= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = COMP-U-STAT = = = = = = = = STATISTICAL PATTERN GENERATOR AND MATHEMATICAL TREND ANALYZER = = = = = = = = (c) Copyright 2017 by James Ervin Glover, Ph.D. = = = = All Rights Reserved = = = = = = = = = = = = Part IV(a) ( STAT 400 ----> STAT 428 ) = = = = = = = = = = = = The COMP-U-STAT System consists of a cluster of more than 3706 = = = = modular programs, providing the analyst with a clear and distinct = = = = scientific and mathematical edge in generating novel and useful = = = = statistical patterns for analyzing trends from random variables. = = = = The following is a glossary describing the functions of all = = = = routines in the sequence. There are many statistical applications = = = = of the COMP-U-STAT cluster. Please see available DEMO Diskettes, = = = = provided upon request, for numerous examples of output files. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ====================================================================== * * * GLOSSARY OF COMP-U-STAT PROGRAMS 400 ---> 428 * * * ====================================================================== -- L 400 -- READS A SEQUENCE OF IMAX BASE EVENTS AND A SEQUENCE OF LMAX TEST EVENTS AND DETERMINES, FOR A SELECTED EVENT NUMBER, JMAX, AMONG THE SEQUENCE OF BASE EVENTS AND A DESIRED NUMBER OF ELEMENTS IN THE RANGE IN THAT EVENT, A SUBSEQUENCE OF OF TEST EVENTS WHICH CONTAIN BETWEEN q1 > 0 AND q2 < K0 ELEMENTS FALLING WITHIN A SELECTED RANGE OF VALUES FOR EACH OF THE K0 COLUMNS PER TEST EVENT. THE RANGE < A(JMAX,J) - EPSILON , A(JMAX,J) + EPSILON > FOR EACH COLUMN INDEX J = 1 , ... , K0 , AS WELL AS, A DESIRED NON-NEGATIVE INTEGRAL VALUE OF EPSILON FOR A GIVEN ELEMENT A(I,J) SERVE AS THE FILTERING CRITERIA FOR TEST EVENTS. EACH FAVORABLE TEST EVENT IS FILTERED BASED UPON THESE CRITERIA. THE RESULTING MATRIX IS DESIGNED TO INDICATE WHICH ELEMENTS ARE MOST LIKELY TO OCCUR FOLLOWING EACH OF THE K0 ELEMENTS OF THE DESIRED FINAL EVENT. THE ROUTINE ALSO DETERMINES THE SET OF ELEMENTS IN COMMON BETWEEN THE SET OF TEST EVENTS AND THE SET OF ELEMENTS OF THE EVENT FOLLOWING THE DESIRED FINAL EVENT, FOR UP TO 500 EVENTS. ============================================================================== -- L 401 -- READS A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES K0 SUBGROUPS OF EVENTS FROM EACH PERMUTATION, WHERE THE ELEMENTS OF EACH PERMUTATION ARE PRESUMED TO BE LISTED LEXICOGRAPHICALLY. THE AVERAGE INTEGRAL VALUE OF EACH OF THE K0 SUBGROUPS IS DETERMINED FOR EACH OF THE PNUM PERMUTATIONS AND THESE AVERAGES ARE PRINTED AS A SEQUENCE OF HIGH- PROBABILITY K0-ELEMENT EVENTS. PNUM MAY RANGE BETWEEN 1 AND 100 AND THE MAXIMUM VALUE OF L0 IS 51. MOREOVER, IT IS PRESUMED THAT THE NUMBER OF ELEMENTS IN EACH INPUT PERMUTATION IS DIVISIBLE BY K0. EACH GENERATED K0-ELEMENT HIGH-PROBABILITY EVENT IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0-ELEMENT BASE EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED AND ENUMERATED. ============================================================================== -- L 402 -- READS A SEQUENCE OF TEST EVENTS AND MULTIPLIES EACH ELEMENT OF EACH COLUMN BY THE CONSTANT (+/-) 1 , AS DETERMINED BY AN INPUT SEQUENCE OF VECTORS WHOSE ELEMENTS EQUAL (+/-) 1. ELEMENTS OF EACH TEST EVENT ARE MULTIPLIED, COLUMNWISE, BY THE CORRESPONDING ELEMENTS OF EACH TRANSLATION VECTOR OF K0 VALUES. THIS PROCESS IS REPEATED ANY DESIRED NUMBER OF TIMES, THUS CREATING A SEQUENCE OF NEW TEST EVENTS. EACH EXECUTION PROCESSES UP TO 30 EVENTS, WITH J0 DESIRED VECTOR VALUES BEING READ FROM AN INPUT FILE TO DETERMINE J0 CYCLES. STAT402 IS A VARIANT OF THE ROUTINE STAT282, BUT THE ELEMENTS OF THE