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Convert Data Formats

cs2sc(field)

converts the square (L+1)x(L+1) matrix 'field', containing spherical harmonics coefficients in |C\S| storage format into a rectangular (L+1)x(2L+1) matrix in /S|C\ format.

Parameters:

Name Type Description Default
field ndarray

the square (L+1)x(L+1) numpy matrix field , containing spherical harmonics coefficients in |C\S| storage format

 required

Returns:

Type Description

numpy.ndarray: Rectangular (L+1)x(2L+1) numpy matrix in /S|C\ format

Raises:

Type Description
TypeError

Input neither in cs nor in sc format
Todo
  • Rather use TypeError instead of base Exception

Examples:

>>> sc_shcoeff = cs2sc(cs_shcoeff)
TO DO: write the output
Source code in pyshbundle/cs2sc.py 
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def cs2sc(field):
    """converts the square (L+1)x(L+1) matrix 'field', containing
    spherical harmonics coefficients in |C\S| storage format into a 
    rectangular (L+1)x(2L+1) matrix in  /S|C\ format.

    Args:
        field (np.ndarray): the square (L+1)x(L+1) numpy matrix field , containing
                   spherical harmonics coefficients in |C\S| storage format

    Returns:
        numpy.ndarray: Rectangular (L+1)x(2L+1) numpy matrix in  /S|C\ format

    Raises:
        TypeError: Input neither in cs nor in sc format

    Todo:
        + Rather use TypeError instead of base Exception

    Examples:
        >>> sc_shcoeff = cs2sc(cs_shcoeff)
        TO DO: write the output
    """
    rows = len(field)
    cols = len(field[0])

    if (rows != cols) and (cols != 2*rows - 1):
        raise TypeError("Input neither in cs nor in sc format")
    elif cols == 2*rows - 1:
        sc = field
    else:
        c    = numpy.tril(field)
        ut   = numpy.triu(field)
        i = numpy.identity(rows)
        i = 1-i
        s    = numpy.fliplr(numpy.transpose(numpy.multiply(ut, i, )))
        sc   = numpy.concatenate((s[:,1:rows], c), axis=1)

    return(sc)

sc2cs(field)

converts the rectangular \((L+1) imes (2L+1)\) matrix FIELD, containing spherical harmonics coefficients in /S|C\ storage format into a square (L+1)x(L+1) matrix in |C\S| format.

Parameters:

Name Type Description Default
field ndarray

the rectangular (L+1)x(2L+1) matrix FIELD, containing spherical harmonics coefficients in /S|C\ storage format

 required

Returns:

Name Type Description
cs ndarray

square (L+1)x(L+1) matrix in |C\S| format
References

See the SHBundle docs or PySHBundle docs for more info about SH coeff. storage and retrival formats being implementd.

Examples:

>>> cs_fmt = sc2cs(field)
TO DO: show suitable output
Source code in pyshbundle/sc2cs.py 
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def sc2cs(field):
    """converts the rectangular $(L+1) \times (2L+1)$ matrix FIELD, containing
    spherical harmonics coefficients in /S|C\ storage format into a 
    square (L+1)x(L+1) matrix in |C\S| format.

    Parameters:
        field (numpy.ndarray()):
            the rectangular (L+1)x(2L+1) matrix FIELD, containing
            spherical harmonics coefficients in /S|C\ storage format

    Returns: 
        cs (numpy.ndarray): 
            square (L+1)x(L+1) matrix in |C\S| format

    References:
        See the SHBundle docs or PySHBundle docs for more info about SH coeff. storage and retrival formats being implementd.

    Examples:
        >>> cs_fmt = sc2cs(field)
        TO DO: show suitable output
    """

    rows = len(field)
    cols = len(field[0])

    if (rows!=cols) and (cols!=2*rows - 1):
        sc2cs.exit("Input neither in cs nor in sc format")
    elif cols == rows:
        cs = field
    else:
        c    = field[:, rows-1:cols]
        st   = numpy.transpose(numpy.fliplr(field[:, 0:rows-1]))
        z    = numpy.zeros([1,rows])
        s    = numpy.concatenate((st, z), axis=0)
        cs   = numpy.add(c, s)

    return(cs)

clm2cs(data_mat, lmax, sigma_flag=False)

Converts the format from CLM to |C\S| Under the hood uses the clm2sc and sc2cs function

Parameters:

Name Type Description Default
data_mat ndarray

list containing [degree; order; clm; slm; delta clm; delta slm; start data; end date]

 required
lmax int

Max Degree of the spherical harmonic expansion

 required
sigma_flag boolean

Flag to return the standard deviation data in |C\S| format or not. Defaults to False

