Changeset 1230 in lmdz_wrf for trunk/tools
- Timestamp:
- Oct 25, 2016, 7:55:03 PM (8 years ago)
- File:
-
- 1 edited
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trunk/tools/generic_tools.py
r1229 r1230 77 77 # num_split: Function to split a string at each numeric value keeping the number as the last character of each cut 78 78 # oper_submatrix: Function to perform an operation of a given matrix along a sub-set of values along its dimensions 79 # operations: Function to perform different operations to a pair of matrices of values 79 80 # period_information_360d: Function to provide the information of a given period idate, edate (dates in 80 81 # [YYYY][MM][DD][HH][MI][SS] format) in a 360 years calendar … … 9447 9448 if searchInlist(firstchars,noc): firstchars.remove(noc) 9448 9449 9449 newtext = text + ''9450 newtext = text 9450 9451 for char in firstchars: 9452 # newtext = newtext.replace(char.decode('iso-8859-15'),chars[char].decode('iso-8859-15')) 9451 9453 newtext = newtext.replace(char,chars[char]) 9452 9454 chars.pop(char) … … 9488 9490 newln = newln.replace('ï', '\\"i') 9489 9491 newln = newln.replace('ö', '\\"o') 9492 newln = newln.replace('\xf6', '\\"o') 9490 9493 newln = newln.replace('ÃŒ', '\\"u') 9491 9494 … … 9821 9824 timestep.sort() 9822 9825 return timestep 9826 9827 def operations(opN,matA,matB=None): 9828 """ Function to perform different operations to a pair of matrices of values 9829 opN: name of the operation 9830 'add': adding matB to matA (matA + matB) 9831 'centerderiv',[N],[ord],[dim]: un-scaled center [N]-derivative of order [ord] along dimension [dim] of matA 9832 'div': dividing by matB (matA / matB) 9833 'forwrdderiv',[N],[ord],[dim]: un-scaled forward [N]-derivative of order [ord] along dimension [dim] of matA 9834 'inv': inverting matA (1/matA) 9835 'mul': multiplying ny matB (matA * matB) 9836 'pot': powering with matB (matA ** matB) 9837 'sub': substracting matB to matA (matA - matB) 9838 matA: initial values 9839 matB: values to operate with 9840 >>> operations('centerderiv,1,8,0',np.arange(81.).reshape(9,9)) 9841 [[ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9842 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9843 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9844 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9845 [ 9. 9. 9. 9. 9. 9. 9. 9. 9.] 9846 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9847 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9848 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9849 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.]] 9850 >>> operations('forwrdderiv,1,6,0',np.arange(81.).reshape(9,9)) 9851 [[ 9. 9. 9. 9. 9. 9. 9. 9. 9.] 9852 [ 9. 9. 9. 9. 9. 9. 9. 9. 9.] 9853 [ 9. 9. 9. 9. 9. 9. 9. 9. 9.] 9854 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9855 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9856 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9857 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9858 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9859 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.]] 