ZfѿdZddlZddlZddlZddlZdZdZdZdZ d7dZ d8dZ d Z d9d Z d Zd:d Zd ZdZdZdZdZdZd;dZdZdZddZdZdZ d?dZ!dejDzejDgfd Z#d!Z$d@d"Z%dAd#Z&d9d$Z'dBd%Z(d&Z)d'Z*d(Z+d)Z,d*Z-d+Z.dCd,Z/d-Z0dDd.Z1dEd/Z2d:d0Z3d1Z4d2Z5d3Z6d4Z7dFd5Z8d6Z9y)Gz&Miscellaneous utilities - independent.NiJxg3333MXAgHz'D@ctj|}t|tjr d||dkD<|S|dkDrd}|S)aCalculate the resulting coherence due to mis-registration (coregistration error). Reference: Equation (30) in Just and Bamler (1994); Equation (4.4.27) in Hanssen (2001). Parameters: mu - float / np.ndarray, mis-registration in the unit of resolution cell NOTE: the unit is resolution cell, NOT pixel size/spacing. Applicable to both SAR range and azimuth directions. Returns: coh - float / np.ndarray, coherence. r)npsinc isinstancendarray)mucohs L/home/exouser/operations/rsmas_insar/tools/MintPy/src/mintpy/utils/utils0.pymisregistration2coherencer !sH ''"+C"bjj!BF J 6C Jcd|jvr|dkDrd}|r tdt|dt|d}}t|dt|d}}|||dz zz}||zd z }|r*td |ztd |ztd |z|dk(r$t j |tj St j||| } |dk(r$t j | tj St j| |df} t j | tj S)aCalculate slant range distance from input attribute dict Parameters: atr : dict, including the following ROI_PAC attributes: STARTING_RANGE RANGE_PIXEL_SIZE LENGTH WIDTH dimension : int, choices = [0,1,2] 2 for 2d matrix, vary in range direction, constant in az direction, for radar coord only 1 for 1d matrix, in range direction, for radar coord file 0 for center value Returns: np.array (0, 1 or 2 D) : range distance between antenna and ground target in meters Y_FIRSTrzGinput file is geocoded, return center range distance for the whole areaSTARTING_RANGERANGE_PIXEL_SIZELENGTHWIDTHr@znear range : %.2f mzcenter range : %.2f mzfar range : %.2f m)num) keysprintfloatintrarrayfloat32linspacetile) atr dimension print_msgrange_ndRlengthwidthrange_frange_crange_xrange_xys r range_distancer):s$CHHJ9q=  [ \,-.c:L6M0NRGH &CL(9EFE!G $G #%G %12 %12 %12A~xx,,kk'76GA~xx,,777VQK0xx"**--r c >|rtnd}d|jvr|dkDr d}|d|dk(r/d|jvrt|d}|d|dd|St|d }t|d }t|jd t}t|d } t |d } ||| zz} t jt j|dz|dzz|| zdzz d|z|zz z dzt jz } t jt j|dz| dzz|| zdzz d|z| zz z dzt jz } | | zdz }|d| dd|d|dd|d| dd|dk(r|}|S|dk(r*t j| | | dt j}|S|dk(rt |d}|kt|dd}t jt j||zdz|dzz|| zdzz d||zz|zz z dzt jz }|St jt j| | | dt j|df}|Std|)aCalculate 2D matrix of incidence angle from ROI_PAC attributes, very accurate. Parameters: atr : dict - ROI_PAC attributes including the following items: STARTING_RANGE RANGE_PIXEL_SIZE EARTH_RADIUS HEIGHT WIDTH LENGTH #for dimension=2 CENTER_INCIDENCE_ANGLE #for dimension=0 dem : 2D array for height to calculate local incidence angle dimension : int, 2 for 2d matrix 1 for 1d array 0 for one center value print_msg : bool Returns: inc_angle : 2D np.array, incidence angle in degree for each pixel Example: dem = readfile.read('hgt.rdr')[0] atr = readfile.read_attribute('filt_fine.unw') inc_angle = ut.incidence_angle(atr, dem=dem) cyN)argskwargss r z!incidence_angle..xsr rrz9input file is geocoded, return center incident angle onlyCENTER_INCIDENCE_ANGLEzcenter incidence angle : z.4fz( degree (grabbed from metadata directly)rr EARTH_RADIUSHEIGHTrf@rznear incidence angle : z degreezfar incidence angle : rFALSE)rendpointdtyperFrr zun-supported dimension input: )rrrgetr2rrpiarccosrrr)r Exception)rdemrr vprint inc_angler!r"rHr$r% inc_angle_n inc_angle_f inc_angle_cr# range_dists r incidence_anglerGcs* U%AFCHHJ9q= JK A~2chhj@#678 *9S/9abcC()*G s%& 'B cggnl34A c(mA G EU "G55299adWaZ&71Q3(&BQqS[%QRRV[[\^\a\aaK55299adWaZ&71Q3(&BQqS[%QRRV[[\^\a\aaK,3K &{3&7w ?