INITIAL TEST EVENTS ARE EITHER (+/-) 1 OR 0 AND THE ELEMENTS OF THE TRANSLATION VECTORS ARE (+/-) 1. STAT402.INP <===> INITIAL TEST EVENTS STAT402.IN2 <===> TRANSLATION VECTORS ============================================================================== -- L 403 -- READS A SEQUENCE OF TEST EVENTS AND ADDS TO EACH ELEMENT OF EACH COLUMN THE CONSTANT 0 OR (+/-) 1 , AS DETERMINED BY AN INPUT SEQUENCE OF VECTORS WHOSE ELEMENTS EQUAL 0 OR (+/-) 1. ELEMENTS OF EACH TEST EVENT ARE ADDED, COLUMNWISE, TO THE CORRESPONDING ELEMENTS OF EACH TRANSLATION VECTOR OF K0 VALUES. THIS PROCESS IS REPEATED ANY DESIRED NUMBER OF TIMES, THUS CREATING A SEQUENCE OF NEW TEST EVENTS. EACH EXECUTION PROCESSES UP TO 30 EVENTS, WITH J0 DESIRED VECTOR VALUES BEING READ FROM AN INPUT FILE TO DETERMINE J0 CYCLES. STAT403 IS A VARIANT OF THE ROUTINE STAT402, BUT THE ELEMENTS OF THE INITIAL TEST EVENTS ARE IN THE SET < 1 , ... , L0 > AND THE ELEMENTS OF THE TRANSLATION VECTORS ARE EITHER 0 OR (+/-) 1 OR ANY DESIRED INTEGER SELECTED BY THE ANALYST IN STAT403.IN2. STAT403.INP <===> INITIAL TEST EVENTS STAT403.IN2 <===> TRANSLATION VECTORS ============================================================================== -- L 404 -- READS A SEQUENCE OF TEST EVENTS AND ADDS TO EACH ELEMENT OF EACH COLUMN THE CONSTANT 0 OR (+/-) 1 , AS DETERMINED BY AN INPUT SEQUENCE OF VECTORS WHOSE ELEMENTS EQUAL 0 OR (+/-) 1. ELEMENTS OF EACH TEST EVENT ARE ADDED, COLUMNWISE, TO THE CORRESPONDING ELEMENTS OF EACH TRANSLATION VECTOR OF K0 VALUES. THIS PROCESS IS REPEATED ANY DESIRED NUMBER OF TIMES, THUS CREATING A SEQUENCE OF NEW TEST EVENTS. EACH EXECUTION PROCESSES UP TO 30 EVENTS, WITH J0 DESIRED VECTOR VALUES BEING READ FROM AN INPUT FILE TO DETERMINE J0 CYCLES. STAT404 IS A VARIANT OF THE ROUTINE STAT402, BUT THE ELEMENTS OF THE INITIAL TEST EVENTS ARE IN THE SET < 1 , ... , L0 > AND THE ELEMENTS OF THE TRANSLATION VECTORS ARE EITHER 0 OR (+/-) 1 OR ANY DESIRED INTEGER SELECTED BY THE ANALYST IN STAT404.IN2. READS A SEQUENCE OF IMAX STAR EVENTS AND EXAMINES THE LMAX TEST EVENTS TO DETERMINE THE NUMBER OF ELEMENTS IN COMMON BETWEEN THE EVENT SUCCEEDING A SELECTED STAR EVENT (IF IT EXISTS) AND EACH OF THE LMAX TEST EVENTS. MOREOVER, THE NUMBER AND PERCENTAGE OF 0's , 1's, 2's, ... , K0's ARE COMPUTED AS CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND THE SUCCESSIVE EVENT TO THE SELECTED STAR EVENT FOR UP TO 400 STAR EVENTS AND 30 TEST EVENTS. A CONFIGURATION MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN TEST EVENTS AND THE SUCCESSIVE STAR EVENT. THE SAME PROCEDURE IS PERFORMED ON A SUBSEQUENCE OF TEST EVENTS DETERMINED BY THE ANALYST. STAT404.INP <===> INITIAL TEST EVENTS STAT404.IN2 <===> TRANSLATION VECTORS ============================================================================== -- L 405 -- READS A SEQUENCE OF IMAX STAR EVENTS AND DETERMINES, FOR EACH EVENT IN THE INITIAL SEQUENCE, A SUBSEQUENCE OF PERMUTATION SETS OF HIGH- PROBABILITY ELEMENTS, BASED UPON THE COMPLETE COLLECTION OF PAIR-WISE AVERAGES OF ELEMENTS PER K0-ELEMENT EVENT, AS WELL AS, PAIR-WISE DIFFERENCES OVER PAIRS OF ELEMENTS PER K0-ELEMENT EVENT AND PAIR-WISE PRODUCTS AND QUOTIENTS (MOD L0) OF ELEMENTS PER EVENT, WHERE ELEMENTS ARE LISTED ONCE PER EVENT. THIS PROCESS IS EXECUTED FOR A SELECTED INITIAL EVENT NUMBER, JMAX, BACKING UP A DESIRED NUMBER, IBACK, OF EVENTS IN THE STAR SEQUENCE. EACH GENERATED SEQUENCE OF HIGH- PROBABILITY ELEMENTS GENERATED FROM THE I-th EVENT IS INTERSECTED WITH THE ELEMENTS OF THE (I+1)-st EVENT AND THE OCCURRENCE AND NUMBER OF COMMON ELEMENTS INDICATED, WHERE I MAY RANGE FROM 1 TO IMAX-1. THIS PROCESS IS CYCLICAL AND THE ANALYST IS QUERIED FOR A DESIRED