INTERPOL

COMP-U-STAT
STATISTICAL PATTERN GENERATOR AND MATHEMATICAL TREND ANALYZER
(c) Copyright 1976-2015
by James Ervin Glover, Ph.D.
All Rights Reserved
Part VIII(a) ( STAT 2235 ----> STAT 2239 )
Part VIII(b) ( STAT 2241 ----> STAT 2246 )
Part VIII(c) ( STAT 2291 ----> STAT 2296 )
The COMP-U-STAT System consists of a cluster of more than 3470
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.
NO ONE can guarantee the appearance of any specific outcome in
any set of random variables or any speculative endeavor. However,
the serious analyst is herein presented a blueprint for a strictly
scientific approach to analyzing and solving a series of these
very fascinating and challenging problems.
======================================================================
* * * GLOSSARY OF COMP-U-STAT PROGRAMS 2141 ---> 2146 * * *
======================================================================
-- 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 D 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 --
II
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
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
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
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 --
V
STAT2239 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N
.LE. 10, THE CORRESPONDING ( N+1 ) ORDERED PAIRS in { (Xi,Yi) } ,

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 --
.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
FROM STAT2241.IN2, A SEQUENCE OF NPOINT INDICES AND INCREMENTS, DX,
N, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS, { (Yi,Fi) } IN
STAT2241 IS A VARIANT OF STAT2238. CF. ALSO STAT2234, STAT2235,
STAT2236, AND STAT2239. STAT2241 IS ADAPTED FROM CONTE AND DeBOOR,
COLUMNS OF STAR EVENTS IS RECORDED IN STAT2235.OT2. CF. ALSO
GENERATED FROM BASE.INP. EACH K0-ELEMENT PREDICTED VECTOR IS
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 2242 --
( TRANSLATING AND PREDICTING INTERSECTION PERFORMANCE OF EACH EVENT
OF A FIXED BLOCK OF K0-ELEMENT EVENTS )
II
STAT2242 READS A FIXED BLOCK OF BMAX K0-ELEMENT TEST EVENTS FROM
STAT2242.INP, A SEQUENCE OF CMAX 2-ELEMENT TRANSLATION VECTORS
FROM STAT2242.IN2 AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS
FROM BASE.INP. EACH K0-ELEMENT EVENT IS TRANSLATED BY EACH VECTOR
FROM THE SEQUENCE IN STAT2242.IN2 AND THE TRANSFORMED EVENTS ARE
INTERSECTED WITH THE SEQUENCE OF STAR EVENTS FROM BASE.INP.
THE ROUTINE ALSO FLAGS THE ELEMENTS OF A DESIRED RANGE OF STAR
EVENTS AS THEY OCCUR AMONG THE ELEMENTS OF INTERSECTING TEST
EVENTS.
MOREOVER, OUTPUT TEST EVENTS ARE PRINTED IN THE FILE STAT94.INP FOR
FUTURE USE BY OTHER ROUTINES. MOREOVER, THE NUMBER AND PERCENTAGE
OF 0's , 1's, 2's, 3's, 4's, ... , K0's ARE COMPUTED AS DETERMINED
CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND
EACH EVENT IN THE RANGE OF SELECTED STAR EVENTS. A CONFIGURATION
MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN
TEST EVENTS AND THE DESIRED RANGE OF SUCCESSIVE STAR EVENTS.
THE ROUTINE ALSO PREDICTS THE NEXT SUCCESSFUL INTERSECTION INDEX
BETWEEN A STAR EVENT AND THE GENERATED BLOCK OF TEST EVENTS.
STAT2242 IS A VARIANT OF STAT2064, TACITLY GENERATING A SEQUENCE
OF HIGH-PROBABILITY TEST EVENTS IN STAT2242.OUT AND STAT94.INP.
HOWEVER, THE BLOCK OF K0-ELEMENT INPUT EVENTS IS TRANSLATED BY
2-ELEMENT VECTORS, RATHER THAN K0-ELEMENT VECOTRS. THOSE EVENTS
FROM THE SEQUENCE WITH INDICES WHICH ARE CONGRUENT TO AN ELEMENT
OF A DESIRED INTEGRAL VECTOR SELECTED BY THE ANALYST, I.E.,
< M1, M2, M3, M4, ... , M10 > ( MOD T) , FOR SOME DESIRED
INTEGER T AND SOME DESIRED SEQUENCE OF POSITIVE INTEGERS :
M1, M2, M3, M4, M5, M6,M7, M8, M9, AND M10 (NOT NECESSARILY
DISTINCT). EVENTS FROM STAT2242.INP ARE INCLUDED AS OUTPUT EVENT.
CF. STAT1641 FOR GENERATING STAT2242.INP IN THE FORM OF STAT94.INP.
CF. ALSO STAT1323, STAT1505, STAT1506, STAT1511, STAT1618, STAT1631
AND STAT2064. INPUT EVENTS IN STAT2242.INP MAY BE TACITLY
GENERATED BY STAT1438 AS STAT94.INP. CF. STAT1438. CF. STAT204
FOR THE GENERATION OF STAT2242.INP AND CF. STAT2171 FOR THE
GENERATION OF STAT2242.IN2. CF. STAT2239 FOR THE GENERATION OF
CUMULAT.OUT TO BE UTILIZED AS STAT2242.INP. THE MIDDLE ONE OR TWO
ELEMENTS OF EACH INPUT EVENT OF STAT2242.INP SERVE AS FIXED PIVOTS
AND PAIRS OF ELEMENTS FROM STAT2242.IN2 ARE ADDED TO THE REMAINING
PAIRS OF ELEMENTS FROM THE HEAD AND TAIL OF EACH INPUT EVENT.
=====================================================================
-- L 2243 --

