= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = COMP-U-STAT = = = = = = = = STATISTICAL PATTERN GENERATOR AND MATHEMATICAL TREND ANALYZER = = = = = = = = (c) Copyright 2019 by J.E. Glover, Ph.D. = = = = All Rights Reserved = = = = = = = = = = = = ( ENCRYPTION ALGORITHMS ) = = = = = = = = = = = = The COMP-U-STAT System consists of a cluster of more than 3706 = = = modular programs, providing the analyst with a 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 application = = of the COMP-U-STAT cluster. Please see available DEMOs = = = = provided upon request, for numerous examples of output files.= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =================================================================== * * * ABSTRACTS OF COMP-U-STAT PROGRAMS 2593 ---> 2596 * * * * * * and 2234 ---> 2296 * * * =================================================================== -- L 2593 -- ( ALPHANUMERIC ENCRYPTION ALGORITHM ) I ( STAT2593 ENCRYPTS AN ALPHANUMERIC FILE WITH LINES OF LENGTH 72 CHARACTERS FROM PLAINTEXT TO CIPHERTEXT ) STAT2593 READS AN ALPHANUMERIC FILE FROM STAT2495.INP, A PRIVATE KEY FROM STAT2594.KEY (PROVIDED BY THE TRANSMITTER TO THE USER), UTILIZING AN INTERNALLY CREATED ALGORITHM TO ENCRYPT THE FILE FOR SECURITY PURPOSES. EACH LINE OF STAT2594.INP IS RESTRICTED TO 72 CHARACTERS. THE ENCRYPTED OUPUT FILE IS RECORDED AS STAT2594.OUT, UTILIZING THE CONGRUENCES C1 = aP1 + bP2 (mod 51) AND C2 = cP1 + dP2 (mod 51) TO CONVERT CHARACTER BLOCKS OF SIZE n = 2 WITH, E.G., a = 2 , b = 3 , c = 5 AND d = 8 TO CONVERT 2-ELEMENT STRINGS FROM PLAINTEXT TO CIPHERTEXT, WITH gcd(ad-bc,51) = 1. THUS (ad-bc) AND 51 ARE TAKEN TO BE RELATIVELY PRIME FOR THE 26 INPUT ALPHABETIC CHARACTERS, A ---> Z, IN UNION WITH A BLANK CHARACTER, DIGITS 0 --> 9, AND A SELECTED SEQUENCE OF SPECIAL CHARACTERS. ======================================================================== -- L 2594 -- ( ALPHANUMERIC DECRYPTION ALGORITHM ) II ( STAT2594 DECRYPTS AN ALPHANUMERIC FILE WITH LINES OF LENGTH 72 CHARACTERS FROM CIPHERTEXT TO PLAINTEXT ) STAT2594 READS AN ALPHANUMERIC FILE FROM STAT2495.INP, A PRIVATE KEY FROM STAT2594.KEY (PROVIDED TO THE USER FROM THE TRANSMITTER), UTILIZING AN INTERNALLY CREATED ALGORITHM TO DECRYPT THE FILE FOR SECURITY PURPOSES. EACH LINE OF STAT2594.INP IS RESTRICTED TO 72 CHARACTERS. THE DECRYPTED OUPUT FILE IS RECORDED AS STAT2594.OUT, UTILIZING THE CONGRUENCES P1 = dC1 - bC2 (mod 51) AND P2 = -cC1 + aC2 (mod 51) TO CONVERT CHARACTER BLOCKS OF SIZE n = 2 WITH, E.G., a = 2 , b = 3 , c = 5 AND d = 8 TO CONVERT 2-ELEMENT STRINGS FROM CIPHERTEXT TO PLAINTEXT, WITH gcd(ad-bc,51) = 1. THUS (ad-bc) AND 51 ARE TAKEN TO BE RELATIVELY PRIME FOR THE 26 INPUT ALPHABETIC CHARACTERS, A ---> Z, IN UNION WITH A BLANK CHARACTER, DIGITS 0 --> 9, AND A SELECTED SEQUENCE OF SPECIAL CHARACTERS. ======================================================================== -- L 2595 -- ( NON-ALPHABETIC (BINARY) ENCRYPTION ALGORITHM ) III ( STAT2595 ENCRYPTS A NON-ALPHABETIC FILE WITH LINES OF LENGTH 75 CHARACTERS FROM PLAINTEXT TO CIPHERTEXT ) STAT2595 READS A NON-ALPHABETIC FILE FROM STAT2595.INP, A