CONSTANT ALPHA TO BE ADDED TO ELEMENTS RESULTING FROM SELECTED BINARY OPERATIONS ON INITIAL STAR EVENT ELEMENTS ON EACH CYCLE. THE MAXIMIMUM NUMBER OF INITIAL STAR EVENTS PROCESSED IS 20. ============================================================================== -- L 406 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS AND A SEQUENCE OF MMAX K0-ELEMENT TEST EVENTS AND DETERMINES, FOR EVERY EVENT IN THE TEST SEQUENCE, A SUBSEQUENCE OF PERMUTATION SETS OF HIGH-PROBABILITY ELEMENTS, BASED UPON THE COMPLETE COLLECTION OF AVERAGES OF PAIRS OF ELEMENTS PER K0-ELEMENT EVENT, AS WELL AS, PAIR-WISE DIFFERENCES OVER PAIRS OF ELEMENTS PER K0-ELEMENT EVENT AND PAIR-WISE PRODUCTS, AS WELL AS, QUOTIENTS (MOD L0) OF ELEMENTS PER EVENT, WHERE ELEMENTS ARE LISTED ONCE PER EVENT. THE ANALYST IS QUERIED FOR A DESIRED RANGE OF FINAL EVENT NUMBERS, < j1 , ... , j2 > FOR WHICH EACH SUCCESSOR EVENT WILL BE INTERSECTED WITH EACH OF THE MMAX TEST EVENTS OVER EACH CYCLE OF TESTING. EACH GENERATED SEQUENCE OF HIGH- PROBABILITY ELEMENTS GENERATED FROM THE I-th EVENT IS INTERSECTED WITH THE ELEMENTS OF STAR EVENT # JMAX AND THE OCCURRENCE AND NUMBER OF COMMON ELEMENTS INDICATED, WHERE I MAY RANGE FROM 1 TO MMAX. DURING EACH OF THE DESIRED CYCLES, THE ANALYST IS QUERIED FOR A DESIRED CONSTANT ALPHA TO BE ADDED TO ELEMENTS RESULTING FROM SELECTED BINARY OPERATIONS ON INITIAL TEST EVENT ELEMENTS ON EACH CYCLE. THE MAXIMIMUM NUMBER OF INITIAL TEST EVENTS PROCESSED IS 20 AND THE MAXIMUM NUMBER OF STAR EVENTS READ IS 600. ============================================================================== -- L 407 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES A SET OF PERMUTATION SUBSEQUENCES OF A SIZE N/2 FOR EACH INITIAL PERMUTATION SEQUENCE OF SIZE N, WHERE IT IS ASSUMED THAT N IS CONGRUENT TO 0 (MOD 2). THE ANALYST IS QUERIED FOR A DESIRED POSITIVE OR NEGATIVE INTEGRAL VALUE, EPSILON, BY WHICH PAIRS OF CORRESPONDING ELEMENTS IN THE LOWER HALF AND UPPER HALF OF EACH INITIAL PERMUTATION SEQUENCE ARE TO DIFFER. THIS GENERATES A HIGHLY PROBABLE SEQUENCE OF TEST ELEMENTS FROM THE SET < 1, 2, ... , L0 > IN EACH NEW PERMUTATION. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0- ELEMENT STAR EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED. THIS PROCESS IS CYCLICAL AND IS PERFORMED OVER A DESIRED RANGE OF STAR EVENTS. STAT407 IS A VARIANT OF STAT409. ============================================================================== -- L 408 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES OVERLAPPING SUBSEQUENCES OF A DESIRED CONSTANT GROUP SIZE FROM EACH PERMUTATION. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSORS OF A SELECTED RANGE OF K0-ELEMENT STAR EVENTS AND THE OCCURRING COMMON ELEMENTS ARE NOTED. ============================================================================== -- L 409 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES A SET OF PERMUTATION SUBSEQUENCES OF A SIZE N/2 FOR EACH INITIAL PERMUTATION SEQUENCE OF SIZE N, WHERE IT IS ASSUMED THAT N IS CONGRUENT TO 0 (MOD 2). THE ANALYST IS QUERIED FOR A DESIRED POSITIVE OR NEGATIVE INTEGRAL VALUE, EPSILON, BY WHICH PAIRS OF CORRESPONDING ELEMENTS IN THE LOWER HALF AND UPPER HALF OF EACH INITIAL PERMUTATION SEQUENCE ARE TO DIFFER. THIS GENERATES A HIGHLY PROBABLE SEQUENCE OF TEST ELEMENTS FROM THE SET < 1, 2, ... , L0 > IN EACH NEW PERMUTATION. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0- ELEMENT STAR EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED. THIS PROCESS IS CYCLICAL AND IS PERFORMED OVER A DESIRED RANGE OF STAR EVENTS. STAT409 IS A VARIANT AND EMBELLISMENT OF STAT407, GENERATING TWICE AS MANY PERMUTATION SETS. THE MAXIMUM VALUE OF IMAX IS 300 AND THE MAXIMUM VALUE OF PNUM IS 50. ============================================================================== -- L 410 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES A SET OF PERMUTATION SUBSEQUENCES OF A SIZE N/2 FOR EACH INITIAL PERMUTATION SEQUENCE OF SIZE N, WHERE IT IS ASSUMED THAT N IS CONGRUENT TO 0 (MOD 2). THE ANALYST IS QUERIED FOR A DESIRED POSITIVE OR NEGATIVE INTEGRAL VALUE, EPSILON, BY WHICH PAIRS OF CORRESPONDING ELEMENTS IN THE LOWER HALF AND UPPER HALF OF EACH INITIAL PERMUTATION SEQUENCE ARE TO DIFFER. THIS GENERATES A HIGHLY PROBABLE SEQUENCE OF TEST ELEMENTS FROM THE SET < 1, 2, ... , L0 > IN EACH NEW PERMUTATION. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0- ELEMENT STAR EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED. THIS PROCESS IS CYCLICAL AND IS PERFORMED OVER A DESIRED RANGE OF STAR EVENTS. STAT410 IS A VARIANT AND EMBELLISMENT OF STAT409, GENERATING TWICE AS MANY PERMUTATION SETS. THE MAXIMUM VALUE OF IMAX IS 300 AND THE MAXIMUM VALUE OF PNUM IS 50. FOR EACH GENERATED PERMUTATION, IF THE THE REMAINDER OF THE INDEX DIVIDED BY A DESIRED INTEGER MM IS NN, THEN THE ELEMENT 1 IS ADDED TO RESPECTIVE ELEMENTS OF THE BOTTOM AND TOP HALVES OF THE PERMUTATION, RESPECTIVELY. ============================================================================== -- L 411 -- GENERATES A SEQUENCE OF PERMUTATIONS FROM A FIXED PERMUTATION ON K ELEMENTS AND A PNUM SEQUENCE OF VARIABLE PERMUTATIONS ON L0 ELEMENTS. A SET OF IMAX K0-ELEMENT STAR EVENTS IS ALSO READ AND SUCCESSORS OF A DESIRED RANGE OF STAR EVENTS SELECTED BY THE ANALYST IN REAL TIME ARE INTERSECTED WITH EACH PERMUTATION OF THE GENERATED SEQUENCE AND THE OCCURRING COMMOM ELEMENTS ARE NOTED. PNUM MAY RANGE BETWEEN 1 AND 80, THE MAXIMUM VALUE OF K0 IS 6 AND THE MAXIMUM VALUE OF L0 IS 81, AND THE VALUE OF IMAX CAN RANGE FROM 1 TO 300. THE ROUTINE IS DESIGNED TO TACITLY PERMUTE ELEMENTS OF A FIXED PERMUTATION SO AS TO FORCE ELEMENTS WHICH INTERSECT A GIVEN STAR EVENT TO BE DISTRIBUTED IN UNINTERRUPTED STRINGS WITHIN A GENERATED PERMUTATION. THE INITIAL OR SEED PERMUTATION IS ON UNIT 3, THE SEQUENCE OF STAR EVENTS IS ON UNIT 5, AND THE BASE SEQUENCE OF PERMUTATIONS IS ON UNIT 7. THE RIGHT HALF OF GENERATED PERMUTATIONS IS PRINTED FOR FURTHER ANALYSIS. THIS ROUTINE IS CYCLICAL OVER THE DESIRED RANGE OF STAR EVENTS. ============================================================================== -- L 412 -- READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE INDEXES MATCH A DESIRED SEQUENCE OF INTEGERS (MOD K), WHERE K IS A DESIRED INTEGER. THE EXECUTION PROCESSES UP TO 600 TEST EVENTS FROM THE INPUT SEQUENCE, , AND 600 STAR EVENTS. THE ROUTINE DETERMINES THE NUMBER OF ELEMENTS IN COMMON BETWEEN THE EVENT SUCCEEDING A SELECTED STAR EVENT (IF IT EXISTS) AND EACH OF THE LMAX TEST EVENTS. MOREOVER, THE NUMBER AND PERCENTAGE OF 0's , 1's, 2's, ... , K0's ARE COMPUTED AS CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND THE SUCCESSIVE EVENT OF THE SELECTED STAR EVENT FOR UP TO 600 STAR EVENTS AND 600 TEST EVENTS. A CONFIGURATION MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN TEST EVENTS AND THE SUCCESSIVE STAR EVENT. ============================================================================== -- L 413 -- READS A SEQUENCE OF K0 BASE SETS OF VARIABLE SIZES N1,N2, ... , NK0 AND GENERATES A SEQUENCE OF EVENTS CONSISTING OF K0 ELEMENTS, WITH A DISTINCT REPRESENTATIVE FROM EACH OF THE K0 BASE SETS WITH, E.G., K0 = 5. K0 CAN RANGE BETWEEN 2 AND 6. THE MAXIMUM BASE SET SIZES ARE SUCH THAT N1*N2*N3*...