From 220be74252b596f8bc1f68402214fd7560861dc0 Mon Sep 17 00:00:00 2001 From: JoseFerrada <5508624+JoseFelipeFerrada@users.noreply.github.com> Date: Fri, 27 Feb 2026 18:49:05 -0300 Subject: [PATCH] Refactor: Modularized project into src/ layout and integrated pytest-benchmark suite --- pyproject.toml | 27 + vectfit3.py => src/vectfit3.py | 1801 +- test/conftest.py | 71 + MODEH_DATA.csv => test/data/MODEH_DATA.csv | 0 .../data/SYSADMITANCE_DATA.csv | 43804 ++++++++-------- TRANSF_DATA.csv => test/data/TRANSF_DATA.csv | 802 +- test/test_previous.py | 228 + test/test_recover.py | 137 + test/test_vector_recover.py | 87 + .../vectfit_testing.old | 831 +- 10 files changed, 24168 insertions(+), 23620 deletions(-) create mode 100644 pyproject.toml rename vectfit3.py => src/vectfit3.py (97%) create mode 100644 test/conftest.py rename MODEH_DATA.csv => test/data/MODEH_DATA.csv (100%) rename SYSADMITANCE_DATA.csv => test/data/SYSADMITANCE_DATA.csv (92%) rename TRANSF_DATA.csv => test/data/TRANSF_DATA.csv (95%) create mode 100644 test/test_previous.py create mode 100644 test/test_recover.py create mode 100644 test/test_vector_recover.py rename vectfit_testing.py => test/vectfit_testing.old (97%) diff --git a/pyproject.toml b/pyproject.toml new file mode 100644 index 0000000..5941324 --- /dev/null +++ b/pyproject.toml @@ -0,0 +1,27 @@ +[build-system] +requires = ["setuptools>=61.0"] +build-backend = "setuptools.build_meta" + +[project] +name = "vectfit-python" +version = "0.1.0" +description = "Vector Fitting for rational approximation of EMT frequency responses." +readme = "README.md" +requires-python = ">=3.8" +authors = [ + {name = "Sebastian Loaiza Elejalde", email = "author@example.com"}, +] +dependencies = [ + "numpy", + "scipy", + "pandas", +] + +[project.optional-dependencies] +test = [ + "pytest", + "pytest-benchmark", +] + +[tool.setuptools.packages.find] +where = ["src"] \ No newline at end of file diff --git a/vectfit3.py b/src/vectfit3.py similarity index 97% rename from vectfit3.py rename to src/vectfit3.py index cd038a4..7061202 100644 --- a/vectfit3.py +++ b/src/vectfit3.py @@ -1,902 +1,901 @@ -# vectfit3.py module. - -""" -*** FastRelaxed Vector Fitting for Python v1.3.1*** - -vectfit3.py is the implementation of Fast Relaxed Vector Fitting algortihm on python. The original code was written -in Matlab eviroment. The pourpose of this algorithm is to compute a rational approximation from tabuled data in the -frequency domain for scalar or vectorized problems. The resulting model can be expressed in either state-space form -or pole-residue form. - - - Original Matlab code autor: Bjorn Gustavsen (08/2008) - - Transcripted and adapted by: Sebastian Loaiza (03/2024) - - Last revision by: Sebastian Loaiza (01/2025) - - * References: - - [1] B. Gustavsen and A. Semlyen, "Rational approximation of frequency - domain responses by Vector Fitting", IEEE Trans. Power Delivery, - vol. 14, no. 3, pp. 1052-1061, July 1999. - - [2] B. Gustavsen, "Improving the pole relocating properties of vector - fitting", IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, - July 2006. - - [3] D. Deschrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, - "Macromodeling of Multiport Systems Using a Fast Implementation of - the Vector Fitting Method", IEEE Microwave and Wireless Components - Letters, vol. 18, no. 6, pp. 383-385, June 2008. - - [4] B. Gustavsen, "User's Guide for vectfit3.m (Fast, Relaxed Vector - fitting)", SINTEF Energy Research, N-7465 Trondheim, Norway, 2008. Aviable - online: https://www.sintef.no/en/software/vector-fitting/downloads/#menu - accesed on: 2/2/2024 - - * Changes: - - - All options for vectfit3 configuration are defined as boolean variables, except asymp which has 3 posible states - - A new option, "lowert_mat" is added for vectfit3 configuration. This indicates when F(s) samples belong to a - lower triangular matrix function, that reduces the number of elements to fit for a symmetric matrix function. - - A new option, "RMO_data" is added for vecfit3 configuration. This shows that matrix function elements are saved in - Row Major Order into F(s). - - New options mentioned before and "cmplx_ss" flag are also included in SER. - - A new method to sort the poles computed during the identification process is implemented. - - tri2full() function is renamed to flat2full(). It is modified to consider asymmetric matrix problems as well - depending on the status of "lower_mat" and "RMO_data" flags. - - ss2pr() function is replaced by to buildRES(). The new function just compute residues matrixes becouse vectfit returns - the poles already. - - Relative deviations are now computed taking as reference the maximum magnitude value in the reference function -""" - -# Scientific computing modules: -import numpy as np -from scipy.linalg import qr, eigvals, lstsq -from scipy.constants import pi - -### ----------------------------------------------------------- Data structures -------------------------------------------------------------- ### - -#opts{}: vectfit modifiers dictionary. -# Dictionary which contains the default settings fot vectfit. -# Any key can be modified to change som options included in vectfit3 -opts={ - "symm_mat" : False, # Indicates when F(s) samples belong to a lower triangular matrix (symmetric problems) - "RMO_data" : True, # Matrix elements are organized in RMO into F(s) (asymmetric problems) - "relax" : True, # Use vector fitting with relaxed non triviality - "stable" : True, # Enforce stable poles - "asymp" : 2, # Include only D in fitting (not E). See [4] - "skip_pole" : False, # Do NOT skip pole identification - "skip_res" : False, # Do NOT skip residues identification (C,D,E). See [4] - "cmplx_ss" : True, # Create complex state space model - "spy1" : False, # No plotting for first stage of vector fitting - "spy2" : True, # Create magnitude plot for fitting of f(s) - "logx" : True, # Use logarithmic axis for x - "logy" : True, # Use logarithmic axis for y - "errplot" : True, # Include deviation in magnitude plot - "phaseplot" : False, # Exclude plot of phase angle - "legend" : True # Do include legends in plots - } - -### ----------------------------------------------------------------- Functions --------------------------------------------------------------- ### - -# vectfit() subroutine. -def opts_errorCheck(opts): - """Fucntion to check any configuration error into opts dictionary. - *Returns True if an error is found otherwise false""" - if opts["asymp"]!=1 and opts["asymp"]!=2 and opts["asymp"]!=3: - print("vectfit3::ERROR::Ilegal value for [asymp] option. It must be 1, 2 or 0") - return True - opitems=list(opts.items()) - asymp=("asymp",opts["asymp"]) - opitems.remove(asymp) #asymp already checked - for option in opitems: - if not(isinstance(option[1],bool)): - print("vectfit3::ERROR::Ilegal value for ["+option[0]+"] option. It must be boolean: True or False") - return True - return False - -# vectfit() subroutine. -def dim_errorCheck(F,s,poles,weights): - """Function to check dimentions compatibility among vectfit's arguments - *Returns True if an error is found otherwise false""" - if len(s.shape)>1 or len(poles.shape)>1: - print("vectfit3::ERROR::Arguments s and poles must be one-dimentional arrays") - return True - if len(F.shape)>1: - # Vectorized problem: Nc>1 - if s.size!=F.shape[1]: - print("vectfit3::ERROR::The number of frequency samples in s and F does not coincide!") - return True - else: - # Scalar problem: Nc=1 - if s.size!=F.size: - print("vectfit3::ERROR::The number of frequency samples in s and F does not coincide!") - return True - if len(weights.shape)>1: - # Individual weighting configuration: weights [Nc x N] - if s.size!=weights.shape[1]: - print("vectfit3::ERROR::The number of frequency samples in s and elements in weights does not coincide!") - return True - if weights.shape[0]!=F.shape[0]: - print("vectfit3::ERROR::The number of elements in F does not coincide to their weiths for individual weighting") - return True - else: - # Common wighting configuration: weights [1 x N] - if s.size!=weights.size: - print("vectfit3::ERROR::The number of frequency samples in s and elements in weights does not coincide!") - return True - return False - -# vectfit() subroutine. -def identifyPoles(LAMBD): - """Function to classify poles storaged into the LAMBD diagonal matrix. - Argument. - - LAMBD: Diagonal matrix containing the poles of the aproximated model - *Returns cindex array which marks the poles with the following flags: - - 0 for real poles - - 1 and 2 for complex conjugated pairs - """ - n=LAMBD.shape[0] - cindex=np.zeros(n, dtype=np.uint16) - for m in range(n): - if np.imag(LAMBD[m,m])!=0: - if m==0: - cindex[m]=1 - else: - if cindex[m-1]==0 or cindex[m-1]==2: - cindex[m]=1 - cindex[m+1]=2 - else: - cindex[m]=2 - return cindex - -# vectfit() subroutine. -def sortPoles(poles): - """Function to sort the poles obtained in the poles identification process. - the poles array is sorted by magnitud in asending order, real poles go first and - for each pair of complex conjugated poles, the one with positive imaginary is placed first - *Returns a complex array with the required poles arrangement""" - poltype=np.abs(poles.imag)<1e-10 # Real poles are marked as True, complex as false - # *!{it is necesary to use a tolerance instead of np.isreal() due to the numeric error in eigenvalues computation} - # Real poles extraction - realpoles=poltype*poles.real - realpoles=np.take_along_axis(realpoles, np.nonzero(realpoles)[0], axis=None) - # Complex poles extraction - complexpoles=np.logical_not(poltype)*poles - complexpoles=np.take_along_axis(complexpoles, np.nonzero(complexpoles)[0], axis=None) - # Sorting real and complex poles separately: In the following procedure the function sorted() with the list of tuples (abs,pol) - #orders by considering first abs, if reapeted magnitudes are found complex poles are ordered considering their imaginary parts. - realpoles=-1*np.sort(np.abs(realpoles)) - complexpoles=np.array([p for _,p in sorted(zip(np.abs(complexpoles),complexpoles))]) - # Organization of the complex conjugated pairs - cpolesorder=np.array([], dtype=bool) - #desired order [True(+),False(-),...] - for _ in range(int(complexpoles.size/2)): - cpolesorder=np.append(cpolesorder,np.array([True,False])) - polswap=np.logical_xor(complexpoles.imag>0,cpolesorder) #marks the poles that must be swaped as True - complexpoles=complexpoles-2j*polswap*complexpoles.imag #change of sign for the imaginary parts of the marked poles - # Organized poles - return np.append(realpoles,complexpoles) - -# vectfit() subroutine. -def vectfitPlot(F,fit,s,opts, initialState=False, titleLabel="Vector Fitting Resutls"): - """Function to plot vector fitting results. - The number of graphs that are displayed varies in function of opts configuration - - Arguments. - - - F: F(s) frequency samples of the original function - - fit: fit(s) fited function that aproximates F(s) - - s: Complex frequency points of evaluation for F and fit - - opts: Dictionary with the modifiers to change the default configuration of Vector Fitting - - Results. - - - Displays the magnitude plot of F and fit samples with or without error - - May display the phase angle plot of F and fit samples if enabled - """ - # Importing plots and graphs module: - import matplotlib as mpl - import matplotlib.pyplot as plt - #matplotlib configuration: - plt.rcParams["font.family"]="serif" # font type - plt.rcParams["mathtext.fontset"]="dejavuserif" # font type in math expressions - mpl.rcParams["font.size"]=14 # font size in points - mpl.rcParams["figure.dpi"]=100 # canvas figure resolution - mpl.rcParams["savefig.dpi"]=300 # saved figure resolution - - freq=np.real(s/(2*pi*1j)) - # LogLog plots: Graphs with logarithmic x and y axis - if opts["errplot"]: - fig1,ax1=plt.subplots(2,1) - l1=ax1[0].plot(freq,np.abs(F.T),color='c',linewidth=1.2) - l2=ax1[0].plot(freq,np.abs(fit.T),color='k',linewidth=1.3,linestyle="dashed") - ax1[0].set(xlabel="Frequency (Hz)", ylabel="Magnitude",title=titleLabel) - if opts["legend"]: - l2[0].set(label="Fitted function") - l1[0].set(label="F(s) samples") - ax1[0].legend() - ax1[0].grid(True) - #logarithmic error computation - logError=np.zeros(F.shape,dtype=np.float64) - maxError=-1e10 - for i in range(F.shape[0]): - logError[i]=np.log10(np.abs(F[i]-fit[i])/np.max(np.abs(F))) - error=logError[i].max() - if error>maxError: maxError=error - maxLabel=ax1[1].plot(freq,logError.T,color='r',linewidth=1.2) - maxError=(10**maxError)*100 - maxLabel[0].set(label="Max fitting error = "+str(maxError)+"%") - print(" * max fitting error = "+str(maxError)+"% *") - ax1[1].set(xlabel="Frequency (Hz)", ylabel=r"$\log_{10}$(relative error)") - ax1[1].legend() - ax1[1].grid(True) - else: - if initialState: - flabel="Sigma function" - tlabel="Vector Fitting initial state" - else: - flabel="Fitted function" - tlabel=titleLabel - fig1,ax1=plt.subplots() - l1=ax1.plot(freq,np.abs(F.T),color='c',linewidth=1.2,label="F(s) samples") - l2=ax1.plot(freq,np.abs(fit.T),color='k',linewidth=1.3,linestyle="dashed") - ax1.set(xlabel="Frequency (Hz)", ylabel="Magnitude",title=tlabel) - if opts["legend"]: - l2[0].set(label=flabel) - l1[0].set(label="F(s) samples") - ax1.legend() - ax1.grid(True) - if opts["phaseplot"]: - #fisrt function angles are computed in degrees, and then are unwrapped - F_angle=np.unwrap(np.angle(F,deg=True),period=360) - fit_angle=np.unwrap(np.angle(fit,deg=True),period=360) - fig2,ax2=plt.subplots() - l3=ax2.plot(freq,F_angle.T,color='c',linewidth=1.2) - l4=ax2.plot(freq,fit_angle.T,color='k',linewidth=1.3,linestyle="dashed") - ax2.set(xlabel="Frequency (Hz)", ylabel="Phase angle (deg)",title=titleLabel) - if opts["legend"]: - l3[0].set(label="F(s) samples") - l4[0].set(label="Fitted function") - ax2.legend() - ax2.grid(True) - if opts["logx"] and opts["logy"]: - #full logarithmic graphs. Logarithmic x and y axis - if opts["errplot"]: - # Magnitude plot: - ax1[0].set_xscale("log") - ax1[0].set_yscale("log") - # Error plot - ax1[1].set_xscale("log") - else: - # Magnitude plot: - ax1.set_xscale("log") - ax1.set_yscale("log") - if opts["phaseplot"]: - # Phase plot: - ax2.set_xscale("log") - elif