Build a matrix as described in the following paper [10.13140/RG.2.2.19275.55840](10.13140/RG.2.2.19275.55840)
Source:R/matrice_transition.R
build_stacked_matrix.RdBuild a matrix as described in the following paper [10.13140/RG.2.2.19275.55840](10.13140/RG.2.2.19275.55840)
References
Jamme J (2026). “Why not a little bit of bias? In the search of improving the risk-utility trade-off while releasing frequency tables protected with the cell key method.” In the 12th European Conference on Quality in Official Statistics. doi:10.13140/RG.2.2.19275.55840 .
Examples
build_stacked_matrix(15, 20, 5, 15, 5, 0)
#> An object of class "ptable"
#> Slot "tMatrix":
#> 0 6 7 8 9 10
#> 0 1.0000000000 0.0000000000 0.0000000000 0.000000000 0.000000000 0.000000000
#> 1 0.8681485784 0.0501440554 0.0311762362 0.019383305 0.012051250 0.007492668
#> 2 0.7517625092 0.0786861787 0.0540175380 0.037082662 0.025456997 0.017476086
#> 3 0.6461203432 0.0973495133 0.0710128889 0.051801290 0.037787136 0.027564325
#> 4 0.5171308449 0.1346429018 0.1011452874 0.074651872 0.054133813 0.038568203
#> 5 0.3982347304 0.1607829214 0.1254188358 0.095152628 0.070212407 0.050389729
#> 6 0.2783160440 0.2783160440 0.1093223993 0.084286680 0.064511670 0.049017048
#> 7 0.1995705717 0.1995705717 0.1995705717 0.092336495 0.072903979 0.057149472
#> 8 0.1473410952 0.1473410952 0.1473410952 0.147341095 0.090277421 0.074265302
#> 9 0.1056642206 0.1178376804 0.1178376804 0.117837680 0.117837680 0.089698507
#> 10 0.0652795345 0.1040352309 0.1040352309 0.104035231 0.104035231 0.104035231
#> 11 0.0347006914 0.0880062356 0.0921758133 0.092175813 0.092175813 0.092175813
#> 12 0.0159090462 0.0649634178 0.0733999213 0.080311273 0.085096476 0.085841111
#> 13 0.0062289460 0.0440453152 0.0537592605 0.063282684 0.071844609 0.078665048
#> 14 0.0021966545 0.0275772866 0.0365080572 0.046420864 0.056692423 0.066500384
#> 15 0.0007570619 0.0163115767 0.0233520153 0.032002333 0.041982445 0.052720894
#> 16 0.0000000000 0.0093769634 0.0143958967 0.021110292 0.029568465 0.039558730
#> 17 0.0000000000 0.0051337448 0.0084266862 0.013189610 0.019686098 0.028018179
#> 18 0.0000000000 0.0027316693 0.0047659186 0.007920995 0.012540864 0.018914280
#> 19 0.0000000000 0.0014071135 0.0025987409 0.004569361 0.007649035 0.012190359
#> 20 0.0000000000 0.0006989345 0.0013626425 0.002528376 0.004464942 0.007504199
#> 21 0.0000000000 0.0003335713 0.0006852734 0.001339599 0.002491849 0.004410688
#> 11 12 13 14 15 16
#> 0 0.000000000 0.000000000 0.00000000 0.000000000 0.0000000000 0.000000000
#> 1 0.004658442 0.002896309 0.00180073 0.001119575 0.0006960765 0.000432774
#> 2 0.011997186 0.008236005 0.00565395 0.003881397 0.0026645618 0.001829202
#> 3 0.020107161 0.014667434 0.01069935 0.007804785 0.0056933037 0.004153056
#> 4 0.026997468 0.018567334 0.01254610 0.008329159 0.0054328313 0.003481642
#> 5 0.035172663 0.023878307 0.01576657 0.010125248 0.0063241812 0.003841816
#> 6 0.036973074 0.027685572 0.02058027 0.015187202 0.0111259153 0.008091355
#> 7 0.044479137 0.034370324 0.02636902 0.020085729 0.0151902287 0.011405758