*NK0 < 6400/K0. THE TOTAL NUMBER OF EVENTS IS LIMITED, AS DESIRED. THE ANALYST IS PROMPTED FOR THE MAXIMUM NUMBER OF EVENTS DESIRED AND THE INDEX OF THE STARTING OR INITIAL EVENT DESIRED, FROM WHICH THE ROUTINE DETERMINES THE APPROPRIATE STEP-SIZE FOR PRINTING THE DESIRED NUMBER OF EVENTS. THE ROUTINE PROCESSES UP TO 10 INITIAL STAR EVENTS AND GENERATES UP TO 729 TEST EVENTS. A SEQUENCE OF IMAX STAR EVENTS IS READ AND THE ANALYST IS QUERIED FOR A DESIRED EVENT NUMBER WHOSE SUCCESSOR IS INTERSECTED WITH EACH GENERATED TEST EVENT FOR WHICH COMMON ELEMENTS AND THEIR CARDINALITIES ARE IDENTIFIED. ROUTINE ALSO READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE INDEXES MATCH A DESIRED SEQUENCE OF INTEGERS (MOD K), WHERE K IS A DESIRED INTEGER. THE EXECUTION PROCESSES UP TO 729 TEST EVENTS FROM THE INPUT SEQUENCE, , AND 10 STAR EVENTS. THIS ROUTINE IS A VARIANT OF STAT361. ============================================================================== -- L 414 -- READS A SEQUENCE OF K0 BASE SETS OF VARIABLE SIZES N1,N2, ... , NK0 AND GENERATES A SEQUENCE OF EVENTS CONSISTING OF K0 ELEMENTS, WITH A DISTINCT REPRESENTATIVE FROM EACH OF THE K0 BASE SETS WITH, E.G., K0 = 5. K0 CAN RANGE BETWEEN 2 AND 6. THE MAXIMUM BASE SET SIZES ARE SUCH THAT N1*N2*N3*...*NK0 < 6400/K0. THE TOTAL NUMBER OF EVENTS IS LIMITED, AS DESIRED. THE ANALYST IS PROMPTED FOR THE MAXIMUM NUMBER OF EVENTS DESIRED AND THE INDEX OF THE STARTING OR INITIAL EVENT DESIRED, FROM WHICH THE ROUTINE DETERMINES THE APPROPRIATE STEP-SIZE FOR PRINTING THE DESIRED NUMBER OF EVENTS. THE ROUTINE PROCESSES UP TO 10 INITIAL STAR EVENTS AND GENERATES UP TO 729 TEST EVENTS. A SEQUENCE OF IMAX STAR EVENTS IS READ AND THE ANALYST IS QUERIED FOR A DESIRED EVENT NUMBER WHOSE SUCCESSOR IS INTERSECTED WITH EACH GENERATED TEST EVENT FOR WHICH COMMON ELEMENTS AND THEIR CARDINALITIES ARE IDENTIFIED. ROUTINE ALSO READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE K0-ELEMENT SUMS LIE WITHIN A DESIRED RANGE, , WHERE J1 AND J2 ARE INTEGERS. THE EXECUTION PROCESSES UP TO 729 TEST EVENTS FROM THE INPUT SEQUENCE, , AND 10 STAR EVENTS. THIS ROUTINE IS A VARIANT OF STAT413. ============================================================================== -- L 415 -- READS A SEQUENCE OF K0 BASE SETS OF VARIABLE SIZES N1,N2, ... , NK0 AND GENERATES A SEQUENCE OF EVENTS CONSISTING OF K0 ELEMENTS, WITH A DISTINCT REPRESENTATIVE FROM EACH OF THE K0 BASE SETS WITH, E.G., K0 = 5. K0 CAN RANGE BETWEEN 2 AND 6. THE MAXIMUM BASE SET SIZES ARE SUCH THAT N1*N2*N3*...*NK0 < 6400/K0. THE TOTAL NUMBER OF EVENTS IS LIMITED, AS DESIRED. THE ANALYST IS PROMPTED FOR THE MAXIMUM NUMBER OF EVENTS DESIRED AND THE INDEX OF THE STARTING OR INITIAL EVENT DESIRED, FROM WHICH THE ROUTINE DETERMINES THE APPROPRIATE STEP-SIZE FOR PRINTING THE DESIRED NUMBER OF EVENTS. THE ROUTINE PROCESSES UP TO 10 INITIAL STAR EVENTS AND GENERATES UP TO 729 TEST EVENTS. A SEQUENCE OF IMAX STAR EVENTS IS READ AND THE ANALYST IS QUERIED FOR A DESIRED EVENT NUMBER WHOSE SUCCESSOR IS INTERSECTED WITH EACH GENERATED TEST EVENT FOR WHICH COMMON ELEMENTS AND THEIR CARDINALITIES ARE IDENTIFIED. ROUTINE ALSO READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE INDEXES MATCH A DESIRED SEQUENCE OF INTEGERS (MOD K), WHERE K IS A DESIRED INTEGER. FOR EMBELLISHED FILTERING, STAT415 ALSO READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE K0-ELEMENT SUMS LIE WITHIN A DESIRED RANGE, , WHERE J1 AND J2 ARE INTEGERS. THE EXECUTION PROCESSES UP TO 729 TEST EVENTS FROM THE INPUT SEQUENCE, , AND 10 STAR EVENTS. THIS ROUTINE IS A VARIANT AND UNIFICATION OF STAT413 AND STAT414. ============================================================================== -- L 416 -- READS A SEQUENCE OF PERMUTATIONS ON K0 ELEMENTS TO BE USED IN DETERMINING POSITIONS