@ &{3&7w ?@ &{3&7w ?@A~ & # aKK [e)0 D  aS]# ?'qEJJQsUQJQ,F!A#PQ,Q,-quIj,@,B"CCFKLLNEERI   K%5>% eS! &&hun% & &&  :!] : & &sBB%B##B, cddlm}|jdt|dd|dj dk(d}|j d}|S) aConvert UTM Zone string to EPSG code. Reference: https://docs.up42.com/data/reference/utm#utm-wgs84 https://pyproj4.github.io/pyproj/stable/examples.html#initializing-crs Parameters: utm_zone - str, atr['UTM_ZONE'], comprises a zone number and a hemisphere, e.g. 11N, 36S, etc. Returns: epsg_code - str, EPSG code Examples: epsg_code = utm_zone2epsg_code('11N') rCRSutmNS)projzonesouthr)pyprojrp from_dictrupper to_authority)utm_zonerpcrs epsg_codes r utm_zone2epsg_coder~s[ --HSbM""##%, C   "1%I r cnddlm}|j|}|j}|st d|d|S)aConvert EPSG code to UTM Zone string. Reference: https://docs.up42.com/data/reference/utm#utm-wgs84 https://pyproj4.github.io/pyproj/stable/examples.html#initializing-crs Parameters: epsg_code - str / int, EPSG code Returns: utm_zone - str, atr['UTM_ZONE'], comprises a zone number and a hemisphere, e.g. 11N, 36S, etc. None for a EPSG code not in a UTM coordnate system Examples: utm_zone = epsg_code2utm_zone('32736') rrozWARNING: input EPSG code (z.) is NOT a UTM zone, return None and continue.)rwrp from_epsgr{r)r}rpr|r{s r epsg_code2utm_zoner$s9 -- "C||H  *9+5cde Or cBddlm}ddlm}m}|j |}|j }|js|jddk(r||fS||j}|d} |j|| } | j||\}}||fS)aConvert x, y in the projection coordinates of the file to lat/lon in degree. Similar functionality also exists in utm.to_latlon() at: https://github.com/Turbo87/utm#utm-to-latitudelongitude Parameters: infile - str, GDAL supported file path x/y - scalar or 1/2D np.ndarray, coordinates in x and y direction Returns: y/x - scalar or 1/2D np.ndarray, coordinates in latitutde and longitude r)gdal)Proj Transformerunitdegreez epsg:4326) osgeorrwrrOpen GetSpatialRef IsProjected GetAttrValue GetProjection from_proj transform) infilerkyrrrdssrsp_inp_out transformers r to_latlonr9s( 6 B   C OO C$4$4V$<$H!t    " #D  E''e4K  A &DAq a4Kr cLddl}t|ddd}|ddjdk(}|jt j |t j |||d\}}t d||fDr |j}|j}||fS) a)Convert UTM easting/northing in meters to lat/lon in degrees. Parameters: meta - dict, mintpy attributes that includes: UTM_ZONE easting - scalar/list/tuple/1-2D np.ndarray, UTM coordinates in x direction northing - scalar/list/tuple/1-2D np.ndarray, UTM coordinates in y direction Returns: lat - scalar/list/tuple/1-2D np.ndarray, WGS 84 coordinates in y direction lon - scalar/list/tuple/1-2D np.ndarray, WGS 84 coordinates in x direction rNUTM_ZONErrNF)northernstrictc3HK|]}t|ttfywr,rlisttuple.0rks r zutm2latlon..ls EA:a$ ' E ")rqrryrrranytolist)metaeastingnorthingrqzone_numrlatlons r