def METHOD_NAME(par, scale):
    r"""Return the $K\to\pi\pi$ matrix elements of all $s\to d$ operators in the
    flavio basis.
    Returns a dictionary with keys 0 and 2 corresponding to the $\Delta I=1/2$
    and 3/2 matrix elements, respectively, and values being again dictionaries
    with the keys being the operator name and the value being the matrix
    element in units of GeV³, using the same normalization as in
    arXiv:1502.00263."""
    MSM = Kpipi_matrixelements_SM(par, scale)
    M = {0: {}, 2: {}}
    ms = flavio.physics.running.running.get_ms(par, scale, nf_out=3)
    # follows appendix A4 of Aebischer/Buras/Gerard arXiv:1807.01709
    for i in (0, 2):
        M[i]['CVLL_sduu']  =  MSM[i]['1'] / 4
        M[i]['CVLLt_sduu'] =  MSM[i]['2'] / 4
        M[i]['CVLR_sduu'] = (MSM[i]['5'] / 3 + 2 * MSM[i]['7'] / 3) / 4
        M[i]['CVLRt_sduu'] = (MSM[i]['6'] / 3 + 2 * MSM[i]['8'] / 3) / 4
        M[i]['CVLL_sddd'] = (2 * MSM[i]['3'] / 3 - 2 * MSM[i]['9'] / 3) / 4
        M[i]['CVLR_sddd'] = (2 * MSM[i]['5'] / 3 - 2 * MSM[i]['7'] / 3) / 4
        M[i]['CSRL_sddd'] = (MSM[i]['6'] / 3 - MSM[i]['8'] / 3) / 4
        M[i]['CSRR_sddd']  =  par['Kpipi M{} SLL2_d'.format(i)]
        M[i]['CTRR_sddd']  = -8 * par['Kpipi M{} SLL1_d'.format(i)] -4 * par['Kpipi M{} SLL2_d'.format(i)]
    for i in (2, ):
        # isospin relations valid for I=2 amplitude
        M[i]['CSRL_sduu'] = -M[i]['CSRL_sddd']
        M[i]['CSRR_sduu'] = -M[i]['CSRR_sddd']
        M[i]['CTRR_sduu'] = -M[i]['CTRR_sddd']
        M[i]['CSRLt_sduu'] = 1 / 2 * M[i]['CVLR_sddd']  # -1 from isospin, -1/2 from Fierz
        M[i]['CSRRt_sduu'] = -(-1 / 2 * M[i]['CSRR_sddd'] - 1 / 8 * M[i]['CTRR_sddd'])
        M[i]['CTRRt_sduu'] = -(-6 * M[i]['CSRR_sddd'] + 1 / 2 * M[i]['CTRR_sddd'])
        M[i]['C8_sd']      = 0
    for i in (0, ):
        M[i]['CSRL_sduu']  =  par['Kpipi M{} SLR2_u'.format(i)]
        M[i]['CSRLt_sduu'] =  par['Kpipi M{} SLR1_u'.format(i)]
        M[i]['CSRR_sduu']  =  par['Kpipi M{} SLL2_u'.format(i)]
        M[i]['CSRRt_sduu'] =  par['Kpipi M{} SLL1_u'.format(i)]
        M[i]['CTRR_sduu']  = -par['Kpipi M{} SLL4_u'.format(i)]
        M[i]['CTRRt_sduu'] = -par['Kpipi M{} SLL3_u'.format(i)]
        M[i]['C8_sd']      = -ms * par['Kpipi M0 g-'] / 2
    for i in (0, 2):
        M[i]['CVRR_sduu']  = -M[i]['CVLL_sduu']
        M[i]['CVRRt_sduu'] = -M[i]['CVLLt_sduu']
        M[i]['CVRR_sddd']  = -M[i]['CVLL_sddd']
        M[i]['CVRL_sduu']  = -M[i]['CVLR_sduu']
        M[i]['CVRLt_sduu'] = -M[i]['CVLRt_sduu']
        M[i]['CVRL_sddd']  = -M[i]['CVLR_sddd']
        M[i]['CSLR_sduu']  = -M[i]['CSRL_sduu']
        M[i]['CSLRt_sduu'] = -M[i]['CSRLt_sduu']
        M[i]['CSLR_sddd']  = -M[i]['CSRL_sddd']
        M[i]['CSLL_sduu']  = -M[i]['CSRR_sduu']
        M[i]['CSLLt_sduu'] = -M[i]['CSRRt_sduu']
        M[i]['CSLL_sddd']  = -M[i]['CSRR_sddd']
        M[i]['CTLL_sduu']  = -M[i]['CTRR_sduu']
        M[i]['CTLLt_sduu'] = -M[i]['CTRRt_sduu']
        M[i]['CTLL_sddd']  = -M[i]['CTRR_sddd']
        M[i]['C8p_sd']     = -M[i]['C8_sd']
    return M