OF ELEMENTS TO BE FILTERED FROM AN INPUT BASE SEQUENCE OF ELEMENTS OF ARBITRARY SIZE. THE ELEMENTS WHICH ARE FILTERED FROM THIS SEQUENCE ARE PRINTED FOR FURTHER USE, E.G., AS HIGH-PROBABILITY ELEMENTS IN A SEQUENCE OF UP TO 900 GENERATED EVENTS DETERMINED FROM UP TO 30 BASE PERMUTATIONS AND 30 INDEX EVENTS. AN INITIAL STRING OF K0 ELEMENTS FROM EACH PERMUTATION IS USED AS A SEED FOR GENERATING A SEQUENCE OF K0-ELEMENT STRINGS, BY ADDING 1 SUCCESSIVELY TO ALL ELEMENTS OF THE STRING. THIS PROCESS IS CYCLICALLY REPEATED N TIMES, (MOD N), WHERE N IS THE NUMBER OF ELEMENTS OF THE PERMUTATION, TO GENERATE A SEQUENCE OF N STRINGS PER PERMUTATION. THE ELEMENTS OF EACH K0-ELEMENT STRING IN THE SEQUENCE SERVE AS INDEXES FOR GENERATING N EVENTS COVERING THE SPECTRUM OF ELEMENTS IN EACH PERMUTATION. THIS GENERATES A SEQUENCE OF LMAX NEW TEST EVENTS. STAT417 ALSO READS A SEQUENCE OF STAR EVENTS AND DETERMINES THE NUMBER OF ELEMENTS IN COMMON BETWEEN THE EVENT SUCCEEDING A SELECTED STAR EVENT (IF IT EXISTS) AND EACH OF THE LMAX TEST EVENTS. MOREOVER, THE NUMBER AND PERCENTAGE OF 0's , 1's, 2's, ... , K0's ARE COMPUTED AS CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND THE SUCCESSIVE EVENT TO THE SELECTED STAR EVENT FOR UP TO 400 STAR EVENTS AND 60 TEST EVENTS. A CONFIGURATION MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN TEST EVENTS AND THE SUCCESSIVE STAR EVENT. STAT416 IS A VARIANT AND EMBELLISHMENT OF STAT238. ============================================================================== -- L 417 -- READS A SEQUENCE, , OF JMAX K0-ELEMENT TEST EVENTS AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, IDENTIFYING AND FILTERING THOSE TEST EVENTS WHOSE INDEXES MATCH A DESIRED SEQUENCE OF INTEGERS (MOD K), WHERE K IS A DESIRED INTEGER. THE EXECUTION PROCESSES UP TO 600 TEST EVENTS FROM THE INPUT SEQUENCE, , AND 600 STAR EVENTS. THE ROUTINE DETERMINES THE NUMBER OF ELEMENTS IN COMMON BETWEEN THE EVENT SUCCEEDING A SELECTED STAR EVENT (IF IT EXISTS) AND EACH OF THE LMAX TEST EVENTS. MOREOVER, THE NUMBER AND PERCENTAGE OF 0's , 1's, 2's, ... , K0's ARE COMPUTED AS CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND THE SUCCESSIVE EVENT OF THE SELECTED STAR EVENT FOR UP TO 600 STAR EVENTS AND 600 TEST EVENTS. A CONFIGURATION MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN TEST EVENTS AND THE SUCCESSIVE STAR EVENT. STAT417 ALSO FILTERS TEST EVENTS WHOSE K0-ELEMENT SUMS LIE WITHIN A DESIRED RANGE, , WHERE J1 AND J2 ARE INTEGERS. THE ROUTINE IS AN EMBELLISHMENT OF STAT412, PROVIDING TWO FILTERING CRITERIA, INSTEAD OF ONE. ============================================================================== -- L 418 -- READS A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES K0 SUBGROUPS OF EVENTS FROM EACH PERMUTATION, WHERE THE ELEMENTS OF EACH PERMUTATION ARE PRESUMED TO BE LISTED LEXICOGRAPHICALLY. THE AVERAGE INTEGRAL VALUE OF EACH OF THE K0 SUBGROUPS IS DETERMINED FOR EACH OF THE PNUM PERMUTATIONS AND THESE AVERAGES ARE PRINTED AS A SEQUENCE OF HIGH- PROBABILITY K0-ELEMENT EVENTS. PNUM MAY RANGE BETWEEN 1 AND 100 AND THE MAXIMUM VALUE OF L0 IS 51. MOREOVER, IT IS PRESUMED THAT THE NUMBER OF ELEMENTS IN EACH INPUT PERMUTATION IS DIVISIBLE BY K0. THE MEAN ELEMENT IN EACH OF THE K0 SUBGROUPS OVER PNUM PERMUTATONS, AS WELL AS, A SEQUENCE OF M0 DESIRED K0 x 3 ELEMENT BLOCKS ARE DETERMINED FOR ANALYSIS IN STAT361.INP. THE ROUTINE THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF A DESIRED STAR EVENT AND THE SET OF ELEMENTS GENERATED FROM MEANS AND TRANSLATIONS. THIS PROCESS IS CYCLICALLY REPEATED FOR A DESIRED SEQUENCE OF SUCCESSIVE STAR EVENTS. STAT418 IS AN HYBRID OF STAT193 AND