RANDOMLY GENERATED BINARY STRING OF LENGTH 75 (THE ENCRYPTION KEY) FROM STAT2595.KEY, CONSISTING OF ELEMENTS FROM THE SET { 0,1 }, USING AN INTERNALLY CREATED ALGORITHM TO ENCRYPT THE FILE FOR SECURITY. EACH LINE OF INPUT FILE STAT2595.INP,(RESTRICTED TO 15 CHARACTERS) EACH REPRESENTED INTERNALLY AS A STRING OF 5 BINARY DIGITS. THE ENCRYPTED OUPUT FILE IS RECORDED AS STAT2595.OUT, AUTOMATICALLY TRANSFORMING STAT2595.INP INTO A BINARY FILE FOR PROCESSING. THE CIPHERTEXT IS GENERATED BY ADDING (MOD 2) THE DIGITS WHICH HAVE EQUIVALENT INDICES IN TWO BINARY STRINGS. THE RECIPIENT MUST POSSESS IN ADVANCE THE ENCRYPTION KEY. THE NUMERICAL PLAINTEXT CAN BE RECONSTRUCTED BY MERELY ADDING (MOD 2) TWO CORRESPONDING DIGITS OF THE ENCRYPTION KEY AND THE CIPHERTEXT. A COMPLETE TABLE OF BINARY EQUIVALENCES FOR THE 26 ALPHABETIC CHARACTERS , A --> Z, IS AUTOMATICALLY INCLUDED IN THE ALGORITHM, RECORDED AS STAT2595.OT5. ======================================================================== -- L 2596 -- ( NON-ALPHABETIC (BINARY) DECRYPTION ALGORITHM ) IV ( STAT2596 DECRYPTS A NON-ALPHABETIC FILE WITH LINES OF LENGTH 75 CHARACTERS FROM CIPHERTEXT TO PLAINTEXT ) STAT2596 READS A NON-ALPHABETIC FILE FROM STAT2596.INP, A RANDOMLY GENERATED BINARY STRING OF LENGTH 75 (THE ENCRYPTION KEY) FROM STAT2596.KEY, CONSISTING OF ELEMENTS FROM THE SET { 0,1 }, AND USES AN INTERNALLY CREATED ALGORITHM TO DECRYPT THE FILE FOR SECURITY. EACH LINE OF INPUT FILE STAT2596.INP IS RESTRICTED TO 15 CHARACTERS, EACH OF WHICH IS REPRESENTED INTERNALLY AS A STRING OF 5 BINARY DIGITS. THE DECRYPTED OUPUT FILE IS RECORDED AS STAT2596.OUT, AUTOMATICALLY TRANSFORMING STAT2596.INP INTO A BINARY FILE FOR PROCESSING. THE PLAINTEXT IS GENERATED BY ADDING (MOD 2) THE DIGITS WHICH HAVE EQUIVALENT INDICES IN THE TWO BINARY STRINGS. THE RECIPIENT MUST POSSESS IN ADVANCE THE ENCRYPTION KEY. THEN THE NUMERICAL PLAINTEXT CAN BE RECONSTRUCTED BY MERELY ADDING (MOD 2) THE TWO CORRESPONDING DIGITS OF THE ENCRYPTION KEY AND THE CIPHERTEXT. A COMPLETE TABLE OF BINARY EQUIVALENCES FOR THE 26 ALPHABETIC CHARACTERS , A ---> Z , IS AUTOMATICALLY INCLUDED IN THE ALGORITHM, RECORDED AS STAT2596.OT5. ======================================================================== -- L 2234 -- ( GENERATING K0 FILES FROM THE K0 COLUMNS OF A STAR EVENT SEQUENCE CONSISTING OF IMAX ELEMENTS PER COLUMN TO SERVE AS INPUT FILES FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARES FITS FOR INTERPOLATING POLYNOMIALS ) STAT2234 READS A SET OF UP TO 1000 STAR EVENTS AND GENERATES A SET K0 FILES FROM THE K0 COLUMNS OF A STAR EVENT SEQUENCE CONSISTING OF IMAX ELEMENTS PER COLUMN TO SERVE AS INPUT FILES FOR EITHER TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR INTERPOLATING POLYNOMIALS IN ANOTHER ROUTINE SELECTED BY THE ANALYST. AND RECORDS THEM IN STAT2234.IN1 , STAT2234.IN2, STAT2234.IN3, STAT2234.IN4, STAT2234.IN5, AND STAT2234.IN6 FOR FURTHER PROCESSING. ======================================================================== -- L 2235 -- COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF A SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL, P(X) , WITH