opts["logx"]: - #semilogarithmic graphs. Logarithmic x and linear y axis - if opts["errplot"]: - ax1[0].set_xscale("log") - ax1[1].set_xscale("log") - else: - ax1.set_xscale("log") - if opts["phaseplot"]: - ax2.set_xscale("log") - elif opts["logy"]: - #semilogarithmic graphs. Linear x and logarithmic y axis - if opts["errplot"]: - ax1[0].set_yscale("log") - else: - ax1.set_yscale("log") - #else default linear axis configuration of plot() is used - plt.show() - -# vectfit3() subroutine. -def buildSER(Ac,Bc,Cc,Dr,Er,complex_format,symmetric_data,RMO_matrixData): - """Function to build the state-space model of the fitted function such as: - F(s) = C * (sI-A)^-1 * B + D + sE - - Arguments. c subindex indicates complex system - - - Ac: Diagonal matrix containing the poles of F(s). Shape [n x n] for n the number fo poles - - Bc: Input matrix for complex form. Must be a vector of ones. Shape [n x 1] - - Cc: Residues matrix. Complex and shaped [Nc x n] with Nc as the number of elements in F(s) - - D: Constant terms matrix. Real matrix of shape [Nc x 1] - - E: Proportional terms matrix. Real matrix of shape [Nc x 1] - - complex_format: Boolean option from opts{} which indicates if a complex system is needed - - symmetric_data: Boolean option from opts{} which indicates if data come from a symmetric matrix problem - - RMO_matrixData: Boolean option from opts{} which indicates if matrix elements are ordered in RMO - - Results. - - - SER: Dictionary that storages A,B,C,D,E system matrixes adapted as indicated by cmplx_ss and symm_mat - """ - SER=dict(A=Ac,B=Bc,C=Cc,D=Dr,E=Er, cmplx_ss=True, symm_mat=symmetric_data, RMO_data=RMO_matrixData) #complex state-space system - if not(complex_format): - # Real state-space system is required so the matrixes are modified - Ar=np.real(Ac) #importing real poles to Ar - Br=Bc #real poles remains realated with ones in B - Cr=np.real(Cc) #importing real values to Cr - cindex=identifyPoles(Ac) #poles identification - # Reorganization of A as a real and block diagonal matrix - k=0 - for m in range(Ac.shape[0]): - if cindex[m]==1: - #complex pole to modify: - cpole=Ac[k,k] - re_cpole=np.real(cpole) #real part - im_cpole=np.imag(cpole) #imaginary part - # Real system adaptation - Ar[k:k+2,k:k+2]=np.array([[re_cpole,im_cpole],[-im_cpole,re_cpole]]) #complex pair block in Ar - # Input matrix modification to consider the complex pair block in Ar - Br[k,0]=2 - Br[k+1,0]=0 - # Real and imaginary part separation for data in output matrix - Cr[:,k]=np.real(Cc[:,k]) - Cr[:,k+1]=np.imag(Cc[:,k]) - k+=1 - # Updating SER with new real matrixes: - SER["A"]=Ar - SER["B"]=Bc - SER["C"]=Cr - SER["cmplx_ss"]=False - return SER - -# build_RES() subroutine. -def flat2full(SER): - """Function to transform data arrays in SER from its default representation (flattened and element-wise) to a full matrix representation. - This function works with symmetric or asymmetric matrix functions. If "lower_mat" flag is true, this function considers that the matrix - problem need to be decompressed from lower triangular representation. - - *vectfit() function works with flattened element-wise data, therefore if data comes from a matrix problem, this function returns - a new SER with modified shapes: - - A shape [n x n] => [Ny*n x Ny*n] for Ny as the original dimentions of the fitted matrix and n as the order of aproximation - - B shape [n x 1] => [Ny*n x Ny] - - C shape [Nc x n] => [Ny x Ny*n] for Nc as the number fitted elements into the matrix (organized element-wise) - - D shape [Nc x 1] => [Ny x Ny] - - E shape [Nc x 1] => [Ny x Ny] - - Important!: lower trinagular compression of symmetric matrix data need to be applied prior vector fitting application - """ - A=SER["A"] - B=SER["B"] - C=SER["C"] - D=SER["D"] - E=SER["E"] - # Unzip process parameters: - n=B.shape[0] # Order of approximation - Nc=C.shape[0] # Number of different elements in the flattened problem - if SER["symm_mat"]: - # Case for a symmetric problem, data must be decompressed and organized in symmetric format - zum=0 # Sum counter - Ny=0 # Shape of the full unzipped matrix function - while zum1: - Nc=F.shape[0] # Number of elements to fit - else: - Nc=1 - # Reshaping arrays to ensure a good vectorized computation - F=np.reshape(F,(1,N)) - - # Problem arrays declaration - LAMBD=np.diag(poles) # Diagonal matriz with searching poles - B=np.ones((n,1), np.float64) # Column vector of ones - SERA=poles # A Matrix in the space state model - SERB=np.ones((n,1), np.float64) # B Matrix in the space state model - SERC=np.zeros((Nc,n),dtype=np.complex128) # C Matrix in the space state model - SERD=np.zeros(Nc,dtype=np.float64) # D Matrix in the space state model - SERE=np.zeros(Nc,dtype=np.float64) # E Matrix in the space state model - fit=np.zeros((Nc,N),dtype=np.complex128) # Array to store fitted values - rmserr=-1 # Root mean squared error - # Weighting type identification - if len(weights.shape)==1: - commonWeighting=True - # Reshaping arrays to ensure a good vectorized computation - #weights=np.reshape(weights,(1,N)) - else: - commonWeighting=False - # Space state selected structure - if opts["asymp"]==1: - offs=0 # for [D=0; E=0] - elif opts["asymp"]==2: - offs=1 # [D!=0; E=0] - else: - offs=2 # [D!=0; E!=0] - - # *-- POLES IDENTIFICATION PROCESS - - if not(opts["skip_pole"]): - Escale=np.zeros(Nc+1) - # Initial complex poles identification: cindex marks 0 for reals, 1 and 2 for complex conjugated pairs - cindex=identifyPoles(LAMBD) - # Building System Matrix - Dk=np.zeros((N,n),dtype=np.complex128) - for m in range(n): - if cindex[m]==0: - # real pole defined - Dk[:,m]=1/(s-LAMBD[m,m]) - elif cindex[m]==1: - #complex pole first part defined - Dk[:,m]=1/(s-LAMBD[m,m])+1/(s-np.conj(LAMBD[m,m])) - Dk[:,m+1]=1j/(s-LAMBD[m,m])-1j/(s-np.conj(LAMBD[m,m])) - # Depending on the D and E option selected - if offs==0 or offs==1: - # for E=0 - Dk=np.hstack((Dk,np.ones((N,1)))) #note that Dk.shape changed to (N,n+1) - else: - # for E!=0 - Dk=np.hstack((Dk,np.ones((N,1)))) - Dk=np.hstack((Dk,np.reshape(s,(N,1)))) #note that Dk.shape changed to (N,n+2) - # Scaling for last row of LS-Problem - scale=0 - for m in range(Nc): - if commonWeighting: - scale+=np.linalg.norm(weights*F[m,:])**2 - else: - scale+=np.linalg.norm(weights[m,:]*F[m,:])**2 - scale=np.sqrt(scale)/N - # Applying relaxed version of the algorithm - if opts["relax"]: - AA=np.zeros((Nc*(n+1),n+1),dtype=np.float64) - bb=np.zeros(Nc*(n+1),dtype=np.float64) - Escale=np.zeros(n+1,dtype=np.float64) - offset=n+offs - for k in range(Nc): - Ac=np.zeros((N,offset+n+1),dtype=np.complex128) - if commonWeighting: - weig=weights - else: - weig=weights[k,:] - for m in range(offset): #left block - Ac[:,m]=weig*Dk[:,m] - for m in range(n+1): #right block - Ac[:,offset+m]=-weig*Dk[:,m]*F[k,:] - # Partitioned problem in real and imaginary part, a real array is obtained: - A=np.vstack((Ac.real,Ac.imag)) - # Integral criterion for sigma - if k==Nc-1: - A=np.vstack((A,np.zeros((1,A.shape[1])))) # adding extra row - for m in range(n+1): - A[2*N,offset+m]=np.real(scale*np.sum(Dk[:,m])) - # Obtaining QR transformation of A - (Q,R)=qr(A,mode="economic") #routine imported from scipy module - R22=R[offset:offset+n+1,offset:offset+n+1] - AA[k*(n+1):(k+1)*(n+1),:]=R22 - if k==Nc-1: - bb[k*(n+1):(k+1)*(n+1)]=Q[-1,offset:]*N*scale - for m in range(AA.shape[1]): - Escale[m]=1/np.linalg.norm(AA[:,m]) - AA[:,m]=Escale[m]*AA[:,m] - # LS solution routine imported from scipy module: - # - check_finite option is disabled to improve performance. NaN should not appear into the arrays - # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") - # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: - x=lstsq(AA,bb, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] - x=x*Escale - # ...end of opts["relax"]=True segment - # Case for non relaxion version of the algorithm. - # Also may be needed when D of sigma results extremely small and large. I needs to be solved again. - if not(opts["relax"]) or np.abs(x[-1])TOLhigh: - AA=np.zeros((Nc*n,n),dtype=np.float64) - bb=np.zeros(Nc*n,dtype=np.float64) - if opts["relax"]: - Dnew=1 - else: - if x[-1]==0: - Dnew=1 - elif np.abs(x[-1])TOLhigh: - Dnew=np.sign(x[-1])*TOLhigh - offset=n+offs - for k in range(Nc): - Ac=np.zeros((N,offset+n),dtype=np.complex128) - Escale=np.zeros(n,dtype=np.float64) - if commonWeighting: - weig=weights - else: - weig=weights[k,:] - for m in range(offset): #left block - Ac[:,m]=weig*Dk[:,m] - for m in range(n): #right block - Ac[:,offset+m]=-weig*Dk[:,m]*F[k,:] - bc=Dnew*weig*F[k,:] - # Partitioned problem in real and imaginary part, real arrays are obtained: - A=np.vstack((Ac.real,Ac.imag)) - b=np.append(bc.real,bc.imag) - # Obtaining QR transformation of A - (Q,R)=qr(A,mode="economic") - R22=R[offset:offset+n,offset:offset+n] - AA[k*n:(k+1)*n,:]=R22 - # The following arrays must be reshaped in order to perform the matrix product - bb[k*n:(k+1)*n]=np.ravel(np.transpose(Q[:,offset:offset+n])@np.reshape(b,(b.size,1))) - for m in range(AA.shape[1]): - Escale[m]=1/np.linalg.norm(AA[:,m]) - AA[:,m]=Escale[m]*AA[:,m] - # LS solution routine imported from scipy module: - # - check_finite option is disabled to improve performance. NaN should not appear into the arrays - # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") - # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: - x=lstsq(AA,bb, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] - x=x*Escale - x=np.append(x,Dnew) - # ...end of opts["relax"]=False or out of tolerance segment - # Changing back to make C complex: - C=np.zeros(x.size-1,dtype=np.complex128) - C[0:C.size]=x[0:-1] - D=x[-1] - for m in range(n): - if cindex[m]==1: - r1=C[m] #real part of the complex number - r2=C[m+1] #imaginary part of the complex number - #building the conjugated complex pair - C[m]=r1+1j*r2 - C[m+1]=r1-1j*r2 - # Graphs of initial stage of vector fitting process - if opts["spy1"]: - print("\n...vectfit3::spy1_Enabled::Building and showing graph for initial fitting state...") - # First fitting state evaluation: - # As mentioned in [1] pole identification begins with the aproximation of sigma(s). sigma(s) is an unknown function whose - #approximation has the same poles of F(s). Furtheremore it is formulated that (sigma*f)_fit(s) = sigma_fit*f(s), whence can be - #demostrated that zeros of sigma are a better set of poles to fit f(s), therefore sigma(s) is called the initial fitting state. - Dk=np.zeros((N,n),dtype=np.complex128) - for m in range(n): - Dk[:,m]=1/(s-LAMBD[m,m]) - sigma=D+Dk@C - #setting temporal options to plot initial vector fitting state - opts_temp=opts - opts_temp["errplot"]=False - opts_temp["phaseplot"]=False - vectfitPlot(F,sigma,s,opts_temp,initialState=True) - # Calculating the zeros for sigma - m=0 #auxiliar counter - for k in range(n): - if mnp.abs(np.real(LAMBD[m,m])): - # Complex poles clasification: diagonal blocks of the form: - # [ real, -imag ] - # [ imag, real ] - LAMBD[m+1,m]=-np.imag(LAMBD[m,m]) - LAMBD[m,m+1]=np.imag(LAMBD[m,m]) - LAMBD[m,m]=np.real(LAMBD[m,m]) - LAMBD[m+1,m+1]=LAMBD[m,m] - # B vector modification for complex poles - B[m,0]=2 - B[m+1,0]=0 - ccval=C[m] - # Complex values clasification: - C[m]=np.real(ccval) - C[m+1]=np.imag(ccval) - m+=1 - m+=1 - #to perform the vectorized B*C and obtain a matrix C need to be reshaped - C=np.reshape(C,(1,C.size)) - #also just the real parts of LAMBD and C are taken in order to obtain a real[float64] matrix for ZER - ZER=LAMBD.real-B@C.real/D - # Computation of ZER eigenvalues - poles=eigvals(ZER) #routine imported from scipy module - # Unstabla values identification - unstable=poles.real>0 #generates a logical array - if opts["stable"]: - if np.any(unstable): - #the product of roetter and unstable extracts the unstable poles - extracted=poles*unstable - poles=poles-2*extracted.real - poles=sortPoles(poles) - SERA=poles - #...end of poles identification process - - # --* RESIDUES IDENTIFICATION PROCESS - - if not(opts["skip_res"]): - # Now SER for f is calculated by using modified zeros of sigma as new poles: - LAMBD=np.diag(poles) - # Initial complex poles identification: cindex marks 0 for reals, 1 and 2 for complex conjugated pairs - cindex=identifyPoles(LAMBD) - # Building System Matrix - Dk=np.zeros((N,n),dtype=np.complex128) - for m in range(n): - if cindex[m]==0: - # real pole defined - Dk[:,m]=1/(s-LAMBD[m,m]) - elif cindex[m]==1: - #complex pole first part defined - Dk[:,m]=1/(s-LAMBD[m,m])+1/(s-np.conj(LAMBD[m,m])) - Dk[:,m+1]=1j/(s-LAMBD[m,m])-1j/(s-np.conj(LAMBD[m,m])) - if commonWeighting: #case for common wighting - C=np.zeros((Nc,n),dtype=np.complex128) - for m in range(n): #same weight for all frequency samples - Dk[:,m]=weights*Dk[:,m] - # The SER for the new fitting is calculated by using the calculated zeros as new poles - if opts["asymp"]==1: - A=np.zeros((2*N,n),dtype=np.float64) - A[0:N,:]=Dk.real - A[N:2*N,:]=Dk.imag - elif opts["asymp"]==2: - A=np.zeros((2*N,n+1),dtype=np.float64) - A[0:N,0:n]=Dk.real - A[N:2*N,0:n]=Dk.imag - A[0:N,n]=weights - else: - A=np.zeros((2*N,n+2),dtype=np.float64) - A[0:N,0:n]=Dk.real - A[N:2*N,0:n]=Dk.imag - A[0:N,n]=weights - A[N:2*N,n+1]=np.imag(weights*s) - BB=np.zeros((2*N,Nc),dtype=np.float64) - BBc=np.zeros((N,Nc),dtype=np.complex128) - for m in range(Nc): - BBc[:,m]=weights*F[m,:] #complex values for BB - BB[0:N,:]=BBc.real - BB[N:2*N,:]=BBc.imag - Escale=np.zeros(A.shape[1],dtype=np.float64) - for m in range(A.shape[1]): - Escale[m]=np.linalg.norm(A[:,m]) - A[:,m]=A[:,m]/Escale[m] - # LS solution routine imported from scipy module: - # - check_finite option is disabled to improve performance. NaN should not appear into the arrays - # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") - # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: - x=lstsq(A,BB, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] - for m in range(Nc): - x[:,m]=x[:,m]/Escale - x=np.transpose(x) - C[:,0:n]=x[:,0:n] - if opts["asymp"]==2: - SERD=x[:,n] - elif opts["asymp"]==3: - SERD=x[:,n] - SERE=x[:,n+1] - else: #no common wighting used - C=np.zeros((Nc,n),dtype=np.complex128) - for k in range(Nc): - # The SER for the new fitting is calculated by using the calculated zeros as new poles - if