G):
                 material.type = 'debye'
                 material.poles = poles
                 material.averagable = False
-                    # for pole in range(1, 2 * poles, 2):
-                    # if float(tmp[pole]) > 0 and float(tmp[pole + 1]) > G.dt:
-                    #    material.deltaer.append(float(tmp[pole]))
-                    #    material.tau.append(float(tmp[pole + 1]))
-                    # else:
-                    #    raise CmdInputError("'" + cmdname + ': ' + ' '.join(tmp) + "'" + ' requires positive values for the permittivity difference, and relaxation times that are greater than the time step for the model.')
                 for pole in range(1, 2 * poles, 2):
+                    # N.B Not checking if relaxation times are greater than time-step
                     if float(tmp[pole]) > 0:
                         material.deltaer.append(float(tmp[pole]))
                         material.tau.append(float(tmp[pole + 1]))

gprMax/input_cmds_singleuse.py

@@ -203,7 +203,7 @@ def process_singlecmds(singlecmds, G):
         G.timewindow = (tmp - 1) * G.dt
         G.iterations = tmp
     # If real floating point value given
-    except:
+    except ValueError:
         tmp = float(tmp)
         if tmp > 0:
             G.timewindow = tmp
@@ -312,7 +312,7 @@ def process_singlecmds(singlecmds, G):
                 waveformvalues = waveformvalues[:len(waveformtime)]
             # Zero-pad end of waveform array if it is shorter than time array
             elif len(waveformvalues) < len(waveformtime):
-                waveformvalues = np.lib.pad(waveformvalues, (0,len(waveformtime)-len(waveformvalues)), 'constant', constant_values=0)
+                waveformvalues = np.lib.pad(waveformvalues, (0, len(waveformtime) - len(waveformvalues)), 'constant', constant_values=0)
 
             # Interpolate waveform values
             w.userfunc = interpolate.interp1d(waveformtime, waveformvalues, **kwargs)

gprMax/materials.py

@@ -148,14 +148,14 @@ class Material(object):
 
         Args:
             freq (float): Frequency used to calculate complex relative permittivity.
-            
+
         Returns:
             er (float): Complex relative permittivity.
         """
-        
+
-        # This will be permittivity at infinite frequency if the material is dispersive
+        # Permittivity at infinite frequency if the material is dispersive
         er = self.er
-        
+
         if self.poles > 0:
             w = 2 * np.pi * freq
             er += self.se / (w * e0)
@@ -166,10 +166,11 @@ class Material(object):
                 for pole in range(self.poles):
                     er += (self.deltaer[pole] * self.tau[pole]**2) / (self.tau[pole]**2 + 2j * w * self.alpha[pole] - w**2)
             elif 'drude' in self.type:
+                ersum = 0
                 for pole in range(self.poles):
                     ersum += self.tau[pole]**2 / (w**2 - 1j * w * self.alpha[pole])
                     er -= ersum
-    
+
         return er
 
 

gprMax/receivers.py

@@ -44,7 +44,7 @@ class Rx(object):
 
 def gpu_initialise_rx_arrays(G):
     """Initialise arrays on GPU for receiver coordinates and to store field components for receivers.
-        
+
     Args:
         G (class): Grid class instance - holds essential parameters describing the model.
     """

gprMax/source_updates_gpu.py

@@ -52,7 +52,7 @@ __global__ void update_hertzian_dipole(int NHERTZDIPOLE, int iteration, $REAL dx
     int src = blockIdx.x * blockDim.x + threadIdx.x;
 
     if (src < NHERTZDIPOLE) {
-    
+
         $REAL dl;
         int i, j, k, polarisation;
 
@@ -104,7 +104,7 @@ __global__ void update_magnetic_dipole(int NMAGDIPOLE, int iteration, $REAL dx,
     int src = blockIdx.x * blockDim.x + threadIdx.x;
 
     if (src < NMAGDIPOLE) {
-    
+
         int i, j, k, polarisation;
 
         i = srcinfo1[INDEX2D_SRCINFO(src,0)];
@@ -154,10 +154,10 @@ __global__ void update_voltage_source(int NVOLTSRC, int iteration, $REAL dx, $RE
     int src = blockIdx.x * blockDim.x + threadIdx.x;
 
     if (src < NVOLTSRC) {
-    
+
         $REAL resistance;
         int i, j, k, polarisation;
-    
+
         i = srcinfo1[INDEX2D_SRCINFO(src,0)];
         j = srcinfo1[INDEX2D_SRCINFO(src,1)];
         k = srcinfo1[INDEX2D_SRCINFO(src,2)];

gprMax/sources.py

@@ -217,17 +217,17 @@ class MagneticDipole(Source):
 
 def gpu_initialise_src_arrays(sources, G):
     """Initialise arrays on GPU for source coordinates/polarisation, other source information, and source waveform values.
-        
+
     Args:
         sources (list): List of sources of one class, e.g. HertzianDipoles.
         G (class): Grid class instance - holds essential parameters describing the model.
-        
+
     Returns:
         srcinfo1_gpu (int): numpy array of source cell coordinates and polarisation information.
         srcinfo2_gpu (float): numpy array of other source information, e.g. length, resistance etc...
         srcwaves_gpu (float): numpy array of source waveform values.
     """
-        
+
     import pycuda.gpuarray as gpuarray
 
     srcinfo1 = np.zeros((len(sources), 4), dtype=np.int32)
@@ -237,14 +237,14 @@ def gpu_initialise_src_arrays(sources, G):
         srcinfo1[i, 0] = src.xcoord
         srcinfo1[i, 1] = src.ycoord
         srcinfo1[i, 2] = src.zcoord
-        
+
         if src.polarisation == 'x':
             srcinfo1[i, 3] = 0
         elif src.polarisation == 'y':
             srcinfo1[i, 3] = 1
         elif src.polarisation == 'z':
             srcinfo1[i, 3] = 2
-        
+
         if src.__class__.__name__ == 'HertzianDipole':
             srcinfo2[i] = src.dl
             srcwaves[i, :] = src.waveformvaluesJ
@@ -253,7 +253,7 @@ def gpu_initialise_src_arrays(sources, G):
             srcwaves[i, :] = src.waveformvaluesJ
         elif src.__class__.__name__ == 'MagneticDipole':
             srcwaves[i, :] = src.waveformvaluesM
-        
+
     srcinfo1_gpu = gpuarray.to_gpu(srcinfo1)
     srcinfo2_gpu = gpuarray.to_gpu(srcinfo2)
     srcwaves_gpu = gpuarray.to_gpu(srcwaves)

gprMax/utilities.py

@@ -152,7 +152,7 @@ def fft_power(waveform, dt):
     """
 
     # Calculate magnitude of frequency spectra of waveform (ignore warning from taking a log of any zero values)
-    with np.errstate(divide='ignore'): #
+    with np.errstate(divide='ignore'):
         power = 10 * np.log10(np.abs(np.fft.fft(waveform))**2)
 
     # Replace any NaNs or Infs from zero division