N .LE. 10 ) I STAT2235 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING ( N+1 ) COEFFICIENTS OF A DESIRED INTERPOLATING POLYNOMIAL, P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL. CF. STAT2234 AND MS EXCEL FOR GENERATING THE REQUISITE COEFFICIENTS. STAT2235 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2235.OT2. CF. ALSO STAT2236. ======================================================================== -- L 2236 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF A SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL, P(X) , WITH N .LE. 10 ) II STAT2236 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING ( N+1 ) COEFFICIENTS OF A DESIRED INTERPOLATING POLYNOMIAL, P(X), AND COMPUTES THE PREDICTED RESPONSE, P( X0 ) , FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARES FITS FOR THE INTERPOLATING POLYNOMIAL. CF. STAT2234 AND MS EXCEL FOR GENERATING THE REQUISITE COEFFICIENTS. STAT2236 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN CUMULAT.OUT. THE ROUTINE STAT2236 IS A VARIANT OF STAT2235. HOWEVER, A SEQUENCE OF INPUT COEFFICIENTS FOR A SEQUENCE OF INTERPOLATING POLYNOMIALS IS READ FROM FILE STAT2236.INP, RATHER THAN BEING SUBMITTED FOR A SINGLE POLYNOMIAL BY THE ANALYST IN REAL-TIME. THIS ALLOWS FOR THE GENERATION OF PREDICTED RESPONSES FOR A SEQUENCE OF INTERPOLATING POLYNOMIALS, E.G., OVER THE K0 COLUMNS OF STAR EVENTS IN BASE.INP. THE INPUT COEFFICIENTS OF STAT2236.INP ARE EXPECTED TO BE LISTED IN DESCENDING ORDER OF THE CORRESPONDING POWERS OF X0. CF. ALSO STAT2235. A PERMUTATION OF MTC UNIQUE QUALIFYING RESPONSES , P( X0 ) , FOR THE CURRENT EXECUTION IS RECORDED IN THE FILE PERM.INP FOR FURTHER PERMUTATION ANALYSIS, IN STAT543, FOR EXAMPLE. ======================================================================== -- L 2237 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) IS THE LAGRANGE FORM OF THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Xi,Yi } , WHERE Yi = F(Xi) ) III STAT2237 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS in { (Xi,Yi) } , WHERE Yi = F(Xi) AND THE < Xi > ARE PRESUMED TO BE DISTINCT . THE LAGRANGE FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN CUMULAT.OUT. THE ROUTINE STAT2237 IS A VARIANT OF STAT2238. HOWEVER, A SEQUENCE OF INPUT PAIRS IS READ FROM FILE STAT2237.INP, RATHER THAN BEING READ AS SINGLE FUNCTIONAL VALUES WITH IMPLICIT DOMAIN INDICES AS IN STAT2238. THIS ALLOWS FOR THE GENERATION OF PREDICTED RESPONSES FOR A SEQUENCE OF INTERPOLATING POLYNOMIALS, E.G., OVER THE K0 COLUMNS OF STAR EVENTS IN BASE.INP. THE INPUT COEFFICIENTS OF STAT2237.INP ARE EXPECTED TO BE LISTED IN DESCENDING ORDER OF THE CORRESPONDING POWERS OF X0. CF. ALSO STAT2235. A PERMUTATION OF MTC UNIQUE QUALIFYING RESPONSES , P( X0 ) , FOR THE CURRENT EXECUTION IS RECORDED IN THE FILE PERM.INP FOR FURTHER PERMUTATION ANALYSIS, IN STAT543, FOR EXAMPLE. CF. STAT2234, STAT2235, STAT2236, AND STAT2238. ======================================================================== -- L 2238 -- ( CALCULATION OF THE NEWTON FORM FOR THE POLYNOMIAL OF DEGREE .LE. N, WHICH INTERPOLATES F(X) AT Y(i),i = 1,...,NP1 , NAMELY , THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Yi,Fi } , WHERE Yi = F(Yi) ) IV STAT2238 READS A SEQUENCE OF CMAX K0-ELEMENT TRANSLATION EVENTS FROM STAT2238.IN2, A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS, { (Yi,Fi) } IN STAT2238.INP, Fi = F(Yi) AND THE < Xi > , NOT NECESSARILY DISTINCT. THE NEWTON FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL, SUBJECT TO THE FOLLOWING RESTRICTIONS: (1) IF Y(I) = Y(I+K), THEN Y(I) = Y(I+J), J = 1, ... , K AND (2) IF ALSO Y(I-1) .NE. Y(I), OR IF I = 1, THEN F(I+J) = THE VALUE OF THE Jth DERIVATIVE OF F(X) AT X = Y(I), J = 0 ... , K. STAT2238 IS A VARIANT OF STAT2239. CF. ALSO STAT2234, STAT2235, STAT2236, AND STAT2239. STAT2238 IS ADAPTED FROM CONTE and DeBOOR, ELEMENTARY NUMERICAL ANALYSIS: AN ALGORITHMIC APPROACH. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , OVER K0 COLUMNS OF STAR EVENTS IS RECORDED IN CUMULAT.OUT. CF. ALSO STAT2235 AND STAT2236. EVENTS FOR STAT2238.INP ARE AUTOMATICALLY GENERATED FROM BASE.INP. EACT K0-ELEMENT PREDICTED VECTOR IS TRANSLATED BY THE CMAX K0-ELEMENT VECTORS OF STAT2238.IN2 TO GENERATE HIGH-PROBABILITY K0-ELEMENT EVENTS IN STAT94.INP. CF. ALSO STAT2241 AND STAT2244. ======================================================================== -- L 2239 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) IS THE LAGRANGE FORM OF THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Xi,Yi } , WHERE Yi = F(Xi) ) V STAT2239 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N .LE. 10 THE CORRESPONDING ( N+1 ) ORDERED PAIRS in { (Xi,Yi) } , WHERE Yi = F(Xi) AND THE < Xi > ARE PRESUMED TO BE DISTINCT . THE LAGRANGE FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN CUMULAT.OUT. THE ROUTINE STAT2239 IS A VARIANT OF STAT2239. HOWEVER, A SEQUENCE OF INPUT PAIRS IS READ FROM FILE STAT2239.INP, RATHER THAN BEING READ AS SINGLE FUNCTIONAL VALUES WITH IMPLICIT DOMAIN INDICES AS IN STAT2237. THIS ALLOWS FOR THE GENERATION OF PREDICTED RESPONSES FOR A SEQUENCE OF INTERPOLATING POLYNOMIALS, E.G., OVER THE K0 COLUMNS OF STAR EVENTS IN BASE.INP. THE INPUT COEFFICIENTS OF STAT2239.INP ARE EXPECTED TO BE LISTED IN DESCENDING ORDER OF THE CORRESPONDING POWERS OF X0. CF. ALSO STAT2235. A PERMUTATION OF MTC UNIQUE QUALIFYING RESPONSES , P( X0 ) , FOR THE CURRENT EXECUTION IS RECORDED IN THE FILE PERM.INP FOR FURTHER PERMUTATION ANALYSIS, IN STAT543, FOR EXAMPLE. CF. STAT2234, STAT2235, STAT2236, AND STAT2239. ======================================================================== -- L 2241 -- ( CALCULATION OF THE NEWTON FORM FOR THE POLYNOMIAL OF DEGREE .LE. N, WHICH INTERPOLATES F(X) AT Y(i),i = 1,...,NP1 , NAMELY , THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Yi,Fi } , WHERE Yi = F(Yi) ) VI STAT2241 READS A SEQUENCE OF CMAX K0-ELEMENT TRANSLATION EVENTS FROM STAT2241.IN2, A SEQUENCE OF NPOINT INDICES AND INCREMENTS, DX , FROM STAT2241.IN3, A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS, { (Yi,Fi) } IN STAT2241.INP, Fi = F(Yi) AND THE < Xi > , NOT NECESSARILY DISTINCT. THE NEWTON FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL, SUBJECT TO THE FOLLOWING RESTRICTIONS: (1) IF Y(I) = Y(I+K), THEN Y(I) = Y(I+J), J = 1, ... , K AND (2) IF ALSO Y(I-1) .NE. Y(I), OR IF I = 1, THEN F(I+J) = THE VALUE OF THE Jth DERIVATIVE OF F(X) AT X = Y(I), J = 0 ... , K. STAT2241 IS A VARIANT OF STAT2238. CF. ALSO STAT2234, STAT2235, STAT2236, AND STAT2239. STAT2241 IS ADAPTED FROM CONTE AND DeBOOR, ELEMENTARY NUMERICAL ANALYSIS: AN ALGORITHMIC APPROACH. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , OVER K0 COLUMNS OF STAR EVENTS IS RECORDED IN STAT2235.OT2. CF. ALSO STAT2235 AND STAT2236. EVENTS FOR STAT2241.INP ARE AUTOMATICALLY GENERATED FROM BASE.INP. EACH K0-ELEMENT PREDICTED VECTOR IS TRANSLATED BY THE CMAX K0-ELEMENT VECTORS OF STAT2241.IN2 TO GENERATE HIGH-PROBABILITY K0-ELEMENT EVENTS IN STAT94.INP. STAT2241 FOLLOWS CONTE AND DeBOOR's TREATMENT MORE DIRECTLY THAN DOES STAT2238. READ(5,101) NPOINT,X,DX FROM STAT2241.IN3, (FORMAT: I3,(2F10.3)). ======================================================================== -- L 2243 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) IS THE LAGRANGE FORM OF THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Xi,Yi } , WHERE Yi = F(Xi) ) VII STAT2243 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N .LE. 10, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS in { (Xi,Yi) } , WHERE Yi = F(Xi) AND THE < Xi > ARE PRESUMED TO BE DISTINCT . THE LAGRANGE FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN CUMULAT.OUT. THE ROUTINE STAT2243 IS A VARIANT OF STAT2239. HOWEVER, A QUADRUPLE OF TRANSLATION ELEMENTS IS ENTERED IN REAL TIME, RATHER THAN A PAIR OF TRANSLATION ELEMENTS, TO PAIRS OF ELEMENTS IN THE HEAD AND TAIL OF EVENTS. THIS ALLOWS FOR THE GENERATION OF PREDICTED RESPONSES FOR A SEQUENCE OF INTERPOLATING POLYNOMIALS, E.G., OVER THE K0 COLUMNS OF STAR EVENTS IN BASE.INP. THE INPUT COEFFICIENTS OF STAT2243.INP ARE EXPECTED TO BE LISTED IN DESCENDING ORDER OF THE CORRESPONDING POWERS OF X0. CF. ALSO STAT2235. A PERMUTATION OF MTC UNIQUE QUALIFYING RESPONSES , P( X0 ) , FOR THE CURRENT EXECUTION IS RECORDED IN THE FILE PERM.INP FOR FURTHER PERMUTATION ANALYSIS, IN STAT543, FOR EXAMPLE. CF. STAT2234, STAT2235, STAT2236, AND STAT2239. ======================================================================== -- L 2244 -- ( CALCULATION OF THE NEWTON FORM FOR THE POLYNOMIAL OF DEGREE .LE. N, WHICH INTERPOLATES F(X) AT Y(i),i = 1,...,NP1 , WHERE N+1 ASSUMES A RANGE OF VALUES IN A DESIRED INTERVAL, [ Q0,Q1 ], WITH THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Yi,Fi } , WHERE Yi = F(Yi) ) VIII STAT2244 READS A SEQUENCE OF CMAX K0-ELEMENT TRANSLATION EVENTS FROM STAT2244.IN2, A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING (N+1=NP1) ORDERED PAIRS, { (Yi,Fi) } IN STAT2244.INP Fi = F(Yi) AND THE < Xi > , NOT NECESSARILY DISTINCT. THE NEWTON FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL, SUBJECT TO THE FOLLOWING RESTRICTIONS: (1) IF Y(I) = Y(I+K), THEN Y(I) = Y(I+J), J = 1, ... , K AND (2) IF ALSO Y(I-1) .NE. Y(I), OR IF I = 1, THEN F(I+J) = THE VALUE OF THE Jth DERIVATIVE OF F(X) AT X = Y(I), J = 0 ... , K. STAT2244 IS A VARIANT OF STAT2238. HOWEVER, BLOCKS ARE PROCESSED CYCLICALLY FOR NP1 IN THE RANGE [Q0,Q1]. CF. ALSO STAT2234, STAT2235, STAT2236, AND STAT2238. STAT2244 IS ADAPTED FROM CONTE and DeBOOR, ELEMENTARY NUMERICAL ANALYSIS: AN ALGORITHMIC APPROACH. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , OVER K0 COLUMNS OF STAR EVENTS IS RECORDED IN CUMULAT.OUT. CF. ALSO STAT2235 AND STAT2236. EVENTS FOR STAT2244.INP ARE AUTOMATICALLY GENERATED FROM BASE.INP. EACH K0-ELEMENT PREDICTED VECTOR IS TRANSLATED BY THE CMAX K0-ELEMENT VECTORS OF STAT2244.IN2 TO GENERATE HIGH-PROBABILITY K0-ELEMENT EVENTS IN STAT94.INP. CF. ALSO STAT2238 AND STAT2241. ======================================================================== -- L 2246 -- ( CALCULATION OF THE NEWTON FORM FOR THE POLYNOMIAL OF DEGREE .LE. N, WHICH INTERPOLATES F(X) AT Y(i),i = 1,...,NP1 , WHERE N+1 ASSUMES A RANGE OF VALUES IN A DESIRED INTERVAL, [ Q0,Q1 ] AND A RANGE OF VALUES OF DX IN A DESIRED INTERVAL, [ DX1,DX2 ], WITH THE GENERAL Nth DEGREE INTERPOLATING POLYNOMIAL PASSING THROUGH THE LAST (N+1) POINTS IN { Yi,Fi } , WHERE Yi = F(Yi) ) IX STAT2246 READS A SEQUENCE OF CMAX K0-ELEMENT TRANSLATION EVENTS FROM STAT2246.IN2, A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND THE CORRESPONDING (N+1=NP1) ORDERED PAIRS, { (Yi,Fi) } IN STAT2246.INP Fi = F(Yi) AND THE < Xi > , NOT NECESSARILY DISTINCT. THE NEWTON FORM , P(X) , OF THE Nth DEGREE INTERPOLATING POLYNOMIAL IS GENERATED AND THE ROUTINE TACITLY COMPUTES THE PREDICTED RESPONSE, P( X0 ) . THE POLYNOMIAL, P(X), SERVES AS THE MINIMUM NORM LEAST SQUARES FIT INTERPOLATING POLYNOMIAL, SUBJECT TO THE FOLLOWING RESTRICTIONS: (1) IF Y(I) = Y(I+K), THEN Y(I) = Y(I+J), J = 1, ... , K AND (2) IF ALSO Y(I-1) .NE. Y(I), OR IF I = 1, THEN F(I+J) = THE VALUE OF THE Jth DERIVATIVE OF F(X) AT X = Y(I), J = 0 ... , K. STAT2246 IS A VARIANT OF STAT2244. HOWEVER, BLOCKS ARE PROCESSED CYCLICALLY FOR NP1 IN THE RANGE [Q0,Q1], AS WELL AS, INCREMENTS OF DX IN THE SELECTED INTERVAL [DX1,DX2]. CF. ALSO STAT2234, STAT2235, STAT2236, AND STAT2238. STAT2246 IS ADAPTED FROM CONTE and DeBOOR, ELEMENTARY NUMERICAL ANALYSIS: AN ALGORITHMIC APPROACH. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , OVER K0 COLUMNS OF STAR EVENTS IS RECORDED IN CUMULAT.OUT. CF. ALSO STAT2235 AND STAT2236. EVENTS FOR STAT2246.INP ARE AUTOMATICALLY GENERATED FROM BASE.INP. EACH K0-ELEMENT PREDICTED VECTOR IS TRANSLATED BY THE CMAX K0-ELEMENT VECTORS OF STAT2246.IN2 TO GENERATE HIGH-PROBABILITY K0-ELEMENT EVENTS IN STAT94.INP. CF. ALSO STAT2238, STAT2241 AND STAT2244. ======================================================================== -- L 2291 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL(S), P(X) , WITH N .LE. 6 ) X STAT2292 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A Q0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR INTERPOLATING POLYNOMIAL(S), P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL(S). CF. STAT2234 AND MS EXCEL TO GENERATE THE REQUISITE COEFFICIENTS. STAT2291 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2291.OT2. CF. ALSO STAT2236. STAT2291 IS A VARIANT OF STAT2235 AND STAT2292. INTERPOLAT. POLYNOMIAL COEFFICIENTS ARE READ FROM THE FILE STAT2291.INP, RATHER