9860 >>> operations('forwrdderiv,2,2,0',np.arange(81.).reshape(9,9)) 9861 [[ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9862 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9863 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9864 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9865 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9866 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9867 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9868 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.] 9869 [ 0. 0. 0. 0. 0. 0. 0. 0. 0.]] 9870 """ 9871 fname = 'operations' 9872 newmat = None 9873 9874 matAshape = list(matA.shape) 9875 print fname + '; Lluis matAshape:', matAshape 9876 9877 # From: https://en.wikipedia.org/wiki/Finite_difference_coefficient 9878 # Coefficients for center derivatives at different orders (as key) 9879 centerderiv = np.zeros((6,8,9), dtype=np.float) 9880 # Different available orders for each derivative 9881 centerorder = {} 9882 centerorder[0] = [1,3,5,7] 9883 centerorder[1] = [1,3,5,7] 9884 centerorder[2] = [1,3,5] 9885 centerorder[3] = [1,3,5] 9886 centerorder[4] = [1] 9887 centerorder[5] = [1] 9888 9889 # First derivative 9890 centerderiv[0,1,:]= [ 0., 0., 0., -1./2., 0., 1./2., 0., 0., 0.] 9891 centerderiv[0,3,:]= [ 0., 0., 1./12., -2./3., 0., 2./3., -1./12., 0., 0.] 9892 centerderiv[0,5,:]= [ 0., -1./60., 3./20., -3./4., 0., 3./4., -3./20., 1./60, 0.] 9893 centerderiv[0,7,:]= [ 1./280., -4./105., 1./5., -4./5., 0., 4./5., -1./5., 4./105., -1./280.] 9894 # Second derivative 9895 centerderiv[1,1,:]= [ 0., 0., 0., 1., -2., 1., 0., 0., 0.] 9896 centerderiv[1,3,:]= [ 0., 0., -1./12., 4./3., -5./2., 4./3., -1./12., 0., 0.] 9897 centerderiv[1,5,:]= [ 0., 1./90., -3./20., 3./2., -49./18., 3./2., -.3/20., 1./90., 0.] 9898 centerderiv[1,7,:]= [ -1./560., 8./315., -1./5., 8./5., -205./72., 8./5., -1./5., 8./315., -1./560.] 9899 # 3rd derivative 9900 centerderiv[2,1,:]= [ 0., 0., -1./2., 1., 0., -1., 1./2., 0., 0.] 9901 centerderiv[2,3,:]= [ 0., 1./8., -1., 13./8., 0., -13./8., 1., -1./8., 0.] 9902 centerderiv[2,5,:]= [ -7./240., 3./10.,-169./120., 61./30., 0., -61./30., 169./120., -3./10., 7./240.] 9903 # 4th derivative 9904 centerderiv[3,1,:]= [ 0., 0., 1., -4., 6., -4., 1., 0., 0.] 9905 centerderiv[3,3,:]= [ 0., -1./6., 2., -13./2., 28./3., -13./2., 2., -1./6., 0.] 9906 centerderiv[3,5,:]= [ 7./240., -2./5., 169./60., -122./15., 91./8., -122./15., 169./60., -2./5., 7./240.] 9907 # 5th derivative 9908 centerderiv[4,1,:]= [ 0., -1./2., 2., -5./2., 0., 5./2., -2., 1./2., 0.] 9909 # 6th derivative 9910 centerderiv[5,1,:]= [ 0., 1., -6., 15., -20., 15., -6., 1., 0.] 9911 9912 # Coefficients for forward derivatives at different orders (as key) 9913 forwrdderiv = np.zeros((6,6,9), dtype=np.float) 9914 # Different available orders for each derivative 9915 forwrdorder = {} 9916 forwrdorder[0] = range(6) 9917 forwrdorder[1] = range(6) 9918 forwrdorder[2] = range(6) 9919 forwrdorder[3] = range(4) 9920 9921 # First derivative 9922 forwrdderiv[0,0,:]= [ -1., 1., 0., 0., 0., 0., 0., 0., 0.] 9923 forwrdderiv[0,1,:]= [ -3./2., 2., -1./2., 0., 0., 0., 0., 0., 0.] 9924 forwrdderiv[0,2,:]= [ -11./6., 3., -3./2., 1./3., 0., 0., 0., 0., 0.] 9925 forwrdderiv[0,3,:]= [ -25./12., 4., -3., 4./3., -1./4., 0., 0., 0., 0.] 9926 forwrdderiv[0,4,:]= [ -137./60., 5., -5., 10./3., -5./4., 1./5., 0., 0., 0.] 9927 forwrdderiv[0,5,:]= [ -49./20., 6., -15./2., 20./3., -15./4., 6./5., -1./6., 0., 0.] 9928 # Second derivative 9929 forwrdderiv[1,0,:]= [ 1., -2., 1., 0., 0., 0., 0., 0., 0.] 9930 forwrdderiv[1,1,:]= [ 2., -5., 4., -1., 0., 0., 0., 0., 0.] 