STAT401. ============================================================================== -- L 419 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, A SEQUENCE OF PNUM PERMUTATION SETS OF VARIABLE SIZES DEFINED ON A SELECTED SUBSET OF THE SET, < 1, 2, ... , L0 > AND A SEQUENCE OF KMAX K0-ELEMENT INDEXES BASED UPON PERMUTATION SIZES, AND DETERMINES K0-ELEMENT HIGH-PROBABILITY EVENTS FROM EACH PERMUTATION, WHERE THE ELEMENTS OF EACH PERMUTATION ARE SELECTED BY USING THE K0 INDEX ELEMENTS FOR EACH K0-ELEMENT EVENT. THE PROCESS IS CYCLICALLY REPEATED FOR EACH INDEX SET. MAXIMUM VALUES OF PNUM, KMAX, IMAX, AND L0 ARE 200, 20, 100, AND 51, RESPECTIVELY. STAT419 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF A DESIRED STAR EVENT AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. THIS PROCESS IS CYCLICALLY REPEATED FOR A DESIRED SEQUENCE OF SUCCESSIVE STAR EVENTS. STAT419 IS A VARIANT OF STAT418. ============================================================================== -- L 420 -- READS A SEQUENCE OF IMAX STAR ON ELEMENTS < 1, 2, ... , L0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES ON A SUBSET OF THE ELEMENTS IN < 1, 2, ... , L0 >. A SEQUENCE OF ICNT K0-ELEMENT EVENTS IS GENERATED BY SELECTING ELEMENTS FROM EACH PERMUTATION BASED UPON INDICES DETERMINED BY ADDING SUCCESSIVE INTEGERS TO A DESIRED INITIAL ELEMENT OF EACH PERMUTATION. EACH GENERATED EVENT IS INTERSECTED WITH EACH EVENT IN A DESIRED RANGE OF STAR EVENTS AND COMMON ELEMENTS ARE DETERMINED AND LISTED. MOREOVER, THE PERCENTAGE AND NUMBER OF EVENTS HAVING 0 , 1, 2, ... , K0 ELEMENTS IN COMMON WITH A SPECIFIED STAR EVENT IS INDICATED IN A MATRIX. THE EXECUTION PROCESSES UP TO 600 STAR EVENTS AND 200 PERMUTATIONS OF SIZES UP TO 51. ============================================================================== -- L 421 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, A SEQUENCE OF KMAX K0-ELEMENT TEST EVENTS, AND A SET OF LMAX INDEX SETS OF PERMUTATIONS OF VARYING SIZES WHICH ARE USED TO FILTER VARIOUS COMBINATIONS OF K0-ELEMENT EVENTS FROM THE TEST SET. THE FILTERED K0-ELEMENT EVENTS ARE PRINTED AS STRINGS OF PERMUTATIONS SETS FOR FURTHER ANALYSIS. STAT421 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. ============================================================================== -- L 422 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, A SEQUENCE OF KMAX K0-ELEMENT TEST EVENTS, AND A SEQUENCE OF INTEGERS CONGRUENT (MOD t) FOR SOME INTEGER t, TO A SEQUENCE OF SETS OF FIVE (NOT NECESSARILY DISTINCT) INTEGERS CHOSEN FROM AN INPUT FILE. THESE INTEGERS ARE USED AS INDEXES TO FILTER VARIOUS SELECTED COMBINATIONS OF K0-ELEMENT EVENTS FROM THE TEST SET. THE FILTERED K0-ELEMENT EVENTS ARE THEN PRINTED AS STRINGS OF PERMUTATIONS SETS FOR FURTHER ANALYSIS. STAT422 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. THE ROUTINE IS AN HYBRID OF STAT301 AND STAT421, READING A SEQUENCE OF INDEXES (MOD t) FROM STAT422.IN2, INSTEAD OF ARBITRARY PERMUTATION ELEMENTS. ============================================================================== -- L 423 -- PROGRAM READS A SEQUENCE A PNUM PERMUTATION SETS AND A SEQUENCE OF IMAX STAR EVENTS, DETERMINING THE SUBSEQUENCE OF ELEMENTS <1, ... , k> WHICH OCCUR IN EACH PERMUTATION PRINTING THE ELEMENTS AT MOST ONCE. STAT421 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. ============================================================================== -- L 424 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, A SEQUENCE OF KMAX K0-ELEMENT TEST EVENTS, AND A SET OF LMAX INDEX SETS OF PERMUTATIONS OF VARYING SIZES WHICH ARE USED TO FILTER VARIOUS COMBINATIONS OF K0-ELEMENT EVENTS FROM THE TEST SET. THE FILTERED