VII
STAT2243 READS A SPECIFIC PREDICTOR VARIABLE, X0, THE DEGREE, N
.LE. 10, AND THE CORRESPONDING ( N+1 ) ORDERED PAIRS in {(Xi,Yi)}
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 --
.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
VIII
N, AND THE CORRESPONDING (N+1=NP1) ORDERED PAIRS, { (Yi,Fi) } IN
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 2245 --
( GENERATING K0-ELEMENT EVENTS FROM ELEMENTS OF A FIXED BLOCK
OF EVENTS VIA SCROLLING ROWS FROM SELECTED UNIONS OF COLUMNS )
X
STAT2245 READS A FIXED BLOCK OF BMAX K0-ELEMENT TEST EVENTS FROM
STAT2245.INP AND A SEQUENCE OF IMAX K0-ELEMENT STAR EVENTS FROM
BASE.INP. HIGH-PROBABILITY K0-ELEMENT EVENTS ARE GENERATED FROM
STAT2245.INP VIA SCROLLING ROWS FROM SELECTED UNIONS OF COLUMNS.
THE ROUTINE FLAGS THE ELEMENTS OF A DESIRED RANGE OF STAR EVENTS
AS THEY OCCUR AMONG THE ELEMENTS OF INTERSECTING TEST EVENTS.
MOREOVER, OUTPUT TEST EVENTS ARE PRINTED IN THE FILE STAT94.INP FOR
FUTURE USE BY OTHER ROUTINES. MOREOVER, THE NUMBER AND PERCENTAGE
OF 0's , 1's, 2's, 3's, 4's, ... , K0's ARE COMPUTED AS DETERMINED
CARDINALITIES OF INTERSECTION NUMBERS BETWEEN TEST EVENTS AND
EACH EVENT IN THE RANGE OF SELECTED STAR EVENTS. A CONFIGURATION
MATRIX IS GENERATED WHICH INDICATES THE ELEMENTS IN COMMON BETWEEN
TEST EVENTS AND THE DESIRED RANGE OF SUCCESSIVE STAR EVENTS.
THE ROUTINE ALSO PREDICTS THE NEXT SUCCESSFUL INTERSECTION INDEX
BETWEEN A STAR EVENT AND THE GENERATED BLOCK OF TEST EVENTS.
STAT2245 IS A VARIANT OF STAT2107 AND STAT2020, GENERATING A SET
OF HIGH-PROBABILITY TEST EVENTS IN STAT2245.OUT AND STAT94.INP.
MOREOVER, THE BLOCK OF K0-ELEMENT INPUT EVENTS IS FILTERED BY
VECTORS OF THE FORM < M1, M2, M3, M4, ... , M10 > ( MOD T) ,
FOR AN INTEGER T A SELECTED SEQUENCE OF POSITIVE INTEGERS.
CF. STAT1641 AND STAT2003 FOR GENERATING STAT2245.INP IN THE FORM
OF STAT94.INP. CF. ALSO STAT1323, STAT1505, STAT1506, STAT1511,
STAT1618, AND STAT1631. CF. STAT2107, STAT2024, AND STAT2025.
=====================================================================
-- L 2246 --
.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
IX
N, AND THE CORRESPONDING (N+1=NP1) ORDERED PAIRS, { (Yi,Fi) } IN
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:
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,
COLUMNS OF STAR EVENTS IS RECORDED IN CUMULAT.OUT. CF. ALSO
GENERATED FROM BASE.INP. EACH K0-ELEMENT PREDICTED VECTOR IS
GENERATE HIGH-PROBABILITY K0-ELEMENT EVENTS IN STAT94.INP. CF.
ALSO STAT2238, STAT2241 AND STAT2244.
=====================================================================
-- L 2291 --
VALUE X0 , WHERE Y0 = P(X0) , FROM THE GIVEN COEFFICIENTS OF
POLYNOMIAL(S), P(X) , WITH N .LE. 6 )
X
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.
INTERPOLATING 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 --

XII
AND A K0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR THE
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
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 --
XIII
STAT2236. STAT2293 IS A VARIANT OF STAT2235 AND STAT2291.
INTERPOLATING 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 --
XIV
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
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 --
( PREDICTOR VARIABLES Xi NORMALIZED (MOD L0) )
XIII
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 --
( PREDICTOR VARIABLES Xi NORMALIZED (MOD L0) )
XIV
AND A K0x(N+1)-DIMENSIONAL ARRAY OF COEFFICIENTS FOR THE
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
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.
=====================================================================

INTERPOL

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

Similar to INTERPOL

Similar to INTERPOL (20)

More from James Ervin Glover, Ph.D.

More from James Ervin Glover, Ph.D. (10)

INTERPOL