THAN BEING ENTERED IN REAL-TIME. REAL-VALUED COEFFICIENTS ARE PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS BEING SET TO 0.0, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. ======================================================================== -- L 2292 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF A SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL, P(X) , WITH N .LE. 6 ) XII STAT2292 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A K0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR THE INTERPOLATING POLYNOMIAL, P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL. CF. STAT2234 AND MS EXCEL FOR GENERATING THE REQUISITE COEFFICIENTS. STAT2292 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2292.OT2. CF. ALSO STAT2236. STAT2292 IS A VARIANT OF STAT2291. HOWEVER, INTERPOLATING POLYNOMIAL COEFFICIENTS ARE READ FROM THE FILE STAT2292.INP AS A K0x(N+1)-DIMENSIONAL ARRAY. REAL-VALUED COEFFICIENTS ARE TACITLY PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR UP TO A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS TRUNCATED, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. MOREOVER, FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. A CUMULATIVE FILE OF GENERATED HIGH-PROBABILITY EVENTS IS RECORDED IN CUMULAT.OUT. ======================================================================== -- L 2293 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL(S), P(X) , WITH N .LE. 6 ) XIII STAT2292 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A Q0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR INTERPOLATING POLYNOMIAL(S), P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL(S). CF. STAT2234 AND MS EXCEL TO GENERATE THE REQUISITE COEFFICIENTS. STAT2293 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2293.OT2. CF. ALSO STAT2236. STAT2293 IS A VARIANT OF STAT2235 AND STAT2291. INTERPOLAT. POLYNOMIAL COEFFICIENTS ARE READ FROM THE FILE STAT2293.INP, RATHER THAN BEING ENTERED IN REAL-TIME. REAL-VALUED COEFFICIENTS ARE PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS BEING SET TO 0.0, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. STAT2294 IS A VARIANT OF STAT2291. HOWEVER, A FIXED VALUE OF X0 = ( N+2 ) IS UTILIZED AS THE PREDICTOR VARIABLE IN EACH COLUMN IN THE DETERMINATION OF Y0. ======================================================================== -- L 2294 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF A SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL, P(X) , WITH N .LE. 6 ) XIV STAT2294 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A K0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR THE INTERPOLATING POLYNOMIAL, P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL. CF. STAT2234 AND MS EXCEL FOR GENERATING THE REQUISITE COEFFICIENTS. STAT2294 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2294.OT2. CF. ALSO STAT2236. STAT2294 IS A VARIANT OF STAT2292. HOWEVER, A FIXED VALUE OF X0 = ( N+2 ) IS UTILIZED AS THE PREDICTOR VARIABLE IN EACH COLUMN IN THE DETERMINATION OF Y0. REAL-VALUED COEFFICIENTS ARE TACITLY PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR UP TO A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS TRUNCATED, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. MOREOVER, FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. A CUMULATIVE FILE OF GENERATED HIGH-PROBABILITY EVENTS IS RECORDED IN CUMULAT.OUT. ======================================================================== -- L 2295 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL(S), P(X) , WITH N .LE. 6 ) ( PREDICTOR VARIABLES Xi NORMALIZED (MOD L0) ) XIII STAT2292 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A Q0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR INTERPOLATING POLYNOMIAL(S), P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL(S). CF. STAT2234 AND MS EXCEL TO GENERATE THE REQUISITE COEFFICIENTS. STAT2295 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2295.OT2. CF. ALSO STAT2236. STAT2295 IS A VARIANT OF STAT2235 AND STAT2291. INTERPO- LATING POLYNOMIAL COEFFICIENTS ARE READ FROM THE FILE STAT2295.INP, RATHER THAN BEING ENTERED IN REAL-TIME. REAL-VALUED COEFFICIENTS ARE PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS BEING SET TO 0.0, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. STAT2294 IS A VARIANT OF STAT2291. HOWEVER, A FIXED VALUE OF X0 = ( IMAX+1 ) IS UTILIZED AS THE PREDICTOR VARIABLE IN EACH COLUMN IN THE DETERMINATION OF Y0. PREDICTOR VARIABLES Xi ARE EXPECTED TO BE NORMALIZED (MOD (L0)), WHEN PROCESSED BY EXCEL. ======================================================================== -- L 2296 -- ( COMPUTING A FUNCTIONAL RESPONSE VALUE Y0 OF A PRESCRIBED PREDICTOR VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF A SPECIFIED LINEAR, QUADRATIC, CUBIC OR N-th DEGREE INTERPOLATING POLYNOMIAL, P(X) , WITH N .LE. 6 ) ( PREDICTOR VARIABLES Xi NORMALIZED (MOD L0) ) XIV STAT2296 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N, AND A K0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR THE INTERPOLATING POLYNOMIAL, P(X), AND COMPUTES THE PREDICTED RESPONSE, P(X0), FOR TIME SERIES ANALYSIS OR MINIMIM NORM LEAST SQUARE FITS FOR THE INTERPOLATING POLYNOMIAL. CF. STAT2234 AND MS EXCEL FOR GENERATING THE REQUISITE COEFFICIENTS. STAT2296 PROCESSES PARAMETERS FOR POLYNOMIALS HAVING DEGREES .LE. 10. A CUMULATIVE FILE OF COMPUTED RESPONSE VALUES , < Y0 > , IS RECORDED IN STAT2296.OT2. CF. ALSO STAT2236. STAT2296 IS A VARIANT OF STAT2292. HOWEVER, A FIXED VALUE OF X0 = (IMAX+1) IS UTILIZED AS THE PREDICTOR VARIABLE IN EACH COLUMN IN THE DETERMINATION OF Y0. REAL-VALUED COEFFICIENTS ARE TACITLY PRESUMED TO BE LISTED ACCORDING TO ASCENDING POWERS OF X FOR UP TO A 6TH DEGREE POLYNOMIAL ON 7 POINTS, WITH NON-RELEVANT COEFFICIENTS TRUNCATED, WHICH ALLOWS FOR POLYNOMIALS OF SMALLER DEGREE. MOREOVER, FILES FOR TEMPK.INP , K = 1,2,3,...,K0 , RECORD THE LAST N+1 ELEMENTS OF COLUMNS 1,2,3,...,K0 FROM THE IMAX STAR EVENTS OF BASE.INP. A CUMULATIVE FILE OF GENERATED HIGH-PROBABILITY EVENTS IS RECORDED IN CUMULAT.OUT. PREDICTOR VARIABLES Xi ARE EXPECTED TO BE NORMALIZED (MOD (L0)), WHEN PROCESSED BY EXCEL. CF. ALSO STAT2293. ========================================================================