K0-ELEMENT EVENTS ARE PRINTED AS STRINGS OF PERMUTATIONS SETS FOR FURTHER ANALYSIS. STAT424 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. STAT424 IS AN EMBELLISHMENT OF STAT421, WHERE THE KMAX TEST EVENTS ARE PROCESSED CYCLICALLY IN (K0 x K0) - DIMENSIONAL BLOCKS, RATHER THAN BY (KMAX x K0) - DIMENSIONAL BLOCKS. INDEXES IN ANY GIVEN PERMUTATION SET IN PERM.INP ARE EXPECTED TO RANGE BETWEEN 1 AND K0. ============================================================================== -- L 425 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, AND A SEQUENCE OF KMAX K0-ELEMENT TEST EVENTS. THE TRANSPOSE OF EACH K0 x K0 - DIMENSIONAL SUB-MATRIX IS DETERMINED FOR ROWS M1 = (N-1)*K0 +1 THROUGH M2 = N*K0 FOR N = 1, 2, ... , KMAX/K0 AND EACH SUCH SUB-MATRIX AND ITS TRANSPOSE ARE PRINTED FOR STAT424.INP. STAT425 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF EVENTS GENERATED IN THE SUB- MATRICES. THE K0 x K0 - DIMENSIONAL BLOCKS ARE PROCESSED CYCLICALLY. ============================================================================== -- L 426 -- READS A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS, A SEQUENCE OF QNUM PERMUTATION SETS, AND A SET OF PNUM INDEX SETS OF PERMUTATIONS OF VARYING SIZES WHICH ARE USED TO FILTER VARIOUS COMBINATIONS OF K0-ELEMENT EVENTS FROM THE QNUM PERMUTATION SETS. THE FILTERED SET OF K0-ELEMENT EVENTS ARE PRINTED AS STRINGS OF PERMUTATION SETS FOR FURTHER ANALYSIS. STAT426 THEN DETERMINES ELEMENTS IN COMMON BETWEEN THE SUCCESSOR OF DESIRED STAR EVENTS AND THE SET OF ELEMENTS GENERATED FROM THE INPUT PERMUTATION SETS. THE ROUTINE IS A VARIANT OF STAT421, WITH SELECTED PERMUTATION SETS USED AS A SECOND INPUT SET, RATHER THAN K0-ELEMENT TEST EVENTS. ============================================================================== -- L 427 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES OVERLAPPING SUBSEQUENCES OF A DESIRED CONSTANT GROUP SIZE FROM EACH PERMUTATION. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0- ELEMENT STAR EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED. STAT427 IS A VARIANT OF STAT408, WITH A SEQUENCE OF VARYING INITIAL INDEXES AND CONSTANT GROUP SIZES INPUT IN REAL TIME. OVERLAPPING GROUPS SERVE AS MORE JUDICIOUS COVERINGS OF INITIAL PERMUTATIONS. ============================================================================== -- L 428 -- READS A SEQUENCE OF IMAX STAR EVENTS ON ELEMENTS < 1 , ... , K0 > AND A SEQUENCE OF PNUM PERMUTATIONS OF VARIABLE SIZES DEFINED ON A SUBSET OF THE SET, < 1, 2, ... , L0 >, AND DETERMINES OVERLAPPING SUBSEQUENCES OF A DESIRED CONSTANT GROUP SIZE FROM EACH PERMUTATION. THE ROUTINE ALSO READS A SEQUENCE OF INTEGERS CONGRUENT (MOD t), FOR SOME INTEGER t, TO A SEQUENCE OF SETS OF FIVE (NOT NECESSARILY DISTINCT) INTEGERS CHOSEN FROM AN INPUT FILE. THESE INTEGERS ARE USED AS INDEXES TO FILTER VARIOUS SELECTED COMBINATIONS OF ELEMENTS OR SUBSEQUENCES FROM THE INITIAL SET OF PNUM PERMUTATION SEQUENCES. PNUM MAY RANGE BETWEEN 1 AND 100, THE MAXIMUM VALUE OF K0 IS 6, AND THE MAXIMUM VALUE OF L0 IS 81. EACH GENERATED SUBSEQUENCE OF PERMUTATIONS IS INTERSECTED WITH THE SUCCESSOR OF A SELECTED K0- ELEMENT STAR EVENT AND THE OCCURRING COMMON ELEMENTS ARE NOTED. STAT428 IS A VARIANT OF STAT408, WITH A SEQUENCE OF VARYING INITIAL INDEXES AND CONSTANT GROUP SIZES INPUT IN REAL TIME. OVERLAPPING GROUPS SERVE AS MORE JUDICIOUS COVERINGS OF INITIAL PERMUTATIONS. STAT428 IS AN HYBRID OF STAT422 AND STAT427, READING A FILTERING SEQUENCE OF INDEXES (MOD t) FROM STAT422.INP AND USING THEM TO GENERATE HIGHLY PROBABLE SUBSEQUENCES FROM THER PERMUTATION SETS. ==============================================================================