#> 8 0.060026038 0.047669472 0.03719529 0.028515596 0.0214794872 0.015896894
#> 9 0.076272054 0.063159049 0.05093257 0.039998667 0.0305904166 0.022783224
#> 10 0.082497117 0.071714589 0.06068724 0.049992907 0.0400904119 0.031296356
#> 11 0.092175813 0.078861694 0.06998383 0.060336293 0.0505369390 0.041123363
#> 12 0.085841111 0.085841111 0.07780235 0.070209895 0.0613561290 0.051924430
#> 13 0.083070549 0.083849607 0.08384961 0.078724657 0.0719263352 0.063378645
#> 14 0.074922212 0.081074510 0.08419175 0.084191755 0.0806546491 0.074276666
#> 15 0.063376261 0.072928856 0.08033430 0.084709375 0.0855048728 0.082618850
#> 16 0.050551602 0.061703034 0.07193780 0.080110009 0.0852109560 0.086573129
#> 17 0.038025309 0.049210546 0.06072901 0.071463911 0.0801917972 0.085807587
#> 18 0.027174827 0.037192757 0.04849138 0.060226191 0.0712559007 0.080310234
#> 19 0.018496307 0.026718508 0.03674498 0.048110803 0.0599716239 0.071171757
#> 20 0.012003481 0.018273614 0.02647622 0.036509173 0.0479139878 0.059846256
#> 21 0.007428919 0.011906423 0.01815822 0.026351280 0.0363886682 0.047815303
#> 17 18 19 20 21 22
#> 0 0.000000000 0.000000000 0.0000000000 0.0000000000 0.000000000 0.000000000
#> 1 0.000000000 0.000000000 0.0000000000 0.0000000000 0.000000000 0.000000000
#> 2 0.001255726 0.000000000 0.0000000000 0.0000000000 0.000000000 0.000000000
#> 3 0.003029501 0.002209910 0.0000000000 0.0000000000 0.000000000 0.000000000
#> 4 0.002192174 0.001356122 0.0008242429 0.0000000000 0.000000000 0.000000000
#> 5 0.002270056 0.001304467 0.0007291320 0.0003963056 0.000000000 0.000000000
#> 6 0.005841660 0.004186743 0.0029789003 0.0021040710 0.001475359 0.000000000
#> 7 0.008502901 0.006293516 0.0046248943 0.0033743978 0.002444387 0.001758042
#> 8 0.011559727 0.008259044 0.0057977473 0.0039988468 0.002709931 0.001804377
#> 9 0.016524750 0.011671977 0.0080286760 0.0053781735 0.003508338 0.002228893
#> 10 0.023783084 0.017593963 0.0126701081 0.0088821490 0.006061457 0.004026772
#> 11 0.032510053 0.024968710 0.0186304737 0.0135052014 0.009511031 0.006507341
#> 12 0.042553924 0.033772375 0.0259559958 0.0193182541 0.013923622 0.009718302
#> 13 0.053861187 0.044145530 0.0348959953 0.0266037224 0.019560818 0.013871060
#> 14 0.065699596 0.055816206 0.0455454737 0.0356958269 0.026870576 0.019427809
#> 15 0.076418088 0.067661607 0.0573478469 0.0465286941 0.036137110 0.026866736
#> 16 0.084013643 0.077874547 0.0689477776 0.0583074476 0.047098471 0.036338635
#> 17 0.087553601 0.085187312 0.0790366260 0.0699253179 0.058991996 0.047457440
#> 18 0.086225468 0.088189088 0.0859228672 0.0797475382 0.070508330 0.059385195
#> 19 0.080413364 0.086498276 0.0885819717 0.0863658209 0.080167278 0.070845300
#> 20 0.071141993 0.080487682 0.0866656852 0.0888135603 0.086621510 0.080405653
#> 21 0.059786608 0.071133976 0.0805353560 0.0867625160 0.088943464 0.086762526
#> 23 24 25 26 27 28