opts["asymp"]==1: - A=np.zeros((2*N,n),dtype=np.float64) - A[0:N,:]=Dk.real - A[N:2*N,:]=Dk.imag - elif opts["asymp"]==2: - A=np.zeros((2*N,n+1),dtype=np.float64) - A[0:N,0:n]=Dk.real - A[N:2*N,0:n]=Dk.imag - A[0:N,n]=1 - else: #for asymp==3 - A=np.zeros((2*N,n+2),dtype=np.float64) - A[0:N,0:n]=Dk.real - A[N:2*N,0:n]=Dk.imag - A[0:N,n]=1 - A[N:2*N,n+1]=np.imag(s) - for m in range(A.shape[1]): - A[0:N,m]=weights[k,:]*A[0:N,m] - A[N:2*N,m]=weights[k,:]*A[N:2*N,m] - BB=np.zeros(2*N,dtype=np.float64) - BBc=np.zeros(N,dtype=np.complex128) #complex values for BB - BBc=weights[k,:]*F[k,:] - BB[0:N]=BBc.real - BB[N:2*N]=BBc.imag - Escale=np.zeros(A.shape[1],dtype=np.float64) - for m in range(A.shape[1]): - Escale[m]=np.linalg.norm(A[:,m]) - A[:,m]=A[:,m]/Escale[m] - # LS solution routine imported from scipy module: - # - check_finite option is disabled to improve performance. NaN should not appear into the arrays - # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") - # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: - x=lstsq(A,BB, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] - x/=Escale - C[k,:]=x[0:n] - if opts["asymp"]==2: - SERD[k]=x[n] - elif opts["asymp"]==3: - SERD[k]=x[n] - SERE[k]=x[n+1] - #...end of wighting options for residue computation - # Changing back to make C complex: - for m in range(n): - if cindex[m]==1: - for k in range(Nc): - r1=C[k,m] #real part of the complex number - r2=C[k,m+1] #imaginary part of the complex number - #bulding the conjugated complex pair: - C[k,m]=r1+1j*r2 - C[k,m+1]=r1-1j*r2 - # New fitting evaluation: - SERA=np.diag(LAMBD) - SERC=C - for m in range(n): - Dk[:,m]=1/(s-SERA[m]) - for k in range(Nc): - fit[k,:]=Dk@SERC[k,:] - if opts["asymp"]==2: - fit[k,:]=fit[k,:]+SERD[k] - elif opts["asymp"]==3: - fit[k,:]=fit[k,:]+SERD[k]+s*SERE[k] - # Root mean squared error computation: - diff=fit-F #diferrences between samples and the fitted function - rmserr=np.sqrt(np.sum(np.sum(np.abs(diff**2))))/np.sqrt(Nc*N) - - # - Graphs generation for vector fitting results: - if opts["spy2"]: - print("\n...vectfit3::spy2_Enabled::Building and showing graphs for the results...") - vectfitPlot(F,fit,s,opts,titleLabel=graphsTitle) - print(" * rms error = "+str(rmserr)+" *") - #...end of residue identification process - - # - Building the state-space model - A=np.diag(SERA) - B=SERB - C=SERC - D=SERD - E=SERE - SER=buildSER(A,B,C,D,E,opts["cmplx_ss"],opts["symm_mat"], opts["RMO_data"]) - - # Vector fitting process finished. +# vectfit3.py module. + +""" +*** FastRelaxed Vector Fitting for Python v1.3.1*** + +vectfit3.py is the implementation of Fast Relaxed Vector Fitting algortihm on python. The original code was written +in Matlab eviroment. The pourpose of this algorithm is to compute a rational approximation from tabuled data in the +frequency domain for scalar or vectorized problems. The resulting model can be expressed in either state-space form +or pole-residue form. + + - Original Matlab code autor: Bjorn Gustavsen (08/2008) + - Transcripted and adapted by: Sebastian Loaiza (03/2024) + - Last revision by: Sebastian Loaiza (01/2025) + + * References: + + [1] B. Gustavsen and A. Semlyen, "Rational approximation of frequency + domain responses by Vector Fitting", IEEE Trans. Power Delivery, + vol. 14, no. 3, pp. 1052-1061, July 1999. + + [2] B. Gustavsen, "Improving the pole relocating properties of vector + fitting", IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, + July 2006. + + [3] D. Deschrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, + "Macromodeling of Multiport Systems Using a Fast Implementation of + the Vector Fitting Method", IEEE Microwave and Wireless Components + Letters, vol. 18, no. 6, pp. 383-385, June 2008. + + [4] B. Gustavsen, "User's Guide for vectfit3.m (Fast, Relaxed Vector + fitting)", SINTEF Energy Research, N-7465 Trondheim, Norway, 2008. Aviable + online: https://www.sintef.no/en/software/vector-fitting/downloads/#menu + accesed on: 2/2/2024 + + * Changes: + + - All options for vectfit3 configuration are defined as boolean variables, except asymp which has 3 posible states + - A new option, "lowert_mat" is added for vectfit3 configuration. This indicates when F(s) samples belong to a + lower triangular matrix function, that reduces the number of elements to fit for a symmetric matrix function. + - A new option, "RMO_data" is added for vecfit3 configuration. This shows that matrix function elements are saved in + Row Major Order into F(s). + - New options mentioned before and "cmplx_ss" flag are also included in SER. + - A new method to sort the poles computed during the identification process is implemented. + - tri2full() function is renamed to flat2full(). It is modified to consider asymmetric matrix problems as well + depending on the status of "lower_mat" and "RMO_data" flags. + - ss2pr() function is replaced by to buildRES(). The new function just compute residues matrixes becouse vectfit returns + the poles already. + - Relative deviations are now computed taking as reference the maximum magnitude value in the reference function +""" + +# Scientific computing modules: +import numpy as np +from scipy.linalg import qr, eigvals, lstsq + +### ----------------------------------------------------------- Data structures -------------------------------------------------------------- ### + +#opts{}: vectfit modifiers dictionary. +# Dictionary which contains the default settings fot vectfit. +# Any key can be modified to change som options included in vectfit3 +opts={ + "symm_mat" : False, # Indicates when F(s) samples belong to a lower triangular matrix (symmetric problems) + "RMO_data" : True, # Matrix elements are organized in RMO into F(s) (asymmetric problems) + "relax" : True, # Use vector fitting with relaxed non triviality + "stable" : True, # Enforce stable poles + "asymp" : 2, # Include only D in fitting (not E). See [4] + "skip_pole" : False, # Do NOT skip pole identification + "skip_res" : False, # Do NOT skip residues identification (C,D,E). See [4] + "cmplx_ss" : True, # Create complex state space model + "spy1" : False, # No plotting for first stage of vector fitting + "spy2" : True, # Create magnitude plot for fitting of f(s) + "logx" : True, # Use logarithmic axis for x + "logy" : True, # Use logarithmic axis for y + "errplot" : True, # Include deviation in magnitude plot + "phaseplot" : False, # Exclude plot of phase angle + "legend" : True # Do include legends in plots + } + +### ----------------------------------------------------------------- Functions --------------------------------------------------------------- ### + +# vectfit() subroutine. +def opts_errorCheck(opts): + """Fucntion to check any configuration error into opts dictionary. + *Returns True if an error is found otherwise false""" + if opts["asymp"]!=1 and opts["asymp"]!=2 and opts["asymp"]!=3: + print("vectfit3::ERROR::Ilegal value for [asymp] option. It must be 1, 2 or 0") + return True + opitems=list(opts.items()) + asymp=("asymp",opts["asymp"]) + opitems.remove(asymp) #asymp already checked + for option in opitems: + if not(isinstance(option[1],bool)): + print("vectfit3::ERROR::Ilegal value for ["+option[0]+"] option. It must be boolean: True or False") + return True + return False + +# vectfit() subroutine. +def dim_errorCheck(F,s,poles,weights): + """Function to check dimentions compatibility among vectfit's arguments + *Returns True if an error is found otherwise false""" + if len(s.shape)>1 or len(poles.shape)>1: + print("vectfit3::ERROR::Arguments s and poles must be one-dimentional arrays") + return True + if len(F.shape)>1: + # Vectorized problem: Nc>1 + if s.size!=F.shape[1]: + print("vectfit3::ERROR::The number of frequency samples in s and F does not coincide!") + return True + else: + # Scalar problem: Nc=1 + if s.size!=F.size: + print("vectfit3::ERROR::The number of frequency samples in s and F does not coincide!") + return True + if len(weights.shape)>1: + # Individual weighting configuration: weights [Nc x N] + if s.size!=weights.shape[1]: + print("vectfit3::ERROR::The number of frequency samples in s and elements in weights does not coincide!") + return True + if weights.shape[0]!=F.shape[0]: + print("vectfit3::ERROR::The number of elements in F does not coincide to their weiths for individual weighting") + return True + else: + # Common wighting configuration: weights [1 x N] + if s.size!=weights.size: + print("vectfit3::ERROR::The number of frequency samples in s and elements in weights does not coincide!") + return True + return False + +# vectfit() subroutine. +def identifyPoles(LAMBD): + """Function to classify poles storaged into the LAMBD diagonal matrix. + Argument. + - LAMBD: Diagonal matrix containing the poles of the aproximated model + *Returns cindex array which marks the poles with the following flags: + - 0 for real poles + - 1 and 2 for complex conjugated pairs + """ + n=LAMBD.shape[0] + cindex=np.zeros(n, dtype=np.uint16) + for m in range(n): + if np.imag(LAMBD[m,m])!=0: + if m==0: + cindex[m]=1 + else: + if cindex[m-1]==0 or cindex[m-1]==2: + cindex[m]=1 + cindex[m+1]=2 + else: + cindex[m]=2 + return cindex + +# vectfit() subroutine. +def sortPoles(poles): + """Function to sort the poles obtained in the poles identification process. + the poles array is sorted by magnitud in asending order, real poles go first and + for each pair of complex conjugated poles, the one with positive imaginary is placed first + *Returns a complex array with the required poles arrangement""" + poltype=np.abs(poles.imag)<1e-10 # Real poles are marked as True, complex as false + # *!{it is necesary to use a tolerance instead of np.isreal() due to the numeric error in eigenvalues computation} + # Real poles extraction + realpoles=poltype*poles.real + realpoles=np.take_along_axis(realpoles, np.nonzero(realpoles)[0], axis=None) + # Complex poles extraction + complexpoles=np.logical_not(poltype)*poles + complexpoles=np.take_along_axis(complexpoles, np.nonzero(complexpoles)[0], axis=None) + # Sorting real and complex poles separately: In the following procedure the function sorted() with the list of tuples (abs,pol) + #orders by considering first abs, if reapeted magnitudes are found complex poles are ordered considering their imaginary parts. + realpoles=-1*np.sort(np.abs(realpoles)) + complexpoles=np.array([p for _,p in sorted(zip(np.abs(complexpoles),complexpoles))]) + # Organization of the complex conjugated pairs + cpolesorder=np.array([], dtype=bool) + #desired order [True(+),False(-),...] + for _ in range(int(complexpoles.size/2)): + cpolesorder=np.append(cpolesorder,np.array([True,False])) + polswap=np.logical_xor(complexpoles.imag>0,cpolesorder) #marks the poles that must be swaped as True + complexpoles=complexpoles-2j*polswap*complexpoles.imag #change of sign for the imaginary parts of the marked poles + # Organized poles + return np.append(realpoles,complexpoles) + +# vectfit() subroutine. +def vectfitPlot(F,fit,s,opts, initialState=False, titleLabel="Vector Fitting Resutls"): + """Function to plot vector fitting results. + The number of graphs that are displayed varies in function of opts configuration + + Arguments. + + - F: F(s) frequency samples of the original function + - fit: fit(s) fited function that aproximates F(s) + - s: Complex frequency points of evaluation for F and fit + - opts: Dictionary with the modifiers to change the default configuration of Vector Fitting + + Results. + + - Displays the magnitude plot of F and fit samples with or without error + - May display the phase angle plot of F and fit samples if enabled + """ + # Importing plots and graphs module: + import matplotlib as mpl + import matplotlib.pyplot as plt + #matplotlib configuration: + plt.rcParams["font.family"]="serif" # font type + plt.rcParams["mathtext.fontset"]="dejavuserif" # font type in math expressions + mpl.rcParams["font.size"]=14 # font size in points + mpl.rcParams["figure.dpi"]=100 # canvas figure resolution + mpl.rcParams["savefig.dpi"]=300 # saved figure resolution + + freq=np.real(s/(2*np.pi*1j)) + # LogLog plots: Graphs with logarithmic x and y axis + if opts["errplot"]: + fig1,ax1=plt.subplots(2,1) + l1=ax1[0].plot(freq,np.abs(F.T),color='c',linewidth=1.2) + l2=ax1[0].plot(freq,np.abs(fit.T),color='k',linewidth=1.3,linestyle="dashed") + ax1[0].set(xlabel="Frequency (Hz)", ylabel="Magnitude",title=titleLabel) + if opts["legend"]: + l2[0].set(label="Fitted function") + l1[0].set(label="F(s) samples") + ax1[0].legend() + ax1[0].grid(True) + #logarithmic error computation + logError=np.zeros(F.shape,dtype=np.float64) + maxError=-1e10 + for i in range(F.shape[0]): + logError[i]=np.log10(np.abs(F[i]-fit[i])/np.max(np.abs(F))) + error=logError[i].max() + if error>maxError: maxError=error + maxLabel=ax1[1].plot(freq,logError.T,color='r',linewidth=1.2) + maxError=(10**maxError)*100 + maxLabel[0].set(label="Max fitting error = "+str(maxError)+"%") + print(" * max fitting error = "+str(maxError)+"% *") + ax1[1].set(xlabel="Frequency (Hz)", ylabel=r"$\log_{10}$(relative error)") + ax1[1].legend() + ax1[1].grid(True) + else: + if initialState: + flabel="Sigma function" + tlabel="Vector Fitting initial state" + else: + flabel="Fitted function" + tlabel=titleLabel + fig1,ax1=plt.subplots() + l1=ax1.plot(freq,np.abs(F.T),color='c',linewidth=1.2,label="F(s) samples") + l2=ax1.plot(freq,np.abs(fit.T),color='k',linewidth=1.3,linestyle="dashed") + ax1.set(xlabel="Frequency (Hz)", ylabel="Magnitude",title=tlabel) + if opts["legend"]: + l2[0].set(label=flabel) + l1[0].set(label="F(s) samples") + ax1.legend() + ax1.grid(True) + if opts["phaseplot"]: + #fisrt function angles are computed in degrees, and then are unwrapped + F_angle=np.unwrap(np.angle(F,deg=True),period=360) + fit_angle=np.unwrap(np.angle(fit,deg=True),period=360) + fig2,ax2=plt.subplots() + l3=ax2.plot(freq,F_angle.T,color='c',linewidth=1.2) + l4=ax2.plot(freq,fit_angle.T,color='k',linewidth=1.3,linestyle="dashed") + ax2.set(xlabel="Frequency (Hz)", ylabel="Phase angle (deg)",title=titleLabel) + if opts["legend"]: + l3[0].set(label="F(s) samples") + l4[0].set(label="Fitted function") + ax2.legend() + ax2.grid(True) + if opts["logx"] and opts["logy"]: + #full