 False

Returns:

Type Description

numpy.ndarray: Spherical Harmonic Coefficients in |C\S| format
Source code in pyshbundle/clm2cs.py 
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def clm2cs(data_mat: np.ndarray, lmax: int, sigma_flag=False):
    """Converts the format from CLM to |C\S|
    Under the hood uses the `clm2sc` and `sc2cs` function

    Args:
        data_mat (numpy.ndarray): list containing [degree;  order; clm; slm; delta clm; delta slm; start data; end date]
        lmax (int): Max Degree of the spherical harmonic expansion
        sigma_flag (boolean): Flag to return the standard deviation data in |C\S| format or not. Defaults to False

    Returns:
        numpy.ndarray: Spherical Harmonic Coefficients in |C\S| format

    """
    if sigma_flag:
        sc_mat, dev_sc = clm2sc(data_mat=data_mat, lmax=lmax, sigma_flag=True)
        return sc2cs(sc_mat), sc2cs.sc2cs(dev_sc)
    else:
        sc_mat = clm2sc(data_mat=data_mat, lmax=lmax, sigma_flag=False)
        return sc2cs(sc_mat)

clm2sc(data_mat, lmax, sigma_flag=False)

Converts the spherical harmonic coefficients from clm format to /S|C\ format

Parameters:

Name Type Description Default
data_mat ndarray

list containing [degree; order; clm; slm; delta clm; delta slm; start data; end date]

 required
lmax int

Max Degree of the spherical harmonic expansion

 required
sigma_flag boolean

Flag to return the standard deviation data in /S|C\ format or not. Defaults to False

 False

Returns:

Type Description

numpy.ndarray: Spherical Harmonic Coefficients in /S|C\ format
References

Refer to the SHBundle or PySHBundle docs for the different data storage and retrival formats.

Source code in pyshbundle/clm2sc.py 
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def clm2sc(data_mat: np.ndarray, lmax: int, sigma_flag=False):
    """Converts the spherical harmonic coefficients from clm format to /S|C\ format

    Args:
        data_mat (numpy.ndarray): list containing [degree;  order; clm; slm; delta clm; delta slm; start data; end date]
        lmax (int): Max Degree of the spherical harmonic expansion
        sigma_flag (boolean): Flag to return the standard deviation data in /S|C\ format or not. Defaults to False

    Returns:
        numpy.ndarray: Spherical Harmonic Coefficients in /S|C\ format

    References:
        Refer to the SHBundle or PySHBundle docs for the different data storage and retrival formats.

    """    

    sc_mat = np.zeros((lmax+1, 2*lmax + 2))
    dev_sc_mat = np.zeros((lmax+1, 2*lmax + 2))

    # as per the convention
    clm = data_mat[:, 2]
    slm = data_mat[:, 3]
    clm_std_dev = data_mat[:, 4]
    slm_std_dev = data_mat[:, 5]

    i = 0
    for index1 in range(0,lmax+1, 1):
        for index2 in range(0,index1+1, 1):

            sc_mat[index1, lmax-index2] = slm[i]
            sc_mat[index1, lmax+index2+1] = clm[i]

            dev_sc_mat[index1, lmax-index2] = slm_std_dev[i]
            dev_sc_mat[index1, lmax+index2+1] = clm_std_dev[i]

            i = i + 1

    sc_mat = np.delete(sc_mat, lmax, 1)
    dev_sc_mat = np.delete(dev_sc_mat, lmax, 1)

    if sigma_flag:
        return sc_mat, dev_sc_mat
    else:
        return sc_mat

klm2sc(data)

Converts the spherical harmonic coefficients from klm format to /S|C\ format

Parameters:

Name Type Description Default
data list

list containing [degree; order; clm; slm; delta clm; delta slm; start data; end date]

 required

Returns:

Type Description

np.ndarray: Spherical Harmonic Coefficients in /S|C\ format [[files or months]; [2-D matrix of /S|C\ format]]

np.ndarray: Standard Deviations of correcponding Spherical Harmonic Coefficients in /S|C\ format [[files or months]; [2-D matrix of /S|C\ format]]
Source code in pyshbundle/klm2sc.py 
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def klm2sc(data):
    """Converts the spherical harmonic coefficients from klm format to /S|C\ format

    Args:
        data (list): list containing [degree;  order; clm; slm; delta clm; delta slm; start data; end date]