utm2latlonrWs4 #CR()HJ#))+s2H }}RXXg.0BH&.u>HC E'81D EEjjljjl 8Or cddl}t|ddd}|jtj|tj||dd\}}t d||fDr |j }|j }||fS)a4Convert latitude/longitude in degrees to UTM easting/northing in meters. Parameters: meta - dict, mintpy attributes that includes: UTM_ZONE lat - scalar/list/tuple/1-2D np.ndarray, WGS 84 coordinates in y direction lon - scalar/list/tuple/1-2D np.ndarray, WGS 84 coordinates in x direction Returns: easting - scalar/list/tuple/1-2D np.ndarray, UTM coordinates in x direction northing - scalar/list/tuple/1-2D np.ndarray, UTM coordinates in y direction rNrrr)force_zone_numberr4c3HK|]}t|ttfywr,rrs r rzlatlon2utm..s D[>#a&Q-QA">?D @ @ diik !h(h(T)_%CFSL(AAT)_%CFSL(AAa&3q6/a&3q6/h'A+..h'A+.. >$tGBJ"6"&tGBJ"6#78JD$!^;;tTwFD;;tTwFD8 DE EH~((/J$))+4M F G#D$FJD$0 ooo 88D +D 88D +D u}q 99>%=D%=D : YY!^%5()D%5()D :q % %  @ @sJ0;5J=0J:=Kcd|jvr tdt|dt|d}}dDcgc]}t|d|}}dDcgc]}t|d|}}t j ||ftj }t j ||ftj }t|D]n}t|D]^}|d ||d |d z z|z z||d |d z z|z z|||f<|d ||d |d z z|z z||d |d z z|z z|||f<`p||fScc}wcc}w) abGet 2D array of lat and lon for metadata dict in radar-coord. WARNING: This is a rough lat/lon value, NOT accurate! Parameters: meta : dict, including LENGTH, WIDTH and LAT/LON_REF1/2/3/4 Returns: lats : 2D np.array for latitude in size of (length, width) lons : 2D np.array for longitude in size of (length, width) rzJInput file is in geo-coordinates, use more accurate get_lat_lon() instead.rr)rr4rLAT_REFLON_REFrIrrr4)rr=rrrzerosrrange) rr#r$irrrrjs r get_lat_lon_rdcrsDIIKdeeX'T']);EF09 :1E$}% & :D :09 :1E$}% & :D : ((F5>"** 5C ((F5>"** 5C 6]\u \AAwDGd1g$5!6u!<.(s7AqDIIK7c3BK|]}|jvywr,rrs r rz)get_lalo_digit4display..+s9adiik!9rg?g^@g߼xV42?g{Gz?rgMb`?rg-C6*?gh㈵>)rallminabsrrcosdeg2rad) r coord_unitdigit geo_step_keys rdr_step_keysrkmin_step rg_pix_size az_pix_sizes ` r get_lalo_digit4displayrs2W%4 L/"8, +-AB  77 7GACd1g/GHH 9=9 9%7 89BFF2::b>H"H  L   L   L  L)* L%HsC9cd}d}|dz}|dz}dgdz}tt|Dcgc]}dgdz }}|ddz|ddzz}||z } d|z |ddzz|z } | | z|z dz } || z| zd | dzzz } d| ztj| d | zzzd z} | d| zd| z zz}tj|dz|| zz}|||z| z zd |zz }tj||z|dzz|z }|tj|z||zz }tj|d||d<tj|d|d|d<||zdz tj|dz|ddzzz|z |d<tj |d|d<tj |d|d<|d|d<|d}|d|z d zz}tj tjtj|d|dzz|dzz }tj|dz|dzz tj|dz|dzz z}dtj|z }||fScc}w) aCalculate satellite height and ellipsoid local radius from orbital state vector. This is a simplified version of the following functions from ISCE-2: + isce.isceobj.Planet.xyz_to_llh() + isce.isceobj.Ellipsoid.localRadius() Parameters: xyz - tuple of 3 float, orbital state vector Reference: height - float, satellite altitude in m radius - float, Earth radius in m g@TXAgk{?r4rrrg?g@g@rgUUUUUU?r) rrhmathsqrtatan2degreesatantanradiansrrL)xyzrbe2a2e4r_llhrd_llhxy2pqrAstuvwkDr^blatgargradiuss r xyz_to_local_radiusr ?s A B AB QBSUE!#c(O ,qaSU ,E , a&!)c!fai C  A bCFAI"A QrA Q b1a4i A a$))AaL) )g6A R!Vbd]A !Q$a- A a!eaiBF#A !a%!Q$,!#A DIIcNa"f%Azz#a&!