#> 0 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 1 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 2 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 3 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 4 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 5 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 6 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 7 0.000000000 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 8 0.001180445 0.0000000000 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 9 0.001378933 0.0008308286 0.000000000 0.000000000 0.0000000000 0.0000000000
#> 10 0.002604105 0.0016393821 0.001004671 0.000000000 0.0000000000 0.0000000000
#> 11 0.004325424 0.0027932088 0.001752377 0.001068073 0.0000000000 0.0000000000
#> 12 0.006568884 0.0042995773 0.002725400 0.001672918 0.0009944728 0.0000000000
#> 13 0.009486591 0.0062573026 0.003980581 0.002442208 0.0014450732 0.0008246705
#> 14 0.013491430 0.0089986914 0.005764857 0.003547192 0.0020963697 0.0011899777
#> 15 0.019120768 0.0130264040 0.008495181 0.005303321 0.0031692404 0.0018129701
#> 16 0.026779929 0.0188507773 0.012674421 0.008139655 0.0049930152 0.0029254914
#> 17 0.036405592 0.0266308158 0.018576052 0.012355916 0.0078369857 0.0047399716
#> 18 0.047646452 0.0364164462 0.026514240 0.018389732 0.0121502791 0.0076473633
#> 19 0.059605128 0.0477435681 0.036408668 0.026433422 0.0182709299 0.0120233804
#> 20 0.071033264 0.0597243339 0.047792002 0.036397661 0.0263819024 0.0181992332
#> 21 0.080535375 0.0711339975 0.059786602 0.047815295 0.0363886645 0.0263512790
#> 29 30 31 32 33
#> 0 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 1 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 2 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 3 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 4 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 5 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 6 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 7 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 8 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 9 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 10 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 11 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 12 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 13 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 14 0.0006487777 0.0000000000 0.0000000000 0.0000000000 0.0000000000
#> 15 0.0009927860 0.0005204095 0.0000000000 0.0000000000 0.0000000000
#> 16 0.0016372453 0.0008752008 0.0004468694 0.0000000000 0.0000000000
#> 17 0.0027337263 0.0015034427 0.0007884451 0.0003942832 0.0000000000
#> 18 0.0045851315 0.0026188252 0.0014248718 0.0007385157 0.0003646351
#> 19 0.0075327091 0.0044929798 0.0025513876 0.0013793580 0.0007099640
#> 20 0.0119485286 0.0074660361 0.0044399712 0.0025129528 0.0013536398
#> 21 0.0181582237 0.0119064197 0.0074289203 0.0044106858 0.0024918480
#> 34 35 36
#> 0 0.0000000000 0.0000000000 0.0000000000
#> 1 0.0000000000 0.0000000000 0.0000000000
#> 2 0.0000000000 0.0000000000 0.0000000000
#> 3 0.0000000000 0.0000000000 0.0000000000
#> 4 0.0000000000 0.0000000000 0.0000000000
#> 5 0.0000000000 0.0000000000 0.0000000000
#> 6 0.0000000000 0.0000000000 0.0000000000
#> 7 0.0000000000 0.0000000000 0.0000000000
#> 8 0.0000000000 0.0000000000 0.0000000000