    Returns:
        np.ndarray: Spherical Harmonic Coefficients in /S|C\ format [[files or months]; [2-D matrix of /S|C\ format]]
        np.ndarray: Standard Deviations of correcponding Spherical Harmonic Coefficients in /S|C\ format [[files or months]; [2-D matrix of /S|C\ format]]
    """
    # import pickle
    # with open("/path/saved_as_num", "rb") as pk:
    #     data=pickle.load(pk)

    ''' Read variables '''
    no_of_years = len(data[0])
    degree = data[0]
    clm = data[2]
    slm = data[3]
    clm_std_dev = data[4]
    slm_std_dev = data[5]

    lmax=degree[0][-1]
    degree_order=int((lmax+1)*(lmax+2)/2)

    ''' Count no of months of data '''
    month_count =0
    for i in range(0,len(data[0]),1):
        month_count= month_count+round(len(data[0][i])/degree_order)

    ''' klm >>> sc '''
    month = 0
    sc_mat = np.zeros([month_count,lmax+1,2*lmax+2])
    dev_sc_mat = np.zeros((month_count, lmax+1, 2*lmax + 2))

    for year in range(0,no_of_years,1):
        index2 =0
        for tile in range(0,int(len(clm[year])/degree_order),1):  
            for index1 in range(0,lmax+1,1):
                sc_mat[month,index1:,lmax-index1] = slm[year][(index2):(index2+lmax-index1+1)]
                sc_mat[month,index1:,index1+lmax] = clm[year][(index2):(index2+lmax-index1+1)]

                dev_sc_mat[month,index1:,lmax-index1] = slm_std_dev[year][(index2):(index2+lmax-index1+1)]
                dev_sc_mat[month,index1:,index1+lmax] = clm_std_dev[year][(index2):(index2+lmax-index1+1)]



                #print(month,'\t',index1,'\t',Lmax-index1,'\t',year,'\t',index2,'\t',index2+Lmax-index1+1)
                index2 = index2+lmax-index1+1
            month=month+1

    sc_mat=np.delete(sc_mat,lmax,axis=2)
    dev_sc_mat=np.delete(dev_sc_mat,lmax,axis=2)

    print('Conversion into clm format complete')
    return sc_mat, dev_sc_mat

klm2sc_new(data_mat, lmax, sigma_flag=False)

Converts the spherical harmonic coefficients from klm format to /S|C\ format

Parameters:

Name Type Description Default
data_mat ndarray

A 2-D matrix(numpy ndarray)

 required
lmax int

maximum degree of spherical harmonic expansion

 required
sigma_flag bool

Flag to return the associated standard deviation values. Defaults to False.

 False

Returns:

Type Description

np.ndarray: Spherical Harmonic Coefficients or/and associated standard deviations in /S|C\ format
Source code in pyshbundle/klm2sc.py 
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def klm2sc_new(data_mat: np.ndarray, lmax: int, sigma_flag=False):
    """Converts the spherical harmonic coefficients from klm format to /S|C\ format

    Args:
        data_mat (np.ndarray): A 2-D matrix(numpy ndarray)
        lmax (int): maximum degree of spherical harmonic expansion
        sigma_flag (bool, optional): Flag to return the associated standard deviation values. Defaults to False.

    Returns:
        np.ndarray: Spherical Harmonic Coefficients or/and associated standard deviations in /S|C\ format
    """
    sc_mat = np.zeros((lmax+1, 2*lmax + 2))
    dev_sc_mat = np.zeros((lmax+1, 2*lmax + 2))
    clm = data_mat[:, 2]
    slm = data_mat[:, 3]
    clm_std_dev = data_mat[:, 4]
    slm_std_dev = data_mat[:, 5]

    # first place the slm and then clm
    index2 =0
    for index1 in range(0,lmax+1,1):
        sc_mat[index1:, lmax-index1] = slm[(index2):(index2 + lmax-index1+1)]
        sc_mat[index1:, index1+lmax] = clm[(index2):(index2 + lmax-index1+1)]

        dev_sc_mat[index1:, lmax-index1] = slm_std_dev[(index2):(index2 + lmax-index1+1)]
        dev_sc_mat[index1:, index1+lmax] = clm_std_dev[(index2):(index2 + lmax-index1+1)]

        index2 = index2 + lmax-index1+1

    sc_mat=np.delete(sc_mat,lmax,axis=1)
    dev_sc_mat=np.delete(dev_sc_mat,lmax,axis=1)

    if sigma_flag:
        return sc_mat, dev_sc_mat
    else: 
        return sc_mat

Reference

  • Nico Sneeuw, Matthias Weigelt, Markus Antoni, Matthias Roth, Balaji Devaraju, et. al. (2021). SHBUNDLE 2021. http://www.gis.uni-stuttgart.de/research/projects/Bundles.