logarithmic graphs. Logarithmic x and y axis + if opts["errplot"]: + # Magnitude plot: + ax1[0].set_xscale("log") + ax1[0].set_yscale("log") + # Error plot + ax1[1].set_xscale("log") + else: + # Magnitude plot: + ax1.set_xscale("log") + ax1.set_yscale("log") + if opts["phaseplot"]: + # Phase plot: + ax2.set_xscale("log") + elif opts["logx"]: + #semilogarithmic graphs. Logarithmic x and linear y axis + if opts["errplot"]: + ax1[0].set_xscale("log") + ax1[1].set_xscale("log") + else: + ax1.set_xscale("log") + if opts["phaseplot"]: + ax2.set_xscale("log") + elif opts["logy"]: + #semilogarithmic graphs. Linear x and logarithmic y axis + if opts["errplot"]: + ax1[0].set_yscale("log") + else: + ax1.set_yscale("log") + #else default linear axis configuration of plot() is used + plt.show() + +# vectfit3() subroutine. +def buildSER(Ac,Bc,Cc,Dr,Er,complex_format,symmetric_data,RMO_matrixData): + """Function to build the state-space model of the fitted function such as: + F(s) = C * (sI-A)^-1 * B + D + sE + + Arguments. c subindex indicates complex system + + - Ac: Diagonal matrix containing the poles of F(s). Shape [n x n] for n the number fo poles + - Bc: Input matrix for complex form. Must be a vector of ones. Shape [n x 1] + - Cc: Residues matrix. Complex and shaped [Nc x n] with Nc as the number of elements in F(s) + - D: Constant terms matrix. Real matrix of shape [Nc x 1] + - E: Proportional terms matrix. Real matrix of shape [Nc x 1] + - complex_format: Boolean option from opts{} which indicates if a complex system is needed + - symmetric_data: Boolean option from opts{} which indicates if data come from a symmetric matrix problem + - RMO_matrixData: Boolean option from opts{} which indicates if matrix elements are ordered in RMO + + Results. + + - SER: Dictionary that storages A,B,C,D,E system matrixes adapted as indicated by cmplx_ss and symm_mat + """ + SER=dict(A=Ac,B=Bc,C=Cc,D=Dr,E=Er, cmplx_ss=True, symm_mat=symmetric_data, RMO_data=RMO_matrixData) #complex state-space system + if not(complex_format): + # Real state-space system is required so the matrixes are modified + Ar=np.real(Ac) #importing real poles to Ar + Br=Bc #real poles remains realated with ones in B + Cr=np.real(Cc) #importing real values to Cr + cindex=identifyPoles(Ac) #poles identification + # Reorganization of A as a real and block diagonal matrix + k=0 + for m in range(Ac.shape[0]): + if cindex[m]==1: + #complex pole to modify: + cpole=Ac[k,k] + re_cpole=np.real(cpole) #real part + im_cpole=np.imag(cpole) #imaginary part + # Real system adaptation + Ar[k:k+2,k:k+2]=np.array([[re_cpole,im_cpole],[-im_cpole,re_cpole]]) #complex pair block in Ar + # Input matrix modification to consider the complex pair block in Ar + Br[k,0]=2 + Br[k+1,0]=0 + # Real and imaginary part separation for data in output matrix + Cr[:,k]=np.real(Cc[:,k]) + Cr[:,k+1]=np.imag(Cc[:,k]) + k+=1 + # Updating SER with new real matrixes: + SER["A"]=Ar + SER["B"]=Bc + SER["C"]=Cr + SER["cmplx_ss"]=False + return SER + +# build_RES() subroutine. +def flat2full(SER): + """Function to transform data arrays in SER from its default representation (flattened and element-wise) to a full matrix representation. + This function works with symmetric or asymmetric matrix functions. If "lower_mat" flag is true, this function considers that the matrix + problem need to be decompressed from lower triangular representation. + + *vectfit() function works with flattened element-wise data, therefore if data comes from a matrix problem, this function returns + a new SER with modified shapes: + - A shape [n x n] => [Ny*n x Ny*n] for Ny as the original dimentions of the fitted matrix and n as the order of aproximation + - B shape [n x 1] => [Ny*n x Ny] + - C shape [Nc x n] => [Ny x Ny*n] for Nc as the number fitted elements into the matrix (organized element-wise) + - D shape [Nc x 1] => [Ny x Ny] + - E shape [Nc x 1] => [Ny x Ny] + + Important!: lower trinagular compression of symmetric matrix data need to be applied prior vector fitting application + """ + A=SER["A"] + B=SER["B"] + C=SER["C"] + D=SER["D"] + E=SER["E"] + # Unzip process parameters: + n=B.shape[0] # Order of approximation + Nc=C.shape[0] # Number of different elements in the flattened problem + if SER["symm_mat"]: + # Case for a symmetric problem, data must be decompressed and organized in symmetric format + zum=0 # Sum counter + Ny=0 # Shape of the full unzipped matrix function + while zum1: + Nc=F.shape[0] # Number of elements to fit + else: + Nc=1 + # Reshaping arrays to ensure a good vectorized computation + F=np.reshape(F,(1,N)) + + # Problem arrays declaration + LAMBD=np.diag(poles) # Diagonal matriz with searching poles + B=np.ones((n,1), np.float64) # Column vector of ones + SERA=poles # A Matrix in the space state model + SERB=np.ones((n,1), np.float64) # B Matrix in the space state model + SERC=np.zeros((Nc,n),dtype=np.complex128) # C Matrix in the space state model + SERD=np.zeros(Nc,dtype=np.float64) # D Matrix in the space state model + SERE=np.zeros(Nc,dtype=np.float64) # E Matrix in the space state model + fit=np.zeros((Nc,N),dtype=np.complex128) # Array to store fitted values + rmserr=-1 # Root mean squared error + # Weighting type identification + if len(weights.shape)==1: + commonWeighting=True + # Reshaping arrays to ensure a good vectorized computation + #weights=np.reshape(weights,(1,N)) + else: + commonWeighting=False + # Space state selected structure + if opts["asymp"]==1: + offs=0 # for [D=0; E=0] + elif opts["asymp"]==2: + offs=1 # [D!=0; E=0] + else: + offs=2 # [D!=0; E!=0] + + # *-- POLES IDENTIFICATION PROCESS + + if not(opts["skip_pole"]): + Escale=np.zeros(Nc+1) + # Initial complex poles identification: cindex marks 0 for reals, 1 and 2 for complex conjugated pairs + cindex=identifyPoles(LAMBD) + # Building System Matrix + Dk=np.zeros((N,n),dtype=np.complex128) + for m in range(n): + if cindex[m]==0: + # real pole defined + Dk[:,m]=1/(s-LAMBD[m,m]) + elif cindex[m]==1: + #complex pole first part defined + Dk[:,m]=1/(s-LAMBD[m,m])+1/(s-np.conj(LAMBD[m,m])) + Dk[:,m+1]=1j/(s-LAMBD[m,m])-1j/(s-np.conj(LAMBD[m,m])) + # Depending on the D and E option selected + if offs==0 or offs==1: + # for E=0 + Dk=np.hstack((Dk,np.ones((N,1)))) #note that Dk.shape changed to (N,n+1) + else: + # for E!=0 + Dk=np.hstack((Dk,np.ones((N,1)))) + Dk=np.hstack((Dk,np.reshape(s,(N,1)))) #note that Dk.shape changed to (N,n+2) + # Scaling for last row of LS-Problem + scale=0 + for m in range(Nc): + if commonWeighting: + scale+=np.linalg.norm(weights*F[m,:])**2 + else: + scale+=np.linalg.norm(weights[m,:]*F[m,:])**2 + scale=np.sqrt(scale)/N + # Applying relaxed version of the algorithm + if opts["relax"]: + AA=np.zeros((Nc*(n+1),n+1),dtype=np.float64) + bb=np.zeros(Nc*(n+1),dtype=np.float64) + Escale=np.zeros(n+1,dtype=np.float64) + offset=n+offs + for k in range(Nc): + Ac=np.zeros((N,offset+n+1),dtype=np.complex128) + if commonWeighting: + weig=weights + else: + weig=weights[k,:] + for m in range(offset): #left block + Ac[:,m]=weig*Dk[:,m] + for m in range(n+1): #right block + Ac[:,offset+m]=-weig*Dk[:,m]*F[k,:] + # Partitioned problem in real and imaginary part, a real array is obtained: + A=np.vstack((Ac.real,Ac.imag)) + # Integral criterion for sigma + if k==Nc-1: + A=np.vstack((A,np.zeros((1,A.shape[1])))) # adding extra row + for m in range(n+1): + A[2*N,offset+m]=np.real(scale*np.sum(Dk[:,m])) + # Obtaining QR transformation of A + (Q,R)=qr(A,mode="economic") #routine imported from scipy module + R22=R[offset:offset+n+1,offset:offset+n+1] + AA[k*(n+1):(k+1)*(n+1),:]=R22 + if k==Nc-1: + bb[k*(n+1):(k+1)*(n+1)]=Q[-1,offset:]*N*scale + for m in range(AA.shape[1]): + Escale[m]=1/np.linalg.norm(AA[:,m]) + AA[:,m]=Escale[m]*AA[:,m] + # LS solution routine imported from scipy module: + # - check_finite option is disabled to improve performance. NaN should not appear into the arrays + # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") + # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: + x=lstsq(AA,bb, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] + x=x*Escale + # ...end of opts["relax"]=True segment + # Case for non relaxion version of the algorithm. + # Also may be needed when D of sigma results extremely small and large. I needs to be solved again. + if not(opts["relax"]) or np.abs(x[-1])TOLhigh: + AA=np.zeros((Nc*n,n),dtype=np.float64) + bb=np.zeros(Nc*n,dtype=np.float64) + if opts["relax"]: + Dnew=1 + else: + if x[-1]==0: + Dnew=1 + elif np.abs(x[-1])TOLhigh: + Dnew=np.sign(x[-1])*TOLhigh + offset=n+offs + for k in range(Nc): + Ac=np.zeros((N,offset+n),dtype=np.complex128) + Escale=np.zeros(n,dtype=np.float64) + if commonWeighting: + weig=weights + else: + weig=weights[k,:] + for m in range(offset): #left block + Ac[:,m]=weig*Dk[:,m] + for m in range(n): #right block + Ac[:,offset+m]=-weig*Dk[:,m]*F[k,:] + bc=Dnew*weig*F[k,:] + # Partitioned problem in real and imaginary part, real arrays are obtained: + A=np.vstack((Ac.real,Ac.imag)) + b=np.append(bc.real,bc.imag) + # Obtaining QR transformation of A + (Q,R)=qr(A,mode="economic") + R22=R[offset:offset+n,offset:offset+n] + AA[k*n:(k+1)*n,:]=R22 + # The following arrays must be reshaped in order to perform the matrix product + bb[k*n:(k+1)*n]=np.ravel(np.transpose(Q[:,offset:offset+n])@np.reshape(b,(b.size,1))) + for m in range(AA.shape[1]): + Escale[m]=1/np.linalg.norm(AA[:,m]) + AA[:,m]=Escale[m]*AA[:,m] + # LS solution routine imported from scipy module: + # - check_finite option is disabled to improve performance. NaN should not appear into the arrays + # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") + # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: + x=lstsq(AA,bb, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] + x=x*Escale + x=np.append(x,Dnew) + # ...end of opts["relax"]=False or out of tolerance segment + # Changing back to make C complex: + C=np.zeros(x.size-1,dtype=np.complex128) + C[0:C.size]=x[0:-1] + D=x[-1] + for m in range(n): + if cindex[m]==1: + r1=C[m] #real part of the complex number + r2=C[m+1] #imaginary part of the complex number + #building the conjugated complex pair + C[m]=r1+1j*r2 + C[m+1]=r1-1j*r2 + # Graphs of initial stage of vector fitting process + if opts["spy1"]: + print("\n...vectfit3::spy1_Enabled::Building and showing graph for initial fitting state...") + # First fitting state evaluation: + # As mentioned in [1] pole identification begins with the aproximation of sigma(s). sigma(s) is an unknown function whose + #approximation has the same poles of F(s). Furtheremore it is formulated that (sigma*f)_fit(s) = sigma_fit*f(s), whence can be + #demostrated that zeros of sigma are a better set of poles to fit f(s), therefore sigma(s) is called the initial fitting state. + Dk=np.zeros((N,n),dtype=np.complex128) + for m in range(n): + Dk[:,m]=1/(s-LAMBD[m,m]) + sigma=D+Dk@C + #setting temporal options to plot initial vector fitting state + opts_temp=opts + opts_temp["errplot"]=False + opts_temp["phaseplot"]=False + vectfitPlot(F,sigma,s,opts_temp,initialState=True) + # Calculating the zeros for sigma + m=0 #auxiliar counter + for k in range(n): + if mnp.abs(np.real(LAMBD[m,m])): + # Complex poles clasification: diagonal blocks of the form: + # [ real, -imag ] + # [ imag, real ] + LAMBD[m+1,m]=-np.imag(LAMBD[m,m]) + LAMBD[m,m+1]=np.imag(LAMBD[m,m]) + LAMBD[m,m]=np.real(LAMBD[m,m]) + LAMBD[m+1,m+1]=LAMBD[m,m] + # B vector modification for complex poles + B[m,0]=2 + B[m+1,0]=0 + ccval=C[m] + # Complex values clasification: + C[m]=np.real(ccval) + C[m+1]=np.imag(ccval) + m+=1 + m+=1 + #to perform the vectorized B*C and obtain a matrix C need to be reshaped + C=np.reshape(C,(1,C.size)) + #also just the real parts of LAMBD and C are taken in order to obtain a real[float64] matrix for ZER + ZER=LAMBD.real-B@C.real/D + # Computation of ZER eigenvalues + poles=eigvals(ZER) #routine imported from scipy module + # Unstabla values identification + unstable=poles.real>0 #generates a logical array + if opts["stable"]: + if np.any(unstable): + #the product of roetter and unstable extracts the unstable poles + extracted=poles*unstable + poles=poles-2*extracted.real + poles=sortPoles(poles) + SERA=poles + #...end of poles identification process + + # --* RESIDUES IDENTIFICATION PROCESS + + if not(opts["skip_res"]): + # Now SER for f is calculated by using modified zeros of sigma as new poles: + LAMBD=np.diag(poles) + # Initial complex poles identification: cindex marks 0 for reals, 1 and 2 for complex conjugated pairs + cindex=identifyPoles(LAMBD) + # Building System Matrix + Dk=np.zeros((N,n),dtype=np.complex128) + for m in range(n): + if cindex[m]==0: + # real pole defined + Dk[:,m]=1/(s-LAMBD[m,m]) + elif cindex[m]==1: + #complex pole first part defined + Dk[:,m]=1/(s-LAMBD[m,m])+1/(s-np.conj(LAMBD[m,m])) + Dk[:,m+1]=1j/(s-LAMBD[m,m])-1j/(s-np.conj(LAMBD[m,m])) + if commonWeighting: #case for common wighting + C=np.zeros((Nc,n),dtype=np.complex128) + for m in range(n): #same weight for all frequency samples + Dk[:,m]=weights*Dk[:,m] + # The SER for the new fitting is calculated by using the calculated zeros as new poles + if opts["asymp"]==1: + A=np.zeros((2*N,n),dtype=np.float64) + A[0:N,:]=Dk.real + A[N:2*N,:]=Dk.imag + elif opts["asymp"]==2: + A=np.zeros((2*N,n+1),dtype=np.float64) + A[0:N,0:n]=Dk.real + A[N:2*N,0:n]=Dk.imag + A[0:N,n]=weights + else: + A=np.zeros((2*N,n+2),dtype=np.float64) + A[0:N,0:n]=Dk.real + A[N:2*N,0:n]=Dk.imag + A[0:N,n]=weights + A[N:2*N,n+1]=np.imag(weights*s) + BB=np.zeros((2*N,Nc),dtype=np.float64) + BBc=np.zeros((N,Nc),dtype=np.complex128) + for m in range(Nc): + BBc[:,m]=weights*F[m,:] #complex values for BB + BB[0:N,:]=BBc.real + BB[N:2*N,:]=BBc.imag + Escale=np.zeros(A.shape[1],dtype=np.float64) + for m in range(A.shape[1]): + Escale[m]=np.linalg.norm(A[:,m]) + A[:,m]=A[:,m]/Escale[m] + # LS solution routine imported from scipy module: + # - check_finite option is disabled to improve performance. NaN should not appear into the arrays + # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") + # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: + x=lstsq(A,BB, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] + for m in range(Nc): + x[:,m]=x[:,m]/Escale + x=np.transpose(x) + C[:,0:n]=x[:,0:n] + if opts["asymp"]==2: + SERD=x[:,n] + elif opts["asymp"]==3: + SERD=x[:,n] + SERE=x[:,n+1] + else: #no common wighting used + C=np.zeros((Nc,n),dtype=np.complex128) + for k in range(Nc): + # The SER for the new fitting is calculated by using the calculated zeros as new poles + if opts["asymp"]==1: + A=np.zeros((2*N,n),dtype=np.float64) + A[0:N,:]=Dk.real + A[N:2*N,:]=Dk.imag + elif opts["asymp"]==2: + A=np.zeros((2*N,n+1),dtype=np.float64) + A[0:N,0:n]=Dk.real + A[N:2*N,0:n]=Dk.imag + A[0:N,n]=1 + else: #for asymp==3 + A=np.zeros((2*N,n+2),dtype=np.float64) + A[0:N,0:n]=Dk.real + A[N:2*N,0:n]=Dk.imag + A[0:N,n]=1 + A[N:2*N,n+1]=np.imag(s) + for m in range(A.shape[1]): + A[0:N,m]=weights[k,:]*A[0:N,m] + A[N:2*N,m]=weights[k,:]*A[N:2*N,m] + BB=np.zeros(2*N,dtype=np.float64) + BBc=np.zeros(N,dtype=np.complex128) #complex values for BB + BBc=weights[k,:]*F[k,:] + BB[0:N]=BBc.real + BB[N:2*N]=BBc.imag + Escale=np.zeros(A.shape[1],dtype=np.float64) + for m in range(A.shape[1]): + Escale[m]=np.linalg.norm(A[:,m]) + A[:,m]=A[:,m]/Escale[m] + # LS solution routine imported from scipy module: + # - check_finite option is disabled to improve performance. NaN should not appear into the arrays + # - gelsy lapack driver is chosen because is slightly faster than default ("gelsd") + # The routine returns a tuple (solution,residues,rank,svalues), however just the solution is taken: + x=lstsq(A,BB, check_finite=False, lapack_driver="gelsy")[0] # solution <- result[0] + x/=Escale + C[k,:]=x[0:n] + if opts["asymp"]==2: + SERD[k]=x[n] + elif opts["asymp"]==3: + SERD[k]=x[n] + SERE[k]=x[n+1] + #...end of wighting options for residue computation + # Changing back to make C complex: + for m in range(n): + if cindex[m]==1: + for k in range(Nc): + r1=C[k,m] #real part of the complex number + r2=C[k,m+1] #imaginary part of the complex number + #bulding the conjugated complex pair: + C[k,m]=r1+1j*r2 + C[k,m+1]=r1-1j*r2 + # New fitting evaluation: + SERA=np.diag(LAMBD) + SERC=C + for m in range(n): + Dk[:,m]=1/(s-SERA[m]) + for k in range(Nc): + fit[k,:]=Dk@SERC[k,:] + if opts["asymp"]==2: + fit[k,:]=fit[k,:]+SERD[k] + elif opts["asymp"]==3: + fit[k,:]=fit[k,:]+SERD[k]+s*SERE[k] + # Root mean squared error computation: + diff=fit-F #diferrences between samples and the fitted function + rmserr=np.sqrt(np.sum(np.sum(np.abs(diff**2))))/np.sqrt(Nc*N) + + # - Graphs generation for vector fitting results: + if opts["spy2"]: + print("\n...vectfit3::spy2_Enabled::Building and showing graphs for the results...") + vectfitPlot(F,fit,s,opts,titleLabel=graphsTitle) + print(" * rms error = "+str(rmserr)+" *") + #...end of residue identification process + + # - Building the state-space model + A=np.diag(SERA) + B=SERB + C=SERC + D=SERD + E=SERE + SER=buildSER(A,B,C,D,E,opts["cmplx_ss"],opts["symm_mat"], opts["RMO_data"]) + + # Vector fitting process finished. return (SER,poles,rmserr,fit) \ No newline at end of file diff --git a/test/conftest.py b/test/conftest.py new file mode 100644 index 0000000..9a6bf8e --- /dev/null +++ b/test/conftest.py @@ -0,0 +1,71 @@ +import sys +import pytest +import numpy as np +import pandas as pd +from pathlib import Path + + +# Go up one level to the root, then dig into the 'src' folder +root_dir = Path(__file__).parent.parent +src_dir = root_dir / "src" + +# Tell Python to look inside the 'src' folder for your library +sys.path.insert(0, str(src_dir)) + +@pytest.fixture +def default_opts(): + """ + gets the default options for vectfit. + """ + # Adjust this import based on where your vectfit3.py actually lives + # If it's in the same root directory, this will work. + from vectfit3 import opts + return opts.copy() + +@pytest.fixture +def generate_synthetic_fs(): + """ + Factory fixture: Generates an F(s) frequency response. + Supports Scalar (1D) and Vector (2D) responses. + """ + def _generate(s, expected_poles, expected_residues, D=None, E=None): + # Determine if we are doing scalar or vector fitting + # expected_residues shape: (Nc, n_poles) or (n_poles,) + if expected_residues.ndim == 1: + F = np.zeros_like(s, dtype=np.complex128) + for p, r in zip(expected_poles, expected_residues): + F += r / (s - p) + if D is not None: F += D + if E is not None: F += s * E + else: + # Vector case: Nc x N + Nc = expected_residues.shape[0] + N = len(s) + F = np.zeros((Nc, N), dtype=np.complex128) + for i in range(Nc): + for p, r in zip(expected_poles, expected_residues[i]): + F[i, :] += r / (s - p) + if D is not None: F[i, :] += D[i] + if E is not None: F[i, :] += s * E[i] + return F + return _generate + + + +@pytest.fixture +def load_vectfit_csv(): + """ + Clean CSV loader for test datasets. Expects files to be in a 'data' subfolder next to this conftest.py. + """ + data_path = Path(__file__).parent / "data" + + def _loader(filename): + file_path = data_path / filename + if not file_path.exists(): + pytest.fail(f"Dataset {filename} not found in {data_path}") + + # We use pandas to read, then convert to numpy for speed + df = pd.read_csv(file_path) + return df.to_numpy() + + return _loader \ No newline at end of file diff --git a/MODEH_DATA.csv b/test/data/MODEH_DATA.csv similarity index 100% rename from MODEH_DATA.csv rename to test/data/MODEH_DATA.csv diff --git a/SYSADMITANCE_DATA.csv b/test/data/SYSADMITANCE_DATA.csv similarity index 92% rename from SYSADMITANCE_DATA.csv rename to test/data/SYSADMITANCE_DATA.csv index 712cf9e..1d604c4 100644 --- a/SYSADMITANCE_DATA.csv +++ b/test/data/SYSADMITANCE_DATA.csv @@ -1,21902 +1,21902 @@ -6 -300 -62.83185307 -0.343794552 --0.076033989 --0.035853678 --0.035448041 --0.034220471 --0.03099212 --0.34378905 -0.076052698 -0.035853581 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+import pandas as pd +from vectfit3 import vectfit, flat2full, buildRES, sortPoles + +#Original test files: i wanted to benchmark speed + + +# ============================================================================== +# TEST 1: SCALAR ARTIFICIAL (Synthetic Ground Truth) +# ============================================================================== +def test_benchmark_scalar_artificial(benchmark, default_opts): + """Benchmark for Test 1: Scalar artificial frequency domain function.""" + N = 101 + s = 2j * np.pi * np.logspace(0, 4, N, dtype=np.complex128) + f = np.zeros(N, dtype=np.complex128) + for n, sn in enumerate(s): + f[n] = 2/(sn+5) + (30+40j)/(sn-(-100+500j)) + (30-40j)/(sn-(-100-500j)) + 0.5 + + n_order = 3 + poles = -2 * np.pi * np.logspace(0, 4, n_order, dtype=np.complex128) + opts = default_opts.copy() + opts.update({"asymp": 3, "spy2": False}) + + def run(): + return vectfit(f, s, poles, np.ones(N), opts) + + ser, final_poles, rmserr, fit = benchmark(run) + benchmark.extra_info['Final_RMSE'] = f"{rmserr:.2e}" + assert rmserr < 1e-4 + print(f"\n[METRIC] {benchmark.name} -> Final RMSE: {rmserr:.6e}") + +# ============================================================================== +# TEST 2: 2D 18TH ORDER (Iterative Loop) +# ============================================================================== +def test_benchmark_2D_18th_order(benchmark, default_opts): + """Benchmark for Test 2: 18th order frequency response (2 channels).""" + N = 100 + w = 2 * np.pi * np.linspace(1, 1e5, N) + s = 1j * w + + p_raw = np.array([-4500, -41000, -100+5e3j, -100-5e3j, -120+15e3j, -120-15e3j, + -3e3+35e3j, -3e3-35e3j, -200+45e3j, -200-45e3j, -1500+45e3j, + -1500-45e3j, -5e2+70e3j, -5e2-70e3j, -1e3+73e3j, -1e3-73e3j, + -2e3+90e3j, -2e3-90e3j], dtype=np.complex128) + p = 2 * np.pi * p_raw + r_raw = np.array([-3000, -83000, -5+7e3j, -5-7e3j, -20+18e3j, -20-18e3j, + 6e3+45e3j, 6e3-45e3j, 40+60e3j, 40-60e3j, 90+10e3j, + 90-10e3j, 5e4+80e3j, 5e4-80e3j, 1e3+45e3j, 1e3-45e3j, + -5e3+92e3j, -5e3-92e3j], dtype=np.complex128) + r = 2 * np.pi * r_raw + + F = np.zeros((2, N), dtype=np.complex128) + for idx, sn in enumerate(s): + F[0, idx] = np.sum(r[:10] / (sn - p[:10])) + sn*2e-5 + 0.6 + F[1, idx] = np.sum(r[8:] / (sn - p[8:])) + sn*6e-5 + + n_order = 18 + bet = np.linspace(w[0], w[-1], 9) + initial_poles = np.zeros(n_order, dtype=np.complex128) + for k in range(9): + initial_poles[2*k] = -bet[k]*1e-2 - 1j*bet[k] + initial_poles[2*k+1] = -bet[k]*1e-2 + 1j*bet[k] + + opts = default_opts.copy() + opts.update({"asymp": 3, "cmplx_ss": False, "spy2": False}) + + def run_iterative(): + curr_p = initial_poles.copy() + for itr in range(3): + res = vectfit(F, s, curr_p, np.ones(N), opts) + curr_p = res[1] + return res + + ser, final_poles, rmserr, fit = benchmark(run_iterative) + benchmark.extra_info['Final_RMSE'] = f"{rmserr:.2e}" + assert rmserr < 1e-2 + print(f"\n[METRIC] {benchmark.name} -> Final RMSE: {rmserr:.6e}") + +# ============================================================================== +# TEST 3: TRANSFORMER (Measured Data) +# ============================================================================== +def test_benchmark_transformer_measured(benchmark, default_opts, load_vectfit_csv): + """Benchmark for Test 3: Scalar measured transformer response.""" + Mdata = load_vectfit_csv("TRANSF_DATA.csv") + f = Mdata[:160, 0] * np.exp(1j * Mdata[:160, 1] * np.pi / 180) + w = 2 * np.pi * np.linspace(0, 10e6, 401)[1:161] + s = 1j * w + + n_order = 30 + bet = np.linspace(w[0], w[-1], 15) + poles = np.zeros(n_order, dtype=np.complex128) + for k in range(15): + poles[2*k] = -bet[k]*1e-2 - 1j*bet[k] + poles[2*k+1] = -bet[k]*1e-2 + 1j*bet[k] + + opts = default_opts.copy() + opts.update({"asymp": 3, "spy2": False}) + + def run_transformer(): + curr_p = poles.copy() + # Using inverse weighting as in your original script + weights = 1/np.abs(f) + for _ in range(5): + res = vectfit(f, s, curr_p, weights, opts) + curr_p = res[1] + return res + + ser, final_poles, rmserr, fit = benchmark(run_transformer) + benchmark.extra_info['Final_RMSE'] = f"{rmserr:.2e}" + assert rmserr < 0.1 + print(f"\n[METRIC] {benchmark.name} -> Final RMSE: {rmserr:.6e}") + +# ============================================================================== +# TEST 4: ADMITTANCE MATRIX 6x6 (Symmetric) +# ============================================================================== +def test_benchmark_admittance_matrix(benchmark, default_opts, load_vectfit_csv): + """Benchmark for Test 4: 6x6 Symmetric Admittance Matrix.""" + Mdata = np.ravel(load_vectfit_csv("SYSADMITANCE_DATA.csv")) + N = int(Mdata[0]) + F = np.zeros((21, N), dtype=np.complex128) + s = np.zeros(N, dtype=np.complex128) + + k = 0 + for i in range(1, Mdata.size, 73): + s[k] = 1j * Mdata[i] + block = Mdata[i+1 : i+73] + y_mat = block[0::2] + 1j*block[1::2] + y_mat = y_mat.reshape((6, 6)) + # Extract lower triangular (21 elements) + idx_f = 0 + for r in range(6): + for c in range(r, 6): + F[idx_f, k] = y_mat[r, c] + idx_f += 1 + k += 1 + + n_order = 50 + w = s.imag + bet = np.linspace(w[0], w[-1], 25) + poles = np.zeros(n_order, dtype=np.complex128) + for k in range(25): + poles[2*k] = -bet[k]/100 - 1j*bet[k] + poles[2*k+1] = -bet[k]/100 + 1j*bet[k] + + opts = default_opts.copy() + opts.update({"asymp": 3, "symm_mat": True, "spy2": False}) + + def run_admittance(): + curr_p = poles.copy() + weights = 1/np.sqrt(np.abs(F)) + for _ in range(3): + res = vectfit(F, s, curr_p, weights, opts) + curr_p = res[1] + return res + + ser, final_poles, rmserr, fit = benchmark(run_admittance) + benchmark.extra_info['Final_RMSE'] = f"{rmserr:.2e}" + + # Reconstruction Precision Check + ser_full = flat2full(ser) + Res = buildRES(ser_full["C"], ser_full["B"]) + f_rebuilt = np.zeros(N, dtype=np.complex128) + for m in range(n_order): + f_rebuilt += Res[0, 0, m] / (s - final_poles[m]) + f_rebuilt += ser_full["D"][0, 0] + s * ser_full["E"][0, 0] + np.testing.assert_allclose(f_rebuilt, fit[0, :], rtol=1e-8) + + print(f"\n[METRIC] {benchmark.name} -> Final RMSE: {rmserr:.6e}") + +# ============================================================================== +# TEST 5: PROPAGATION MATRIX 3x3 (Asymmetric) +# ============================================================================== +def test_benchmark_propagation_matrix(benchmark, default_opts, load_vectfit_csv): + """Benchmark for Test 5: 3x3 Asymmetric Propagation Matrix.""" + Hdata = pd.DataFrame(load_vectfit_csv("MODEH_DATA.csv")) + w = Hdata.iloc[:, 1].to_numpy() + s = 1j * w + N = len(w) + + F = np.zeros((9, N), dtype=np.complex128) + # Trace of H for initial pole fitting + trH = np.zeros(N, dtype=np.complex128) + + for row in range(3): + for col in range(3): + idx = row * 3 + col + # Data is in RMO: Real, Imag, Real, Imag... starting at col index 2 + col_idx = 2 + (idx * 2) + F[idx, :] = Hdata.iloc[:, col_idx].to_numpy() + 1j*Hdata.iloc[:, col_idx+1].to_numpy() + if row == col: + trH += F[idx, :] + + n_order = 35 + bet = np.logspace(np.log10(w[0]), np.log10(w[-1]), 17) + poles = np.zeros(35, dtype=np.complex128) # Note: 35 is odd, one real pole needed + poles[0] = -bet[0]/100 + for k in range(17): + poles[2*k+1] = -bet[k]/100 - 1j*bet[k] + poles[2*k+2] = -bet[k]/100 + 1j*bet[k] + + opts = default_opts.copy() + opts.update({"asymp": 1, "spy2": False, "cmplx_ss": True}) + + def run_propagation(): + curr_p = poles.copy() + # 1. Fit trace for 10 iterations + for _ in range(10): + res_tr = vectfit(trH, s, curr_p, np.ones(N), opts) + curr_p = res_tr[1] + # 2. Fit full matrix for 10 iterations + for _ in range(10): + res_full = vectfit(F, s, curr_p, np.ones(N), opts) + curr_p = res_full[1] + return res_full + + ser, final_poles, rmserr, fit = benchmark(run_propagation) + benchmark.extra_info['Final_RMSE'] = f"{rmserr:.2e}" + + # Structural integrity check + ser_full = flat2full(ser) + Res = buildRES(ser_full["C"], ser_full["B"]) + f_rebuilt = np.zeros(N, dtype=np.complex128) + for m in range(n_order): + f_rebuilt += Res[0, 0, m] / (s - final_poles[m]) + np.testing.assert_allclose(f_rebuilt, fit[0, :], rtol=1e-8) + + print(f"\n[METRIC] {benchmark.name} -> Final RMSE: {rmserr:.6e}") \ No newline at end of file diff --git a/test/test_recover.py b/test/test_recover.py new file mode 100644 index 0000000..a372ad4 --- /dev/null +++ b/test/test_recover.py @@ -0,0 +1,137 @@ +import numpy as np +import pytest +from vectfit3 import vectfit, sortPoles + +def