#> 9 0.0000000000 0.0000000000 0.0000000000
#> 10 0.0000000000 0.0000000000 0.0000000000
#> 11 0.0000000000 0.0000000000 0.0000000000
#> 12 0.0000000000 0.0000000000 0.0000000000
#> 13 0.0000000000 0.0000000000 0.0000000000
#> 14 0.0000000000 0.0000000000 0.0000000000
#> 15 0.0000000000 0.0000000000 0.0000000000
#> 16 0.0000000000 0.0000000000 0.0000000000
#> 17 0.0000000000 0.0000000000 0.0000000000
#> 18 0.0000000000 0.0000000000 0.0000000000
#> 19 0.0003479001 0.0000000000 0.0000000000
#> 20 0.0006939639 0.0003385985 0.0000000000
#> 21 0.0013395994 0.0006852738 0.0003335726
#>
#> Slot "pClasses":
#> [1] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
#>
#> Slot "pTable":
#> i j p v p_int_lb p_int_ub type
#> <num> <num> <num> <num> <num> <num> <char>
#> 1: 0 0 1.00000000 0 0.0000000 1.0000000 all
#> 2: 1 0 0.86814858 -1 0.0000000 0.8681486 all
#> 3: 1 6 0.05014405 5 0.8681486 0.9182926 all
#> 4: 1 7 0.03117624 6 0.9182926 0.9494689 all
#> 5: 1 8 0.01938331 7 0.9494689 0.9688522 all
#> ---
#> 453: 21 32 0.00000099 11 0.9999989 0.9999999 all
#> 454: 21 33 0.00000010 12 0.9999999 1.0000000 all
#> 455: 21 34 0.00000001 13 1.0000000 1.0000000 all
#> 456: 21 35 0.00000001 14 1.0000000 1.0000000 all
#> 457: 21 36 0.00000001 15 1.0000000 1.0000000 all
#>
#> Slot "empResults":
#> i p_mean p_var p_sum p_stay
#> <num> <num> <num> <num> <num>
#> 1: 0 0.000000e+00 0.000000 1 1.00000000
#> 2: 1 -1.000000e-08 7.070678 1 0.00000000
#> 3: 2 -3.330669e-16 13.447100 1 0.00000000
#> 4: 3 2.220446e-16 18.935405 1 0.00000000
#> 5: 4 2.000000e-08 20.000000 1 0.00000000
#> 6: 5 1.000000e-08 20.000000 1 0.00000000
#> 7: 6 1.000000e-08 20.000000 1 0.27831605
#> 8: 7 1.000000e-08 20.000000 1 0.19957058
#> 9: 8 -2.000000e-08 20.000000 1 0.14734109
#> 10: 9 1.000000e-08 20.000000 1 0.11783768
#> 11: 10 1.000000e-08 20.000000 1 0.10403523
#> 12: 11 5.551115e-17 20.000000 1 0.09217581
#> 13: 12 -3.000000e-08 20.000000 1 0.08584111
#> 14: 13 -2.000000e-08 20.000000 1 0.08384960
#> 15: 14 5.000000e-08 20.000000 1 0.08419175
#> 16: 15 2.000000e-08 20.000000 1 0.08550488
#> 17: 16 2.000000e-08 20.000000 1 0.08657312
#> 18: 17 1.387779e-16 20.000000 1 0.08755360
#> 19: 18 -1.000000e-08 20.000000 1 0.08818909
#> 20: 19 -5.898060e-17 20.000000 1 0.08858198
#> 21: 20 -1.179612e-16 20.000000 1 0.08881356
#> 22: 21 1.000000e-08 5.000000 1 0.17841262
#> i p_mean p_var p_sum p_stay
#> <num> <num> <num> <num> <num>
#>
#> Slot "pParams":
#> An object of class "ptable_params"
#> Slot "D":
#> [1] 15
#>
#> Slot "V":
#> [1] 20
#>
#> Slot "js":
#> [1] 5
#>
#> Slot "ncat":
#> [1] 21
#>
#> Slot "pstay":
#> [1] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
#>
#> Slot "optim":
#> [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#>
#> Slot "mono":
#> [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE
#>
#> Slot "table":
#> [1] "cnts"
#>
#> Slot "icat":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
#>
#> Slot "step":
#> [1] 1
#>
#> Slot "type":
#> [1] "all"
#>
#> Slot "label":
#> [1] "D15V2000"
#>
#>
#> Slot "tStamp":
#> [1] "20260814095357"
#>
#> Slot "type":
#> [1] "all"
#>
#> Slot "table":
#> [1] "cnts"
#>