$E!Hzz#a&#a&)E!HB tyyAA )9::Q>E!H||E!H%E!H||E!H%E!HQxE!H 1XF S2XOA 99dhht||E!H56A=1D FD 88D>1 q!t #(9AqD(@ AC 499S> !F 6>5 -s I9cb|dk(r|dz }n|dz}|tj|dz dzz}|S)a3Convert the azimuth angle of the LOS vector to the one of the orbit flight vector. Parameters: los_az_angle - np.ndarray or float, azimuth angle of the LOS vector from the ground to the SAR platform measured from the north with anti-clockwise direction as positive, in the unit of degrees Returns: orb_az_angle - np.ndarray or float, azimuth angle of the SAR platform along track/orbit direction measured from the north with anti-clockwise direction as positive, in the unit of degrees rightZv@rround) los_az_anglelook_direction orb_az_angles r los2orbit_azimuth_angler*sC #b( #b( BHH\D01D88L r cn|dk(r |dz dz}n|dzdz}|tj|dz dzz}|S)aConvert azimuth angle from ISCE los.rdr band2 into satellite orbit heading angle ISCE-2 los.* file band2 is azimuth angle of LOS vector from ground target to the satellite measured from the north in anti-clockwise as positive Below are typical values in deg for satellites with near-polar orbit: ascending orbit: heading angle of -12 and azimuth angle of 102 descending orbit: heading angle of -168 and azimuth angle of -102 r"r#rrr$r%)az_angler( head_angles r azimuth2heading_angler.sK mr) mr) "((:,-44J r cn|dk(r |dz dz}n|dzdz}|tj|dz dzz}|S)zNConvert satellite orbit heading angle into azimuth angle as defined in ISCE-2.r"r#rrr$r%)r-r(r,s r heading2azimuth_angler0sG Or)Or) D)D00H Or c|| t|}ntd|d|tjtj|ztjtj|zdz|tjtj|ztj tj|zz|tj tj|zz}|S)aProject east/north/up motion into the line-of-sight (LOS) direction defined by incidence/azimuth angle. Parameters: v_e - np.ndarray or float, displacement in east-west direction, east as positive v_n - np.ndarray or float, displacement in north-south direction, north as positive v_u - np.ndarray or float, displacement in vertical direction, up as positive inc_angle - np.ndarray or float, incidence angle from vertical, in the unit of degrees head_angle - np.ndarray or float, azimuth angle of the SAR platform along track direction measured from the north with clockwise direction as positive, in the unit of degrees az_angle - np.ndarray or float, azimuth angle of the LOS vector from the ground to the SAR platform measured from the north with anti-clockwise direction as positive, in the unit of degrees head_angle = 90 - az_angle Returns: v_los - np.ndarray or float, displacement in LOS direction, motion toward satellite as positive zinvalid az_angle: !rr)r0rrrLrr)v_ev_nv_ur@r-r,v_loss r enu2losr7s  !,Z8H1(1=> >RVVBJJy122RVVBJJxs,BJJrzz$677#=H Or c gd}||vrtd|d||dk(r | tdd}|dvrtjtj|tjtj|zdztjtj|tjtj|ztjtj|g}|S|d vrtjtj|tjtj|zdztjtj|tjtj|ztj |g}|S|d vrStj |tj |tjtj|g}|S|d vrtt |}tjtj|dztjtj|tj |g}|S|d vrgd }|S|dvrgtjtj|dztjtj|tj |g}|S)aGet the unit vector for the component of interest. Parameters: los_inc_angle - np.ndarray or float, incidence angle from vertical, in the unit of degrees los_az_angle - np.ndarray or float, azimuth angle of the LOS vector from the ground to the SAR platform measured from the north with anti-clockwise direction as positive, in the unit of degrees comp - str, component of interest, choose among the following values: enu2los, en2los, hz2los, u2los, up2los, orb(it)_az, vert, horz horz_az_angle - np.ndarray or float, azimuth angle of the horizontal direction of interest measured from the north with anti-clockwise direction as positive, in the unit of degrees Returns: unit_vec - list(np.ndarray/float), unit vector of the ENU component for the component of interest )r7en2loshz2loshorz2losu2losvert2losr:hz2azorb_azorbit_azvertverticalhorz horizontalzun-recognized comp input: z. choose from: rJNz'comp=horz requires horz_az_angle input!)r7rr)r@rArB)rCrD)r:rErFrG)rHrI)rrr)rJrK)rrrLrr zeros_liker*) los_inc_angler'comp horz_az_anglecompsunit_vecr)s r %get_unit_vector4component_of_interestrRsi E  55dV;KE7STT v~-/BCCH { FF2::m, -rzz,7O0P PSU U FF2::m, -rzz,7O0P P FF2::m, - L OA 1 1 FF2::m, -rzz,7O0P PSU U FF2::m, -rzz,7O0P P MM- ( > O3 & & MM- ( MM- ( FF2::m, - 0 O% 9 9.|< FF2::l+ ,r 1 FF2::l+ , MM, '  O % % O ' ' FF2::m, - 2 FF2::m, - MM- (  Or gcx|\}}tj|}|tj||z ||z z}|S)zWrap data into a range. Parameters: data_in : np.array, array to be wrapped wrap_range : list of 2 float, range to be wrapped into Returns: data : np.array, data after wrapping )rrmod)data_in wrap_rangew0w1datas r wraprZ.s= FB 88G D tby"r'* *D Kr c tjtjd|ztjtjd|zz}|S)a Calculate the difference between two input wrapped phase. Parameters: pha1 - np.ndarray, (un)wrapped phase pha2 - np.ndarray / float, (un)wrapped phase Returns: pha_diff - np.ndarray, wrapped phase difference for (pha1 - pha2) y)rangleexpconj)pha1pha2pha_diffs r diff_wrapped_phaserb:s?xxsTz*RWWRVVC$J5G-HHIH Or ctj|}g}t|d}tj|s:|j |||z}t|d}tj|s:|S)aHGet all connected component with number of pixels larger than threshold Parameters: mask_in : 2D np.array with zero as background and non-zero as foreground min_num_pixel : int/float, minimum number of pixels to be identified and output Returns: mask_out : list of 2D np.array in np.bool_ format @) min_num_pixel)rrget_largest_conn_componentrappend)mask_inremask_outmask_ccs r get_all_conn_componentsrkEsj hhwGH(DGffgX 7,WCHffgX Or cxddlm}ddlm}t j |j tj}|j|d}t jt j|jdd}||kr|St jt j|jdddz}||k(}|rh|jddddg\} } | dj|| dj|| d j||z |j|S) aExtract the largest connected component from an 2D array with zero as background value Parameters: mask_in : 2D np.array with zero as background and non-zero as foreground min_num_pixel : int/float, minimum number of pixels to be identified and output display : bool, display the result or not. Returns: mask_out : 2D np.array in np.bool_ format rN)ndimagerrr)nrowsncolsfigsizer4)matplotlib.pyplotpyplotscipyrmrrshapebool_labelmaxbincountflattenargmaxsubplotsimshowshow) rhredisplaypltrmrilabels num_pixel max_label_axs r rfrfUs$xx rxx0H ]]7 #A &Fr{{6>>#34QR89I=  "++fnn&67;?G7#++I6H Or cddlm}m}|\}}|jd||fd}|j |j |ddt j|t j}|S)arCreate a 2D mask (numpy array in binary) from a polygon. Link: https://stackoverflow.com/questions/3654289/scipy-create-2d-polygon-mask Parameters: polygon - list of tuples of 2 int, e.g. [(x1, y1), (x2, y2), ...] shape - list/tuple of 2 int, for length and width Returns: mask - 2D np.ndarray in bool in size