test_scalar_3_poles_recovery(default_opts, generate_synthetic_fs): + """ + Tests if vectfit can recover a known 3-pole scalar transfer function. + """ + # ========================================== + # 1. ARRANGE (Set up the ground truth) + # ========================================== + N = 100 + w = 2 * np.pi * np.logspace(0, 4, N) + s = 1j * w + + # Define our mathematical ground truth (stable poles in the left half-plane) + expected_poles = np.array([ + -500 + 0j, + -100 + 5000j, + -100 - 5000j + ], dtype=np.complex128) + + expected_residues = np.array([ + 2000 + 0j, + 300 + 400j, + 300 - 400j + ], dtype=np.complex128) + + F_true = generate_synthetic_fs(s, expected_poles, expected_residues) + weights = np.ones(N, dtype=np.float64) + n_poles = 3 + + #bad poles + initial_poles = np.array([ + -10 + 0j, + -10 + 1000j, + -10 - 1000j + ], dtype=np.complex128) + + opts = default_opts + opts["spy1"] = False + opts["spy2"] = False + opts["phaseplot"] = False + opts["errplot"] = False + opts["asymp"] = 1 # D=0, E=0 for this specific test + + # ========================================== + # 2. ACT (Run the algorithm) + # ========================================== + Niter = 4 + current_poles = initial_poles.copy() + + for itr in range(Niter): + SER, current_poles, rmserr, fit = vectfit(F_true, s, current_poles, weights, opts) + + # ========================================== + # 3. ASSERT (Verify the results) + # ========================================== + assert rmserr < 1e-4, f"Vector fitting failed to converge tightly. RMS Error: {rmserr}" #TODO: is rmserr < 1e-4 ok? + + # B. Check if the reconstructed frequency response matches the true response + # F_true is 1D, fit might be reshaped to (1, N) by vectfit, so we squeeze it to compare safely + np.testing.assert_allclose(np.squeeze(fit), F_true, rtol=1e-3, atol=1e-3, err_msg="Fitted frequency response diverges from ground truth") + + sorted_expected = sortPoles(expected_poles) + sorted_actual = sortPoles(current_poles) + + np.testing.assert_allclose(sorted_actual, sorted_expected, rtol=1e-2, err_msg="Wrong poles recovered. ") +def test_scalar_recovery_asymp_2(default_opts, generate_synthetic_fs): + """ + Tests recovery with asymp=2: includes constant D term. + F(s) = sum(r/(s-p)) + D + """ + # 1. ARRANGE + N = 100 + w = 2 * np.pi * np.logspace(0, 4, N) + s = 1j * w + + expected_poles = np.array([-100 + 1000j, -100 - 1000j], dtype=np.complex128) + expected_residues = np.array([50 + 10j, 50 - 10j], dtype=np.complex128) + expected_D = 0.5 # Constant offset + + # Generate ground truth with D + F_true = generate_synthetic_fs(s, expected_poles, expected_residues, D=expected_D) + + initial_poles = np.array([-10 + 500j, -10 - 500j], dtype=np.complex128) + weights = np.ones(N, dtype=np.float64) + + opts = default_opts.copy() + opts.update({"spy1": False, "spy2": False, "asymp": 2}) + + # 2. ACT + current_poles = initial_poles.copy() + for _ in range(5): + SER, current_poles, rmserr, fit = vectfit(F_true, s, current_poles, weights, opts) + + # 3. ASSERT + assert rmserr < 1e-4 + actual_D = np.squeeze(SER['D']) + np.testing.assert_allclose(actual_D, expected_D, rtol=1e-2, err_msg="Failed to recover D term") + + +def test_scalar_recovery_asymp_3(default_opts, generate_synthetic_fs): + """ + Tests recovery with asymp=3: includes D and E (proportional) terms. + F(s) = sum(r/(s-p)) + D + s*E + """ + # 1. ARRANGE + N = 100 + w = 2 * np.pi * np.logspace(1, 5, N) # Higher frequency range to see E effect + s = 1j * w + + expected_poles = np.array([-500 + 5000j, -500 - 5000j], dtype=np.complex128) + expected_residues = np.array([1000 + 200j, 1000 - 200j], dtype=np.complex128) + expected_D = 1.2 + expected_E = 2e-6 # Small value, but noticeable at high freq (s*E) + + F_true = generate_synthetic_fs(s, expected_poles, expected_residues, D=expected_D, E=expected_E) + + initial_poles = np.array([-100 + 2000j, -100 - 2000j], dtype=np.complex128) + weights = np.ones(N, dtype=np.float64) + + opts = default_opts.copy() + opts.update({"spy1": False, "spy2": False, "asymp": 3}) + + # 2. ACT + current_poles = initial_poles.copy() + for _ in range(5): + SER, current_poles, rmserr, fit = vectfit(F_true, s, current_poles, weights, opts) + + # 3. ASSERT + assert rmserr < 1e-4 + actual_D = np.squeeze(SER['D']) + actual_E = np.squeeze(SER['E']) + + np.testing.assert_allclose(actual_D, expected_D, rtol=1e-2, err_msg="Failed to recover D term") + np.testing.assert_allclose(actual_E, expected_E, rtol=1e-2, err_msg="Failed to recover E term") \ No newline at end of file diff --git a/test/test_vector_recover.py b/test/test_vector_recover.py new file mode 100644 index 0000000..3a80690 --- /dev/null +++ b/test/test_vector_recover.py @@ -0,0 +1,87 @@ +import numpy as np +import pytest +from vectfit3 import vectfit, sortPoles +import numpy as np +import pytest +from scipy.constants import pi +from vectfit3 import vectfit, sortPoles + +def test_vector_4xN_recovery_unitary(default_opts, generate_synthetic_fs): + """ + Standard test: 4xN vector response with unitary (equal) weighting. + """ + # 1. ARRANGE + N = 200 + w = 2 * pi * np.logspace(1, 4, N) + s = 1j * w + expected_poles = np.array([-100, -50 + 2000j, -50 - 2000j], dtype=np.complex128) + expected_residues = np.array([ + [500, 10 + 50j, 10 - 50j], + [1200, 80 + 10j, 80 - 10j], + [100, 200 - 5j, 200 + 5j], + [900, 10 + 100j, 10 - 100j], + ], dtype=np.complex128) + + F_true = generate_synthetic_fs(s, expected_poles, expected_residues) + weights = np.ones(N, dtype=np.float64) + initial_poles = np.array([-10, -10 + 500j, -10 - 500j], dtype=np.complex128) + + opts = default_opts.copy() + opts.update({"spy1": False, "spy2": False, "asymp": 1, "cmplx_ss": True}) + + # 2. ACT + current_poles = initial_poles.copy() + for _ in range(5): + _, current_poles, rmserr, fit = vectfit(F_true, s, current_poles, weights, opts) + + # 3. ASSERT + assert rmserr < 1e-3 + sorted_expected = sortPoles(expected_poles) + sorted_actual = sortPoles(current_poles) + np.testing.assert_allclose(sorted_actual, sorted_expected, rtol=1e-2) + + +def test_vector_4xN_recovery_random_weights(default_opts, generate_synthetic_fs): + """ + Stress test: 4xN vector response with random weights. + This tests the numerical stability of the weighted least-squares implementation. + """ + # 1. ARRANGE + N = 200 + w = 2 * pi * np.logspace(1, 4, N) + s = 1j * w + expected_poles = np.array([-100, -50 + 2000j, -50 - 2000j], dtype=np.complex128) + expected_residues = np.array([ + [500, 10 + 50j, 10 - 50j], + [1200, 80 + 10j, 80 - 10j], + [100, 200 - 5j, 200 + 5j], + [900, 10 + 100j, 10 - 100j], + ], dtype=np.complex128) + + F_true = generate_synthetic_fs(s, expected_poles, expected_residues) + + # Random weights: Testing sensitivity to non-uniform priority + np.random.seed(42) + weights = np.random.uniform(0.5, 5.0, N) + + initial_poles = np.array([-10, -10 + 500j, -10 - 500j], dtype=np.complex128) + + opts = default_opts.copy() + opts.update({"spy1": False, "spy2": False, "asymp": 1, "cmplx_ss": True}) + + # 2. ACT + current_poles = initial_poles.copy() + for _ in range(7): # Extra iterations for potentially slower convergence with random weights + _, current_poles, rmserr, fit = vectfit(F_true, s, current_poles, weights, opts) + + # 3. ASSERT + # We allow a slightly higher RMS error because random weights can pull + # the fit away from the global minimum of the unweighted error. + assert rmserr < 5e-3, f"Random weight fitting failed to converge. RMS: {rmserr}" + + sorted_expected = sortPoles(expected_poles) + sorted_actual = sortPoles(current_poles) + + # Check if the recovered poles are still physically accurate + np.testing.assert_allclose(sorted_actual, sorted_expected, rtol=5e-2, + err_msg="Pole recovery was significantly skewed by random weights") \ No newline at end of file diff --git a/vectfit_testing.py b/test/vectfit_testing.old similarity index 97% rename from vectfit_testing.py rename to test/vectfit_testing.old index 83bd302..f618282 100644 --- a/vectfit_testing.py +++ b/test/vectfit_testing.old @@ -1,417 +1,416 @@ -### Sample code to test Vector Fitting algorthm implemented in Python by Sebastian Loaiza ### - -from vectfit3 import vectfit # Vector Fitting algorithm imported from its external module vectfit3.py -import numpy as np -import pandas as pd -from scipy.constants import pi - -# Example to be applied: -# 1. Scalar and artificial frequency domain function f(s) -# 2. 18th order approximation of a frequency response F(s) with 2 elements -# 3. Escalar measured response of a transformer -# 4. Elementwise approximation of a 6x6 admitance matrix Y(s) -# 5. Approximation of a 3x3 propagation matrix of an aerial transmission line H(s) - -test=5 # <- Test case selection - -if test==1: - print("Test 1: Scalar and artificial frequency domain function f(s)") # -------------------------------------------------------------------- # - - N=101 # Number of frequency samples - s=2j*pi*np.logspace(0,4,N,dtype=np.complex128) # Samples in the frequency domain - f=np.zeros(N,dtype=np.complex128) # Function samples in the frequency domain - weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples - - # Generating test function values - n=0 - for sn in s: - f[n]=2/(sn+5)+(30+40j)/(sn-(-100+500j))+(30-40j)/(sn-(-100-500j))+0.5 - n+=1 - - print("\nFrequency domain samples of f(s) = \n",f) - print("f(s) shape = ",f.shape, "\ndata type in f(s) = ",type(f),type(f[0])) - - n=3 # Order of aproximation - poles=-2*pi*np.logspace(0,4,n,dtype=np.complex128) # Initial searching poles - - print("\nInitial searching poles:\n",poles) - - # vector fitting configuration - from vectfit3 import opts - opts["asymp"]=3 # Modified to include D and E in fitting - opts["phaseplot"]=True # Modified to include the phase angle graph - - # Remaining options by default - - print("\n * Applying vector fitting...") - (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - - -elif test==2: - print("Test 2: 18th order frequency response F(s) of two dimentions") # -------------------------------------------------------------------- # - - w=2*pi*np.linspace(1,1e5,100,dtype=np.complex128) # Frequency points of evaluation - s=1j*w # Complex frequency points of evaluation - N=s.size # Samples in the frequency domain - weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples - - # Test function generation from its SER representation: - #Sample poles for the elements in F(s) - p=np.array([-4500,-41000,-100+5e3j,-100-5e3j,-120+15e3j,-120-15e3j,-3e3+35e3j,-3e3-35e3j],dtype=np.complex128) - p=np.append(p,np.array([-200+45e3j,-200-45e3j,-1500+45e3j,-1500-45e3j],dtype=np.complex128)) - p=np.append(p,np.array([-5e2+70e3j,-5e2-70e3j,-1e3+73e3j,-1e3-73e3j,-2e3+90e3j,-2e3-90e3j],dtype=np.complex128)) - p=2*pi*p - N1=10 - p1=p[:N1] #First element poles - p2=p[N1-2:] #Second element poles - #Sample residues for the elements in F(s) - r=np.array([-3000,-83000,-5+7e3j,-5-7e3j,-20+18e3j,-20-18e3j,6e3+45e3j,6e3-45e3j],dtype=np.complex128) - r=np.append(r,np.array([40+60e3j,40-60e3j,90+10e3j,90-10e3j],dtype=np.complex128)) - r=np.append(r,np.array([5e4+80e3j,5e4-80e3j,1e3+45e3j,1e3-45e3j,-5e3+92e3j,-5e3-92e3j],dtype=np.complex128)) - r=2*pi*r - r1=r[:N1] #First element residues - r2=r[N1-2:] #Second element residues - # SER constant values: - D=0.2 - E=2e-5 - # Generating test function values - F=np.zeros((2,N),dtype=np.complex128) - n=0 - for sn in s: - for k in range(N1): - F[0,n]+=r1[k]/(sn-p1[k]) #evaluation for the first element - F[1,n]+=r2[k]/(sn-p2[k]) #evaluation for the second element - F[0,n]+=sn*E - F[1,n]+=sn*3*E - n+=1 - F[0,:]=F[0,:]+3*D - - print("\nFrequency domain samples of f(s) = \n",F) - print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0][0])) - - # Initial complex poles: - n=18 # Order of aproximation - # Initial - Bet=np.linspace(w[0],w[N-1],int(n/2)) - poles=np.zeros(n,dtype=np.complex128) - #setting poles as complex conjugated pairs - for k in range(int(n/2)): - alf=-Bet[k]*1e-2 - poles[2*k]=alf-1j*Bet[k] - poles[2*k+1]=alf+1j*Bet[k] - - print("\nInitial searching poles:\n",poles) - - # vector fitting configuration - from vectfit3 import opts - opts["asymp"]=3 # Modified to include D and E in fitting - opts["skip_res"]=True # Modified to skip residue computation in the first iteration - opts["cmplx_ss"]=False # Modified to build a real-only state space model - opts["logx"]=False # Modified to use linear axis for x - opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit - opts["phaseplot"]=True # Modified to include the phase angle graph in the results - # Remaining options by default - - print("\n * Applying 3 iterations of vector fitting...") - Niter=3 - for itr in range(Niter): - if itr==Niter-1: - opts["skip_res"]=False #residue computation in final iteration - opts["spy2"]=True #enabling graphs for the results - (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - -elif test==3: - print("Test 3: Escalar measured response of a transformer") # ------------------------------------------------------------------------------ # - # Importing measured data from a .csv file (TRANSF_DATA.csv) - csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\TRANSF_DATA.csv" #local path! Update with your own path - Mdata=pd.read_csv(csv_path) # Measured data - Mdata=Mdata.to_numpy() # Data transfered into a numpy array - f=Mdata[:160,0]*np.exp(1j*Mdata[:160,1]*pi/180) # f(s) samples computation. *Just 160 samples are taken - - print("\nFrequency domain samples of f(s) = \n",f) - print("f(s) shape = ",f.shape, "\ndata type in f(s) = ",type(f),type(f[0])) - - N=f.size # Number of frequency samples - w=2*pi*np.linspace(0,10e6,401)[1:161] # Frequency evaluation for the range of interest - s=1j*w # Samples in the frequency domain - - print("\nFor the first attempt 6 complex starting poles and no weighting are used") - - weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples - n=6 # Order of approximation - # Starting poles generation: - Bet=np.linspace(w[0],w[N-1],int(n/2)) - poles=np.zeros(n,dtype=np.complex128) - #setting poles as complex conjugated pairs - for k in range(int(n/2)): - alf=-Bet[k]*1e-2 - poles[2*k]=alf-1j*Bet[k] - poles[2*k+1]=alf+1j*Bet[k] - - print("\nInitial searching poles:\n",poles) - - # vector fitting configuration - from vectfit3 import opts - opts["asymp"]=3 # Modified to include D and E in fitting - opts["logx"]=False # Modified to use linear axis for x - opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit - opts["phaseplot"]=True # Modified to include the phase angle graph in the results - # Remaining options by default - - print("\n * Applying 5 iterations of vector fitting...") - Niter=5 - for itr in range(Niter): - if itr==Niter-1: - opts["spy2"]=True #enabling graphs for the results - (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - - print("\nFor better results second attempt is carried out with 30 complex starting poles and inverse weighting") - - weights=1/np.abs(f) # Inverse weighting for frequency samples - n=30 # Order of approximation - # Starting poles generation: - Bet=np.linspace(w[0],w[N-1],int(n/2)) - poles=np.zeros(n,dtype=np.complex128) - #setting poles as complex conjugated pairs - for k in range(int(n/2)): - alf=-Bet[k]*1e-2 - poles[2*k]=alf-1j*Bet[k] - poles[2*k+1]=alf+1j*Bet[k] - - print("\nInitial searching poles:\n",poles) - - opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit - # Remaining options as configured before - - print("\n * Applying 5 iterations of vector fitting...") - Niter=5 - for itr in range(Niter): - if itr==Niter-1: - opts["spy2"]=True #enabling graphs for the results - (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - -elif test==4: - print("Test 4: Elementwise approximation of a 6x6 admitance matrix") # --------------------------------------------------------------------------------- # - # Importing measured data from a .csv file (SYSADMITANCE_DATA.csv) - csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\SYSADMITANCE_DATA.csv" #local path! Update with your own path - Mdata=pd.read_csv(csv_path) # Measured data - Mdata=np.ravel(Mdata.to_numpy()) # Data transfered into a numpy array - N=int(Mdata[0]) # Number of frequency samples - Ysys=np.zeros((6,6,N),dtype=np.complex128) # Samples of matrix Y(s) imported from the file - s=np.zeros(N,dtype=np.complex128) # Complex frequency points of evaluation for Y(s) - - # Y(s) and s are compressed in row-major order into Mdata array. Samples are organized in blocks of 73 numbers, inside each block the first - #number matchs the complex frequency samples and the remaining ones corresponds to each element in the admitance matrix Y(s). first comes - #the real part and then the imaginary part. - k=0 #sample index - for i in range(1,Mdata.size,73): - s[k]=1j*Mdata[i] #complex frequency sample - for row in range(6): - ind=row*12+i - Ysys[row,:,k]=Mdata[ind+1:ind+12:2]+1j*Mdata[ind+2:ind+13:2] #entire row is append to Y(s) - k+=1 - # Stacking Y(s) data as elements of a frequency domain function F(s). - # Due to Y(s) is symmetric only the members into the lower trinagular submatrix Y(s) are taken - F=np.zeros((21,N), dtype=np.complex128) - k=0 #element index - for row in range(6): - for col in range(row,6): - F[k,:]=Ysys[row,col,:] #all samples are in z axis - k+=1 - - print("\nFrequency domain samples of F(s) = \n",F) - print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0,0])) - - weights=1/np.sqrt(np.abs(F)) # Weighting with inverse of the square root of the magnitude of F(s) - n=50 # Order of approximation - w=s.imag # Angular frequency samples in rad/s - # Starting poles generation: - Bet=np.linspace(w[0],w[N-1],int(n/2)) - poles=np.zeros(n,dtype=np.complex128) - #setting poles as complex conjugated pairs - for k in range(int(n/2)): - alf=-Bet[k]/100 - poles[2*k]=alf-1j*Bet[k] - poles[2*k+1]=alf+1j*Bet[k] - - print("A better set of initial poles are obtained by fitting the weighted column sum of the first column of Y(s)\n * Applying 5 iterations of vector fitting...") - # These weights are common for all column elements - g=np.zeros(N, dtype=np.complex128) - for k in range(6): - g=g+F[k,:]/np.linalg.norm(F[k,:]) - weights_g=1/np.abs(g) - - # vector fitting configuration - from vectfit3 import opts - opts["asymp"]=3 # Modified to include D and E in fitting - opts["logx"]=False # Modified to use linear axis for x - opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit - opts["phaseplot"]=True # Modified to include the phase angle graph in the results - opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting - opts["symm_mat"]=True # Modified to indicate that F(s) samples belong to the symmetric matrix Y(s) - opts["cmplx_ss"]=True # Modified to create a complex space-state model (Diagonal A) - # Remaining options by default - - print("\n * Applying 5 iterations of vector fitting...") - Niter=5 #number of iterations - for itr in range(Niter): - if itr==Niter-1: - opts["skip_res"]=False #enabling residue computation in the final iteration - (_,poles,rmserr,_)=vectfit(g,s,poles,weights_g,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nInitial poles computed from weighted column sum of Y(s):\n",poles) - - # Final fitting with new initial poles set and all elementos of Y(s) in F(s) - opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting - - Niter=3 #number of iterations - for itr in range(Niter): - if itr==Niter-1: - opts["spy2"]=True #enabling graphs for the results - opts["skip_res"]=False #enabling residue computation in the final iteration - (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - - from vectfit3 import buildRES, flat2full - SER=flat2full(SER) #transforming flattened and compressed data structure of SER to a full matrix representation - Res=buildRES(SER["C"], SER["B"]) #computing residue matrixes of the fitted function - print("\nResidues matrixes computed:\n") - for k in range(n): - print("\n",Res[:,:,k],"\n") - - # Comprobation. Building fitted function from pole-residue representation: - d=SER["D"] - e=SER["E"] - Ffit=np.zeros(fit.shape, dtype=np.complex128) - k=0 # element index - for row in range(6): - for col in range(row,6): - for m in range(n): - Ffit[k,:]=Ffit[k,:]+(Res[row,col,m]/(s-poles[m])) - Ffit[k,:]=Ffit[k,:]+d[row,col]+s*e[row,col] - k+=1 - # Computing the relative error between vectfit fitted function and the function computed from poles and residues - relError=np.abs(Ffit-fit)/np.abs(fit).max() - if np.any(relError>1e-10): - print("\n *** ERRORS found in reconstructing the fitted function from poles-residues model ***") - else: - print("\n *** NO ERRORS found in reconstructing the fitted function from poles-residues model ***") - -elif test==5: - print("Test 5: Elementwise approximation of a 3x3 propagation matrix of an aerial transmission line.\nIt corresponds to single propagation mode and time delay is already extracted.") - # Importing data from a .csv file (lineConstants_H0.csv) - csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\MODEH_DATA.csv" #local path! Update with your own path - # Pandas data frame with H(w) samples in the frequency domain: - #Columns organization: index , OMEGA(Ang. frequency), H_00REAL(1st element's real part), H_00IMAG(1st element's imaginary part), ... H_01REAL(2nd element's real part), ... - Hdata=pd.read_csv(csv_path) - w=np.ravel(Hdata.loc[:,"OMEGA"].to_numpy()) # Angular frequency samples - s=1j*w # Complex frequency samples - N=w.size # Number of samples - Hw=np.zeros((3,3,N),dtype=np.complex128) # Propagation matrix in the frequency domain - #Copying data into H: - k=2 - for row in range(3): - for col in range(3): - Hw[row,col,:]=np.ravel(Hdata.iloc[:,k].to_numpy())+1j*np.ravel(Hdata.iloc[:,k+1].to_numpy()) #elements are read in RMO - k+=2 - - # Stacking H(s) data as elements of a frequency domain function F(s). - # Due to H(s) is asymmetric, F(s) is a flattened version of H(s). Row Major Ordering is used to map H(s) elements into F(s) - F=np.zeros((3*3, N), dtype=np.complex128) - k=0 #element index - for row in range(3): - for col in range(3): - F[k,:]=Hw[row,col,:] #all frequency samples are in z axis - k+=1 - - print("\nFrequency domain samples of F(s) = \n",F) - print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0,0])) - - weights=np.ones(N, dtype=np.float64) # No samples weighting - n=35 # Order of approximation - # Starting poles generation: - Bet=np.logspace(np.log10(w[0]),np.log10(w[N-1]),int(n/2)) - poles=np.zeros(n,dtype=np.complex128) - #setting poles as complex conjugated pairs - for k in range(int(n/2)): - alf=-Bet[k]/100 - poles[2*k]=alf-1j*Bet[k] - poles[2*k+1]=alf+1j*Bet[k] - - print("A set of initial poles are obtained by fitting trace of Hi\n * Applying 10 iterations of vector fitting...") - # Using H trace to identify initial poles: - trH=np.zeros(N, dtype=np.complex128) - for k in range(3): - trH=trH+Hw[k,k,:] - - # vector fitting configuration - from vectfit3 import opts - opts["asymp"]=1 # Modified to omit D and E in fitting - opts["logy"]=False # Modified to set y axis in logarithmic distribution - opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit - opts["phaseplot"]=True # Modified to include the phase angle graph in the results - opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting - opts["cmplx_ss"]=True # Modified to create a real space-state model - # Remaining options by default - - Niter=10 #number of iterations - for itr in range(Niter): - if itr==Niter-1: - #opts["spy2"]=True #enabling graphs for the results - opts["skip_res"]=False #enabling residue computation in the final iteration - (_,poles,rmserr,_)=vectfit(trH,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nInitial poles computed from trace of H(s):\n",poles) - - # Final fitting with computed initial poles and all elementos of H(s) in F(s) - opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting - - Niter=10 #number of iterations - for itr in range(Niter): - if itr==Niter-1: - opts["spy2"]=True #enabling graphs for the results - opts["skip_res"]=False #enabling residue computation in the final iteration - (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) - print(" ...",itr+1," iterations applied") - print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) - print("\nFinal poles computed:\n",poles) - - from vectfit3 import buildRES, flat2full - SER=flat2full(SER) #transforming flattened and compressed data structure of SER to a full matrix representation - Res=buildRES(SER["C"], SER["B"]) #computing residue matrixes of the fitted function - print("\nResidues matrixes computed:\n") - for k in range(n): - print("\n",Res[:,:,k],"\n") - - # Comprobation. Building fitted function from pole-residue representation: - d=SER["D"] - e=SER["E"] - Ffit=np.zeros(fit.shape, dtype=np.complex128) - k=0 # element index - for row in range(3): - for col in range(3): - for m in range(n): - Ffit[k,:]=Ffit[k,:]+(Res[row,col,m]/(s-poles[m])) - Ffit[k,:]=Ffit[k,:]+d[row,col]+s*e[row,col] - k+=1 - # Computing the relative error between vectfit fitted function and the function computed from poles and residues - relError=np.abs(Ffit-fit)/np.abs(fit).max() - if np.any(relError>1e-10): - print("\n *** ERRORS found in reconstructing the fitted function from poles-residues model ***") - else: +### Sample code to test Vector Fitting algorthm implemented in Python by Sebastian Loaiza ### + +from vectfit3 import vectfit # Vector Fitting algorithm imported from its external module vectfit3.py +import numpy as np +import pandas as pd + +# Example to be applied: +# 1. Scalar and artificial frequency domain function f(s) +# 2. 18th order approximation of a frequency response F(s) with 2 elements +# 3. Escalar measured response of a transformer +# 4. Elementwise approximation of a 6x6 admitance matrix Y(s) +# 5. Approximation of a 3x3 propagation matrix of an aerial transmission line H(s) + +test=5 # <- Test case selection + +if test==1: + print("Test 1: Scalar and artificial frequency domain function f(s)") # -------------------------------------------------------------------- # + + N=101 # Number of frequency samples + s=2j*pi*np.logspace(0,4,N,dtype=np.complex128) # Samples in the frequency domain + f=np.zeros(N,dtype=np.complex128) # Function samples in the frequency domain + weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples + + # Generating test function values + n=0 + for sn in s: + f[n]=2/(sn+5)+(30+40j)/(sn-(-100+500j))+(30-40j)/(sn-(-100-500j))+0.5 + n+=1 + + print("\nFrequency domain samples of f(s) = \n",f) + print("f(s) shape = ",f.shape, "\ndata type in f(s) = ",type(f),type(f[0])) + + n=3 # Order of aproximation + poles=-2*pi*np.logspace(0,4,n,dtype=np.complex128) # Initial searching poles + + print("\nInitial searching poles:\n",poles) + + # vector fitting configuration + from vectfit3 import opts + opts["asymp"]=3 # Modified to include D and E in fitting + opts["phaseplot"]=True # Modified to include the phase angle graph + + # Remaining options by default + + print("\n * Applying vector fitting...") + (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + + +elif test==2: + print("Test 2: 18th order frequency response F(s) of two dimentions") # -------------------------------------------------------------------- # + + w=2*np.pi*np.linspace(1,1e5,100,dtype=np.complex128) # Frequency points of evaluation + s=1j*w # Complex frequency points of evaluation + N=s.size # Samples in the frequency domain + weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples + + # Test function generation from its SER representation: + #Sample poles for the elements in F(s) + p=np.array([-4500,-41000,-100+5e3j,-100-5e3j,-120+15e3j,-120-15e3j,-3e3+35e3j,-3e3-35e3j],dtype=np.complex128) + p=np.append(p,np.array([-200+45e3j,-200-45e3j,-1500+45e3j,-1500-45e3j],dtype=np.complex128)) + p=np.append(p,np.array([-5e2+70e3j,-5e2-70e3j,-1e3+73e3j,-1e3-73e3j,-2e3+90e3j,-2e3-90e3j],dtype=np.complex128)) + p=2*pi*p + N1=10 + p1=p[:N1] #First element poles + p2=p[N1-2:] #Second element poles + #Sample residues for the elements in F(s) + r=np.array([-3000,-83000,-5+7e3j,-5-7e3j,-20+18e3j,-20-18e3j,6e3+45e3j,6e3-45e3j],dtype=np.complex128) + r=np.append(r,np.array([40+60e3j,40-60e3j,90+10e3j,90-10e3j],dtype=np.complex128)) + r=np.append(r,np.array([5e4+80e3j,5e4-80e3j,1e3+45e3j,1e3-45e3j,-5e3+92e3j,-5e3-92e3j],dtype=np.complex128)) + r=2*pi*r + r1=r[:N1] #First element residues + r2=r[N1-2:] #Second element residues + # SER constant values: + D=0.2 + E=2e-5 + # Generating test function values + F=np.zeros((2,N),dtype=np.complex128) + n=0 + for sn in s: + for k in range(N1): + F[0,n]+=r1[k]/(sn-p1[k]) #evaluation for the first element + F[1,n]+=r2[k]/(sn-p2[k]) #evaluation for the second element + F[0,n]+=sn*E + F[1,n]+=sn*3*E + n+=1 + F[0,:]=F[0,:]+3*D + + print("\nFrequency domain samples of f(s) = \n",F) + print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0][0])) + + # Initial complex poles: + n=18 # Order of aproximation + # Initial + Bet=np.linspace(w[0],w[N-1],int(n/2)) + poles=np.zeros(n,dtype=np.complex128) + #setting poles as complex conjugated pairs + for k in range(int(n/2)): + alf=-Bet[k]*1e-2 + poles[2*k]=alf-1j*Bet[k] + poles[2*k+1]=alf+1j*Bet[k] + + print("\nInitial searching poles:\n",poles) + + # vector fitting configuration + from vectfit3 import opts + opts["asymp"]=3 # Modified to include D and E in fitting + opts["skip_res"]=True # Modified to skip residue computation in the first iteration + opts["cmplx_ss"]=False # Modified to build a real-only state space model + opts["logx"]=False # Modified to use linear axis for x + opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit + opts["phaseplot"]=True # Modified to include the phase angle graph in the results + # Remaining options by default + + print("\n * Applying 3 iterations of vector fitting...") + Niter=3 + for itr in range(Niter): + if itr==Niter-1: + opts["skip_res"]=False #residue computation in final iteration + opts["spy2"]=True #enabling graphs for the results + (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + +elif test==3: + print("Test 3: Escalar measured response of a transformer") # ------------------------------------------------------------------------------ # + # Importing measured data from a .csv file (TRANSF_DATA.csv) + csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\TRANSF_DATA.csv" #local path! Update with your own path + Mdata=pd.read_csv(csv_path) # Measured data + Mdata=Mdata.to_numpy() # Data transfered into a numpy array + f=Mdata[:160,0]*np.exp(1j*Mdata[:160,1]*pi/180) # f(s) samples computation. *Just 160 samples are taken + + print("\nFrequency domain samples of f(s) = \n",f) + print("f(s) shape = ",f.shape, "\ndata type in f(s) = ",type(f),type(f[0])) + + N=f.size # Number of frequency samples + w=2*pi*np.linspace(0,10e6,401)[1:161] # Frequency evaluation for the range of interest + s=1j*w # Samples in the frequency domain + + print("\nFor the first attempt 6 complex starting poles and no weighting are used") + + weights=np.ones(N,dtype=np.float64) # Common and unitary weiths for all frequency samples + n=6 # Order of approximation + # Starting poles generation: + Bet=np.linspace(w[0],w[N-1],int(n/2)) + poles=np.zeros(n,dtype=np.complex128) + #setting poles as complex conjugated pairs + for k in range(int(n/2)): + alf=-Bet[k]*1e-2 + poles[2*k]=alf-1j*Bet[k] + poles[2*k+1]=alf+1j*Bet[k] + + print("\nInitial searching poles:\n",poles) + + # vector fitting configuration + from vectfit3 import opts + opts["asymp"]=3 # Modified to include D and E in fitting + opts["logx"]=False # Modified to use linear axis for x + opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit + opts["phaseplot"]=True # Modified to include the phase angle graph in the results + # Remaining options by default + + print("\n * Applying 5 iterations of vector fitting...") + Niter=5 + for itr in range(Niter): + if itr==Niter-1: + opts["spy2"]=True #enabling graphs for the results + (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + + print("\nFor better results second attempt is carried out with 30 complex starting poles and inverse weighting") + + weights=1/np.abs(f) # Inverse weighting for frequency samples + n=30 # Order of approximation + # Starting poles generation: + Bet=np.linspace(w[0],w[N-1],int(n/2)) + poles=np.zeros(n,dtype=np.complex128) + #setting poles as complex conjugated pairs + for k in range(int(n/2)): + alf=-Bet[k]*1e-2 + poles[2*k]=alf-1j*Bet[k] + poles[2*k+1]=alf+1j*Bet[k] + + print("\nInitial searching poles:\n",poles) + + opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit + # Remaining options as configured before + + print("\n * Applying 5 iterations of vector fitting...") + Niter=5 + for itr in range(Niter): + if itr==Niter-1: + opts["spy2"]=True #enabling graphs for the results + (SER,poles,rmserr,fit)=vectfit(f,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + +elif test==4: + print("Test 4: Elementwise approximation of a 6x6 admitance matrix") # --------------------------------------------------------------------------------- # + # Importing measured data from a .csv file (SYSADMITANCE_DATA.csv) + csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\SYSADMITANCE_DATA.csv" #local path! Update with your own path + Mdata=pd.read_csv(csv_path) # Measured data + Mdata=np.ravel(Mdata.to_numpy()) # Data transfered into a numpy array + N=int(Mdata[0]) # Number of frequency samples + Ysys=np.zeros((6,6,N),dtype=np.complex128) # Samples of matrix Y(s) imported from the file + s=np.zeros(N,dtype=np.complex128) # Complex frequency points of evaluation for Y(s) + + # Y(s) and s are compressed in row-major order into Mdata array. Samples are organized in blocks of 73 numbers, inside each block the first + #number matchs the complex frequency samples and the remaining ones corresponds to each element in the admitance matrix Y(s). first comes + #the real part and then the imaginary part. + k=0 #sample index + for i in range(1,Mdata.size,73): + s[k]=1j*Mdata[i] #complex frequency sample + for row in range(6): + ind=row*12+i + Ysys[row,:,k]=Mdata[ind+1:ind+12:2]+1j*Mdata[ind+2:ind+13:2] #entire row is append to Y(s) + k+=1 + # Stacking Y(s) data as elements of a frequency domain function F(s). + # Due to Y(s) is symmetric only the members into the lower trinagular submatrix Y(s) are taken + F=np.zeros((21,N), dtype=np.complex128) + k=0 #element index + for row in range(6): + for col in range(row,6): + F[k,:]=Ysys[row,col,:] #all samples are in z axis + k+=1 + + print("\nFrequency domain samples of F(s) = \n",F) + print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0,0])) + + weights=1/np.sqrt(np.abs(F)) # Weighting with inverse of the square root of the magnitude of F(s) + n=50 # Order of approximation + w=s.imag # Angular frequency samples in rad/s + # Starting poles generation: + Bet=np.linspace(w[0],w[N-1],int(n/2)) + poles=np.zeros(n,dtype=np.complex128) + #setting poles as complex conjugated pairs + for k in range(int(n/2)): + alf=-Bet[k]/100 + poles[2*k]=alf-1j*Bet[k] + poles[2*k+1]=alf+1j*Bet[k] + + print("A better set of initial poles are obtained by fitting the weighted column sum of the first column of Y(s)\n * Applying 5 iterations of vector fitting...") + # These weights are common for all column elements + g=np.zeros(N, dtype=np.complex128) + for k in range(6): + g=g+F[k,:]/np.linalg.norm(F[k,:]) + weights_g=1/np.abs(g) + + # vector fitting configuration + from vectfit3 import opts + opts["asymp"]=3 # Modified to include D and E in fitting + opts["logx"]=False # Modified to use linear axis for x + opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit + opts["phaseplot"]=True # Modified to include the phase angle graph in the results + opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting + opts["symm_mat"]=True # Modified to indicate that F(s) samples belong to the symmetric matrix Y(s) + opts["cmplx_ss"]=True # Modified to create a complex space-state model (Diagonal A) + # Remaining options by default + + print("\n * Applying 5 iterations of vector fitting...") + Niter=5 #number of iterations + for itr in range(Niter): + if itr==Niter-1: + opts["skip_res"]=False #enabling residue computation in the final iteration + (_,poles,rmserr,_)=vectfit(g,s,poles,weights_g,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nInitial poles computed from weighted column sum of Y(s):\n",poles) + + # Final fitting with new initial poles set and all elementos of Y(s) in F(s) + opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting + + Niter=3 #number of iterations + for itr in range(Niter): + if itr==Niter-1: + opts["spy2"]=True #enabling graphs for the results + opts["skip_res"]=False #enabling residue computation in the final iteration + (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + + from vectfit3 import buildRES, flat2full + SER=flat2full(SER) #transforming flattened and compressed data structure of SER to a full matrix representation + Res=buildRES(SER["C"], SER["B"]) #computing residue matrixes of the fitted function + print("\nResidues matrixes computed:\n") + for k in range(n): + print("\n",Res[:,:,k],"\n") + + # Comprobation. Building fitted function from pole-residue representation: + d=SER["D"] + e=SER["E"] + Ffit=np.zeros(fit.shape, dtype=np.complex128) + k=0 # element index + for row in range(6): + for col in range(row,6): + for m in range(n): + Ffit[k,:]=Ffit[k,:]+(Res[row,col,m]/(s-poles[m])) + Ffit[k,:]=Ffit[k,:]+d[row,col]+s*e[row,col] + k+=1 + # Computing the relative error between vectfit fitted function and the function computed from poles and residues + relError=np.abs(Ffit-fit)/np.abs(fit).max() + if np.any(relError>1e-10): + print("\n *** ERRORS found in reconstructing the fitted function from poles-residues model ***") + else: + print("\n *** NO ERRORS found in reconstructing the fitted function from poles-residues model ***") + +elif test==5: + print("Test 5: Elementwise approximation of a 3x3 propagation matrix of an aerial transmission line.\nIt corresponds to single propagation mode and time delay is already extracted.") + # Importing data from a .csv file (lineConstants_H0.csv) + csv_path=r"C:\Users\Sebastian\Documents\GitHub\Vector_Fitting_for_python\MODEH_DATA.csv" #local path! Update with your own path + # Pandas data frame with H(w) samples in the frequency domain: + #Columns organization: index , OMEGA(Ang. frequency), H_00REAL(1st element's real part), H_00IMAG(1st element's imaginary part), ... H_01REAL(2nd element's real part), ... + Hdata=pd.read_csv(csv_path) + w=np.ravel(Hdata.loc[:,"OMEGA"].to_numpy()) # Angular frequency samples + s=1j*w # Complex frequency samples + N=w.size # Number of samples + Hw=np.zeros((3,3,N),dtype=np.complex128) # Propagation matrix in the frequency domain + #Copying data into H: + k=2 + for row in range(3): + for col in range(3): + Hw[row,col,:]=np.ravel(Hdata.iloc[:,k].to_numpy())+1j*np.ravel(Hdata.iloc[:,k+1].to_numpy()) #elements are read in RMO + k+=2 + + # Stacking H(s) data as elements of a frequency domain function F(s). + # Due to H(s) is asymmetric, F(s) is a flattened version of H(s). Row Major Ordering is used to map H(s) elements into F(s) + F=np.zeros((3*3, N), dtype=np.complex128) + k=0 #element index + for row in range(3): + for col in range(3): + F[k,:]=Hw[row,col,:] #all frequency samples are in z axis + k+=1 + + print("\nFrequency domain samples of F(s) = \n",F) + print("f(s) shape = ",F.shape, "\ndata type in f(s) = ",type(F),type(F[0,0])) + + weights=np.ones(N, dtype=np.float64) # No samples weighting + n=35 # Order of approximation + # Starting poles generation: + Bet=np.logspace(np.log10(w[0]),np.log10(w[N-1]),int(n/2)) + poles=np.zeros(n,dtype=np.complex128) + #setting poles as complex conjugated pairs + for k in range(int(n/2)): + alf=-Bet[k]/100 + poles[2*k]=alf-1j*Bet[k] + poles[2*k+1]=alf+1j*Bet[k] + + print("A set of initial poles are obtained by fitting trace of Hi\n * Applying 10 iterations of vector fitting...") + # Using H trace to identify initial poles: + trH=np.zeros(N, dtype=np.complex128) + for k in range(3): + trH=trH+Hw[k,k,:] + + # vector fitting configuration + from vectfit3 import opts + opts["asymp"]=1 # Modified to omit D and E in fitting + opts["logy"]=False # Modified to set y axis in logarithmic distribution + opts["spy2"]=False # Modified to omit graphs generation into the iterative application of vectfit + opts["phaseplot"]=True # Modified to include the phase angle graph in the results + opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting + opts["cmplx_ss"]=True # Modified to create a real space-state model + # Remaining options by default + + Niter=10 #number of iterations + for itr in range(Niter): + if itr==Niter-1: + #opts["spy2"]=True #enabling graphs for the results + opts["skip_res"]=False #enabling residue computation in the final iteration + (_,poles,rmserr,_)=vectfit(trH,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nInitial poles computed from trace of H(s):\n",poles) + + # Final fitting with computed initial poles and all elementos of H(s) in F(s) + opts["skip_res"]=True # Modified to skip residue computation during the iterative execution of vector fitting + + Niter=10 #number of iterations + for itr in range(Niter): + if itr==Niter-1: + opts["spy2"]=True #enabling graphs for the results + opts["skip_res"]=False #enabling residue computation in the final iteration + (SER,poles,rmserr,fit)=vectfit(F,s,poles,weights,opts) + print(" ...",itr+1," iterations applied") + print(" v/ Fitting process completed. Aproximation error achieved = ",rmserr) + print("\nFinal poles computed:\n",poles) + + from vectfit3 import buildRES, flat2full + SER=flat2full(SER) #transforming flattened and compressed data structure of SER to a full matrix representation + Res=buildRES(SER["C"], SER["B"]) #computing residue matrixes of the fitted function + print("\nResidues matrixes computed:\n") + for k in range(n): + print("\n",Res[:,:,k],"\n") + + # Comprobation. Building fitted function from pole-residue representation: + d=SER["D"] + e=SER["E"] + Ffit=np.zeros(fit.shape, dtype=np.complex128) + k=0 # element index + for row in range(3): + for col in range(3): + for m in range(n): + Ffit[k,:]=Ffit[k,:]+(Res[row,col,m]/(s-poles[m])) + Ffit[k,:]=Ffit[k,:]+d[row,col]+s*e[row,col] + k+=1 + # Computing the relative error between vectfit fitted function and the function computed from poles and residues + relError=np.abs(Ffit-fit)/np.abs(fit).max() + if np.any(relError>1e-10): + print("\n *** ERRORS found in reconstructing the fitted function from poles-residues model ***") + else: print("\n *** NO ERRORS found in reconstructing the fitted function from poles-residues model ***") \ No newline at end of file