9931 forwrdderiv[1,2,:]= [ 35./12., -26./3., 19./2., -14./3., 11./12., 0., 0., 0., 0.] 9932 forwrdderiv[1,3,:]= [ 15./4., -77./6., 107./6., -13., 61./12., -5./6., 0., 0., 0.] 9933 forwrdderiv[1,4,:]= [ 203./45., -87./5., 117./4., -254./9., 33./2., -27./5., 137./180., 0., 0.] 9934 forwrdderiv[1,5,:]= [ 469./90., -223./10., 879./20., -949./18., 41., -201./10.,1019./180., -7./10., 0.] 9935 # 3rd derivative 9936 forwrdderiv[2,0,:]= [ -1., 3., -3., 1., 0., 0., 0., 0., 0.] 9937 forwrdderiv[2,1,:]= [ -5./2., 9., -12., 7., -3./2., 0., 0., 0., 0.] 9938 forwrdderiv[2,2,:]= [ -17./4., 71./4., -59./2., 49./2., -41./4., 7./4., 0., 0., 0.] 9939 forwrdderiv[2,3,:]= [ -49./8., 29., -461./8., 62., -307./8., 13., -15./8., 0., 0.] 9940 forwrdderiv[2,4,:]= [-967./120., 638./15.,-3929./40., 389./3.,-2545./24., 268./5.,-1849./120, 29./15., 0.] 9941 forwrdderiv[2,5,:]= [ -801./80., 349./6.,-18353./120,2391./10., -1457./6., 4891./30., -561./8., 527./30.,-469./240.] 9942 # 4th derivative 9943 forwrdderiv[3,0,:]= [ 1., -4., 6., -4., 1., 0., 0., 0., 0.] 9944 forwrdderiv[3,1,:]= [ 3., -14., 26., -24., 11., -2., 0., 0., 0.] 9945 forwrdderiv[3,2,:]= [ 35./6., -31., 137./2., -242./3., 107./2., -19., 17./6., 0., 0.] 9946 forwrdderiv[3,3,:]= [ 28./3., -111./2., 142., -1219./6., 176., -185./2., 82./3., -7./2., 0.] 9947 forwrdderiv[3,4,:]= [ 1069./80.,-1316./15.,15289./60., -2144./5.,10993./24.,-4772./15., 2803./20., -536./15., 967./240.] 9948 9949 # Dictionary with the description of the operations 9950 Lopn = {'add': '+', 'div': '/', 'inv': '^(-1)', 'mul': '*', 'pot': '^', \ 9951 'sub': '-'} 9952 9953 opavail = ['add', 'centerderiv', 'div', 'forwrdderiv', 'inv', 'mul', 'pot', 'sub'] 9954 9955 if opN[0:11] == 'centerderiv': 9956 opn = 'centerderiv' 9957 Nderiv = int(opN.split(',')[1]) 9958 order = int(opN.split(',')[2]) 9959 dim = int(opN.split(',')[3]) 9960 Lopn[opn]= str(Nderiv)+'-center_deriv_ord('+str(order)+ ')[' + str(dim) + ']' 9961 if not centerorder.has_key(Nderiv-1): 9962 print errormsg 9963 print ' ' + fname + ': ', Nderiv,'-center derivative does not exist!!' 9964 print ' existing ones:', list(centeroder.keys())+1 9965 quit() 9966 derivorders = centerorder[Nderiv-1] 9967 if not searchInlist(derivorders,order-1): 9968 print errormsg 9969 print ' ' + fname + ': ', Nderiv,'-center derivative does not have ' + \ 9970 'order:', order,'!!' 9971 print ' existing ones:', np.array(derivorders) + 1 9972 quit() 9973 if dim > len(matAshape)-1: 9974 print errormsg 9975 print ' '+fname+ ': wrong dimension:', dim, 'to compute the center-' + \ 9976 'derivative!!' 9977 print ' matrix has a smaller rank:', len(matAshape) 9978 quit(-1) 9979 derivcoeff = centerderiv[Nderiv-1,order-1,:] 9980 9981 elif opN[0:11] == 'forwrdderiv': 9982 opn = 'forwrdderiv' 9983 Nderiv = int(opN.split(',')[1]) 9984 order = int(opN.split(',')[2]) 9985 dim = int(opN.split(',')[3]) 9986 Lopn[opn]= str(Nderiv)+'-forward_deriv_ord('+str(order)+ ')[' + str(dim) + ']' 9987 if not forwrdorder.has_key(Nderiv-1): 9988 print errormsg 9989 print ' ' + fname + ': ', Nderiv,'-forward derivative does not exist!!' 9990 print ' existing ones:', list(forwrdoder.keys())+1 9991 quit() 9992 derivorders = forwrdorder[Nderiv-1] 9993 if not searchInlist(derivorders,order-1): 9994 print errormsg 9995 print ' ' + fname + ': ', Nderiv,'-forward derivative does not have ' + \ 9996 'order:', order,'!!' 