of (length, width) r)Image ImageDrawLr)outlinefillrI) PILrrnewDrawrrrrv)rrurrr#r$imgmasks r polygon2maskrs]%MFE ))C%! ,C NN3; 88Crxx (D Kr cz|\}}tj| ||z | ||z f\}}|dz|dzz|dzk}|S)z5Get mask of pixels within circle defined by (x, y, r)r4)rogrid) rkrrrur#r$rrcmasks r get_circular_maskrsZMFE XXqbkbqj!"FB URU]fai 'E Lr ct|d}t|d}t|tr|}n3t|tr|}n |j ddj }|Dcgc] }t |}} t|d}t|d}tt|d}td|||fztj| ||z | ||z f\} } | dz| dzz|dzk} | Scc}w# t|d} t|d} tt|d}tj| t|d z t|d z }tj| t|d z t|d z }td j| | |n7#td|ztdtdtdYYyxYwY/xYw)aReturn Index of Elements within a Circle centered at input pixel Parameters: atr : dictionary containing the following attributes: WIDT LENGTH circle_par : string in the format of 'y,x,radius' i.e. '200,300,20' for radar coord '31.0214,130.5699,20' for geo coord Returns: idx : 2D np.array in bool type mask matrix for those pixel falling into the circle defined by circle_par Examples: idx_mat = ut.circle_index(atr, '200,300,20') idx_mat = ut.circle_index(atr, '31.0214,130.5699,20') rrrrrrr4z+Input circle index in y/x coord: %d, %d, %drrrSrz7Input circle index in lat/lon coord: {:.4f}, {:.4f}, {}z* ERROR: Unrecognized circle index format: zSupported format:z4--circle 200,300,20 for radar coord inputz5--circle 31.0214,130.5699,20 for geo coord input ) rrrrreplacesplitrKrrrrintformatr)r circle_parr$r#cir_parrc_yc_xrc_latc_lonrrkrs r circle_indexrs G E X F*e$ J %$$S#.446&'!s1v'G''!*o'!*oU71:&' ;sC>PPQ" 88SDOcT%)^3 4DAq Q$A+ "C J5( '!*%E'!*%Ewqz*+F''5s9~!66%H :NNOC''5s9~!66%H :NNOC ''-veUF'C E  ? J K % & H I J K Es2'C7.is_exes)ww~~e$B5"'')BBr rPATH"N)rcrdrenvironpathseprr)programrrdexe_files r whichrsC ww}}Wa '?N  JJv&,,RZZ8 D::c?Dww||D'2Hh  r cd}|dkrd}|r tdd|ddfS ddlm}m}t t j ||}|dkr.d}td td t j n|rtd |z ||||fS#tdtd d}d|ddfcYSxYw#||ddfcYSxYw) aECheck parallel option based file num and installed module Link: https://joblib.readthedocs.io/en/latest/parallel.html Examples: num_cores, inps.parallel, Parallel, delayed = ut.check_parallel(len(file_list)) Parallel(n_jobs=num_cores)(delayed(subset_file)(file, vars(inps)) for file in file_list) TrFz2parallel processing is disabled for one input fileNr)ParalleldelayedzCan not import joblibzparallel is disabled.zNparallel processing is disabled because min of the following two numbers <= 1:z&available cpu number of the computer: z¶llel processing using %d cores ...)rjoblibrrrrc cpu_count)file_numr maxParallelNumenable_parallelrr num_coress r check_parallelr+sO1}  F G/4--.,BLLNHn=IA~ ^_ 6r||~6FGH  6)DE6/8W<cz|}|D])}|jdsd|vr |d|dz }"|d|z }+t|y)zprint the command line with "" for arguments containing *. Parameters: script_name - str, e.g. prep_isce.py args - list(str), list of input arguments -*z "rrN)rr) script_namer.cmdrs r print_command_linerSsZ C~~c"scz RuA; C Qse9 C  #J r ctj|}|jdkDr!|jd}|j |d}|[tj |d}|jdk(r5tj |j ddd|jdf}tj tj||z d|z }|S)aCompute the median absolute deviation (MAD) of the data along the LAST axis. This function is also available in the following packages: + statsmodels.robust.mad() https://www.statsmodels.org/dev/generated/statsmodels.robust.scale.mad.html + scipy.stats.median_abs_deviation() since v1.5.0 https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.median_abs_deviation.html The implementation here is preferred because we would like to: 1. omit the NaN value in the data for the median and MAD calculation 2. scale the returned value to be comparable with standard deviation (STD) for easy interpretation with 1/2/3-sigma rule. While statsmodels could not handle the NaN value in the data; and scipy does not hebave as desired in the default setting (propagate nan and do not scale). The following two are equivalent for a 2D np.ndarray X: + mintpy.utils.utils0.median_abs_deviation(X) + scipy.stats.median_abs_deviation(X, axis=-1, center=np.nanmedian, scale=0.67449, nan_policy='omit') Parameters: data - 1/2D np.ndarray, input array center - 0/1D np.ndarray or None scale - float, the normalization constant Returns: mad - 0/1D np.ndarray r4rrr)axisr)rrrrur nanmedianrr)rYcenterscalentimemads r median_abs_deviationrgs4 88D>D yy1} 1 ||E2&~d, 99>WWV^^B2Q 1 4FGF ,,rvvdVm,2 6 >C Jr c^|tj|}t||}|||zz}|S)zvcalculate rms_threshold based on the standardized residual Outlier detection with median absolute deviation. )r)rrr)rYrcutoffr thresholds r median_abs_deviation_thresholdrs7 ~d# tF 3C#%I r ctj|j}|gtj|j}|j|jk7r&t d|jd|jd||z}|tj |}tj tj|dz|jdz z }|S)z5Calculate the root-mean-square error between x and y.z!Input x & y have different size: z vs. r2r4r)rrrzsizerisnanrsum)rkrrmses r root_mean_sq_errorrs  A} HHQK   ! 66QVV @affXUVWX X Q 288A;,A 77266!Q$<166A:. /D Kr c ttjtjt |}t || }||k\r|}|S|d|zz}|S)z@Return the most significant digit of input number and ceiling it rrfloorlog10rr&)rkrx_roundx_ceils r ceil_to_1rsX #a&)* +EAvG!| M2u9$ Mr c ttjtjt |}t || S)z1Return the most significant digit of input numberr )rkrs r round_to_1rs1 #a&)* +E UF r c|tj|dzdzdz}|jtjS)zfRound a float up to the next odd integer . Link: https://stackoverflow.com/questions/31648729 r4r)rceilastypeint16)rkrs r round_up_to_oddrs2  a!aA 88BHH r ctjdtjtj|}tj|}|S)z7Given a number x, find the highest power of 2 that <= xr4)rpowerr log2r)rkress r highest_power_of_2rs5 ((1bhhrwwqz* +C ((3-C Jr cddlm}||}|j|Dcgc]}|d }}|dk(r|d}|Scc}w)zReturn the k most common item in the list L. Examples: 5, 8 = most_common([4,5,5,5,5,8,8,8,9], k=2) 'duck' = most_common(['goose','duck','duck','dog']) 'goose' = most_common(['goose','duck','duck','goose']) r)Counterr) collectionsr most_common)rrrcntritem_mms r rrsJ$ !*C __Q/0qt0G0Av!* N1s <c: t|y#t$rYywxYw)a Check string is a number. Not using str.isnumeric() because it can not handle floating point nor negative sign. Link: https://elearning.wsldp.com/python3/python-check-string-is-a-number/ Parameters: string - str, a string Returns: True/False TF)rr)strings r is_numberr#s# f  s  )r4T)Nr4T)Fr,)NNr4rr)r)r")NN)r7N)rd)rdF)linear)rT)NgLTo l?)Ng@)r):__doc__rrcrnumpyrSPEED_OF_LIGHTr2Kr r)rGrQrUr`rmr~rrrrrrrrrr r*r.r0r7r:r>rRr;rZrbrkrfrrrrrrrrrrrrrrrrrrr#r-r r r*s<,&   2&.RIX F *6,*<82 L^4$$'V.J $8  BN""%%i/   8@B$3p3"%6P (*Z      r