9997 print ' existing ones:', np.array(derivorders) + 1 9998 quit() 9999 if dim > len(matAshape)-1: 10000 print errormsg 10001 print ' '+fname+ ': wrong dimension:', dim, 'to compute the forward-' + \ 10002 'derivative!!' 10003 print ' matrix has a smaller rank:', len(matAshape) 10004 quit(-1) 10005 derivcoeff = forwrdderiv[Nderiv-1,order-1,:] 10006 else: 10007 opn = opN 10008 10009 valtype = mat.dtype 10010 10011 if opn == 'add': 10012 newmat = matA + matB 10013 elif opn == 'centerderiv': 10014 sdim = matAshape[dim] 10015 # Getting the different slices for each coefficient 10016 # newmat = matA_4*coef_4 + matA_3*coef_3 + matA_2*coef_2 + matA_1*coef_1 + 10017 # matA*coef0 + matA1*coef1 + mat2*coef2 + matA3*coef3 + mat4*coef4 10018 newmat = np.zeros(tuple(matAshape), dtype=valtype) 10019 mat0 = [] 10020 mat1_ = [] 10021 mat1 = [] 10022 mat2_ = [] 10023 mat2 = [] 10024 mat3_ = [] 10025 mat3 = [] 10026 mat4_ = [] 10027 mat4 = [] 10028 10029 Nterms = 2*int((Nderiv-1)/2)+order+1 10030 for idim in range(len(matAshape)): 10031 if idim == dim: 10032 sd = (Nterms-1)/2 10033 ed = sdim - (Nterms-1)/2 10034 mat0.append(slice(sd,ed)) 10035 mat1_.append(slice(sd-1,ed-1)) 10036 mat1.append(slice(sd+1,ed+1)) 10037 mat2_.append(slice(sd-2,ed-2)) 10038 mat2.append(slice(sd+2,ed+2)) 10039 mat3_.append(slice(sd-3,ed-3)) 10040 mat3.append(slice(sd+3,ed+3)) 10041 mat4_.append(slice(sd-4,ed-4)) 10042 mat4.append(slice(sd+4,ed+4)) 10043 else: 10044 mat0.append(slice(0,matAshape[idim]+1)) 10045 mat1_.append(slice(0,matAshape[idim]+1)) 10046 mat1.append(slice(0,matAshape[idim]+1)) 10047 mat2_.append(slice(0,matAshape[idim]+1)) 10048 mat2.append(slice(0,matAshape[idim]+1)) 10049 mat3_.append(slice(0,matAshape[idim]+1)) 10050 mat3.append(slice(0,matAshape[idim]+1)) 10051 mat4_.append(slice(0,matAshape[idim]+1)) 10052 mat4.append(slice(0,matAshape[idim]+1)) 10053 if Nterms == 3: 10054 newmat[tuple(mat0)] = matA[tuple(mat1_)]*derivcoeff[3] + \ 10055 matA[tuple(mat0)]*derivcoeff[4] + matA[tuple(mat1)]*derivcoeff[5] 10056 elif Nterms == 5: 10057 newmat[tuple(mat0)] = matA[tuple(mat2_)]*derivcoeff[2] + \ 10058 matA[tuple(mat1_)]*derivcoeff[3] + \ 10059 matA[tuple(mat0)]*derivcoeff[4] + \ 10060 matA[tuple(mat1)]*derivcoeff[5] + matA[tuple(mat2)]*derivcoeff[6] 10061 elif Nterms == 7: 10062 newmat[tuple(mat0)] = matA[tuple(mat3_)]*derivcoeff[1] + \ 10063 matA[tuple(mat2_)]*derivcoeff[2] + matA[tuple(mat1_)]*derivcoeff[3] + \ 10064 matA[tuple(mat0)]*derivcoeff[4] + \ 10065 matA[tuple(mat1)]*derivcoeff[5] + matA[tuple(mat2)]*derivcoeff[6] + \ 10066 matA[tuple(mat3)]*derivcoeff[7] 10067 elif Nterms == 9: 10068 newmat[tuple(mat0)] = matA[tuple(mat4_)]*derivcoeff[0] + \ 10069 matA[tuple(mat3_)]*derivcoeff[1] + matA[tuple(mat2_)]*derivcoeff[2] + \ 10070 matA[tuple(mat1_)]*derivcoeff[3] + \ 10071 matA[tuple(mat0)]*derivcoeff[4] + \ 10072 matA[tuple(mat1)]*derivcoeff[5] + matA[tuple(mat2)]*derivcoeff[6] + \ 10073 matA[tuple(mat3)]*derivcoeff[7] + matA[tuple(mat4)]*derivcoeff[8] 10074 elif opn == 'div': 10075 newmat = matA / matB 10076 elif opn == 'forwrdderiv': 10077 sdim = matAshape[dim] 10078 # Getting the different slices for each coefficient 10079 # newmat = matA0*coef0 + matA1*coef1 + matA2*coef2 + matA3*coef3 + 10080 # matA4*coef4 + matA5*coef5 + matA6*coef6 + matA7*coef7 + matA8*coef8 10081 newmat = np.zeros(tuple(matAshape), dtype=valtype) 10082 mat0 = [] 10083 mat1 = [] 10084 mat2 = [] 10085 mat3 = [] 10086 mat4 = [] 10087 mat5 = [] 10088 mat6 = [] 10089 mat7 = [] 10090 mat8 = [] 10091 10092 Nterms = Nderiv + order 10093 for idim in range(len(matAshape)): 10094 if idim == dim: 10095 sd = 0 10096 ed = sdim-Nterms+1 10097 mat0.append(slice(sd,ed)) 10098 mat1.append(slice(sd+1,ed+1)) 10099 mat2.append(slice(sd+2,ed+2)) 10100 mat3.append(slice(sd+3,ed+3)) 10101 mat4.append(slice(sd+4,ed+4)) 10102 mat5.append(slice(sd+5,ed+5)) 10103 mat6.append(slice(sd+6,ed+6)) 10104 mat7.append(slice(sd+7,ed+7)) 10105 mat8.append(slice(sd+8,ed+8)) 10106 else: 10107 mat0.append(slice(0,matAshape[idim]+1)) 10108 mat1.append(slice(0,matAshape[idim]+1)) 10109 mat2.append(slice(0,matAshape[idim]+1)) 10110 mat3.append(slice(0,matAshape[idim]+1)) 10111 mat4.append(slice(0,matAshape[idim]+1)) 10112 mat5.append(slice(0,matAshape[idim]+1)) 10113 mat6.append(slice(0,matAshape[idim]+1)) 10114 mat7.append(slice(0,matAshape[idim]+1)) 10115 mat8.append(slice(0,matAshape[idim]+1)) 10116 if Nterms == 2: 10117 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10118 matA[tuple(mat1)]*derivcoeff[1] 10119 elif Nterms == 3: 10120 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10121 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] 10122 elif Nterms == 4: 10123 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10124 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10125 matA[tuple(mat3)]*derivcoeff[3] 10126 elif Nterms == 5: 10127 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10128 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10129 matA[tuple(mat3)]*derivcoeff[3] + matA[tuple(mat4)]*derivcoeff[4] 10130 elif Nterms == 6: 10131 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10132 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10133 matA[tuple(mat3)]*derivcoeff[3] + matA[tuple(mat4)]*derivcoeff[4] + \ 10134 matA[tuple(mat5)]*derivcoeff[5] 10135 elif Nterms == 7: 10136 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10137 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10138 matA[tuple(mat3)]*derivcoeff[3] + matA[tuple(mat4)]*derivcoeff[4] + \ 10139 matA[tuple(mat5)]*derivcoeff[5] + matA[tuple(mat6)]*derivcoeff[6] 10140 elif Nterms == 8: 10141 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10142 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10143 matA[tuple(mat3)]*derivcoeff[3] + matA[tuple(mat4)]*derivcoeff[4] + \ 10144 matA[tuple(mat5)]*derivcoeff[5] + matA[tuple(mat6)]*derivcoeff[6] + \ 10145 matA[tuple(mat7)]*derivcoeff[7] 10146 elif Nterms == 9: 10147 newmat[tuple(mat0)] = matA[tuple(mat0)]*derivcoeff[0] + \ 10148 matA[tuple(mat1)]*derivcoeff[1] + matA[tuple(mat2)]*derivcoeff[2] + \ 10149 matA[tuple(mat3)]*derivcoeff[3] + matA[tuple(mat4)]*derivcoeff[4] + \ 10150 matA[tuple(mat5)]*derivcoeff[5] + matA[tuple(mat6)]*derivcoeff[6] + \ 10151 matA[tuple(mat7)]*derivcoeff[7] + matA[tuple(mat8)]*derivcoeff[8] 10152 elif opn == 'inv': 10153 newmat = retype(1., valtype) / matA 10154 elif opn == 'mul': 10155 newmat = matA * matB 10156 elif opn == 'pot': 10157 newmat = matA ** matB 10158 elif opn == 'sub': 10159 newmat = matA - matB 10160 else: 10161 print ' ' + fname + ": operation '" + opn + "' does not exist !!" 10162 print ' available ones:', opavail 10163 quit(-1) 10164 10165 return newmat 10166 9823 10167 #quit() 9824 10168
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