C                                                                               
C     ==================================================================        
C     *                                                                *        
C     *              - REVISED GUTTMAN-LINGOES PROGRAMS -              *        
C     *                                                                *        
C     *            FORTRAN IV (LEVEL G) VERSION - 10/18/67             *        
C     *                         EDITED BY TIDY*                        *        
C     *                                                                *        
C     *                                                                *        
C     *    *H. M. MURPHY, TIDY, A COMPUTER CODE FOR RENUMBERING AND    *        
C     *         EDITING FORTRAN SOURCE PROGRAMS.  AD-642-099,          *        
C     *             CLEARINGHOUSE, U.S. DEPT. OF COMMERCE,             *        
C     *                  SPRINGFIELD, VIRGINIA 22151                   *        
C     *                                                                *        
C     ==================================================================        
C                                                                               
C     *** THIS F-IV VERSION DIFFERS FROM THE F-II VERSION OF THE G-L            
C     PROGRAM SERIES IN THE FOLLOWING RESPECTS -                                
C     A)  READ AND WRITE STATEMENTS,                                            
C     B)  NAMES OF FORTRAN SUPPLIED SUBPROGRAMS, E.G., AMAX0 AND IABS IN        
C         PLACE OF MAX1F AND XABSF, ETC.,                                       
C     C)  THE USE OF A4 FOR A6 IN FORMAT STATEMENTS,                            
C     D)  THE USE OF THE DEFINE FILE SPECIFICATION FOR SCRATCH STORAGE.         
C         IF THIS FACILITY IS NOT AVAILABLE ONE NEED BUT DELETE THIS            
C         SPECIFICATION, MODIFY READ AND WRITE STATEMENTS HAVING DATA           
C         SET REFERENCE NUMBERS, AND SUBSTITUTE REWIND STATEMENTS WHERE         
C         THE ASSOCIATED VARIABLE APPEARS, E.G., MT=1 WOULD BECOME              
C         REWIND TAPE MT,                                                       
C     E)  THE USE OF RELATIONAL OPERATORS, E.G. .GT., .NE., ETC., IN THE        
C         SORT AND PLOT SUBROUTINES.  THEIR EQUIVALENTS CAN BE EFFECTED         
C         EASILY.                                                               
C                                                                               
C     YOUR TAPE (IF REQUESTED) HAS BEEN WRITTEN ON 7 9 TRACKS WITH ODD          
C     EVEN PARITY AT A DENSITY OF 200 556 800 BPI, WHERE EACH RECORD IS         
C     ONE IBM CARD WRITTEN ACCORDING TO THE FORMAT 20A4.  THE RECORDS           
C     HAVE BEEN WRITTEN IN THE BCD EBCDIC CHARACTER CODE WITH THE TRANS-        
C     LATOR ON OFF.  THERE ARE FIVE EBCDIC CHARACTERS USED (PUNCHED ON          
C     THE IBM-029) WHICH HAVE NO PROPER BCD EQUIVALENTS WHEN A 7 TRACK          
C     TAPE HAS BEEN WRITTEN - I.E., ( OR LEFT PARENTHESIS, ) OR RIGHT           
C     PARENTHESIS, + OR PLUS SIGN, = OR EQUAL SIGN, AND ' OR PRIME.  THE        
C     BA842, 842, AND 841.  THESE TAPE CODES WILL NEED TO BE CONVERTED          
C     TO THE GRAPHICS CORRESPONDING TO THE MNEUMONICS OR NAMES FOR THE          
C     IBM-026 BCD CODES.   ***                                                  
C                                                                               
C     WRITE-UPS FOR VOLUME I OF G-L PROGRAMS ***                        WUP   1 
C     CS-I                                                              WUP 634 
C     GIVEN ANY TWO OF THE FOLLOWING 4 MATRICES DETERMINE THE NONMETRIC WUP 635 
C     FIT AS A FUNCTION OF IMPOSING THE RANK ORDERS OF ONE MATRIX ON THEWUP 636 
C     OTHER MATRIX - 1) AN NXN MATRIX OF COEFFICIENTS REPRESENTING THE  WUP 637 
C     SIMILARITIES AMONG N OBJECTS OR THEIR DISSIMILARITIES BASED UPON  WUP 638 
C     ONE SET OF OBSERVATIONS, 2) AN NXN MATRIX OF COEFFICIENTS REPRE-  WUP 639 
C     SENTING THE INTERRELATIONS AMONG THE SAME N OBJECTS BASED UPON AN-WUP 640 
C     OTHER SET OF OBSERVATIONS, 3) AN NXM MATRIX OF VALUES REPRESENT-  WUP 641 
C     ING THE ORTHOGONAL COORDINATES RESULTING FROM THE ANALYSIS OF THE WUP 642 
C     FIRST MATRIX WHICH GENERATES A MATRIX OF DISTANCES, AND 4) AN NXK WUP 643 
C     COORDINATE MATRIX REPRESENTING A SOLUTION FOR THE SECOND MATRIX   WUP 644 
C     WHICH GENERATES A DISTANCE MATRIX.  THE NORMALIZED PHI (THE COEF- WUP 645 
C     FICIENT OF MONOTONICITY) WHICH IS OUTPUT FOR EACH OBJECT AND OVER WUP 646 
C     ALL OBJECTS FOR ANY PAIR OF THESE MATRICES IS AN INDEX OF CONFIG- WUP 647 
C     URATIONAL OR PATTERN SIMILARITY WHICH ANSWERS SLIGHTLY DIFFERENT  WUP 648 
C     QUESTIONS DEPENDING UPON WHICH TWO MATRICES ARE INVOLVED IN THE   WUP 649 
C     COMPARISON YIELDING SIX POSSIBLE INTERPRETATIONS,I.E., 1) HOW WELLWUP 650 
C     DO THE RELATIVE DISTANCES GENERATED FROM THE THIRD MATRIX MAP INTOWUP 651 
C     THE COEFFICIENTS OF THE FIRST MATRIX, 2) SIMILARLY FOR THE FOURTH WUP 652 
C     AND THE SECOND MATRICES,MUTATIS MUTANDIS, 3) HOW WELL DOES A SOL- WUP 653 
C     UTION OF THE FIRST MATRIX (REPRESENTED BY THE THIRD MATRIX) REPRE-WUP 654 
C     SENT A REASONABLE SOLUTION OF THE SECOND MATRIX, 4) M.M. FOR THE  WUP 655 
C     FOURTH AND SECOND MATRICES, 5) HOW WELL DOES THE CONFIGURATION    WUP 656 
C     GENERATED FROM ONE SOLUTION MATCH THAT FROM ANOTHER SOLUTION (THE WUP 657 
C     TWO MATRICES OF SIMILARITIES OR DISSIMILARITIES. THE FIRST TWO    WUP 659 
C     QUESTIONS RELATE TO THE CONVENTIONAL GOODNESS OF FIT CRITERION    WUP 660 
C     THAT IS STANDARD OUTPUT IN THE G-L PROGRAMS, SO THESE COMPARISONS WUP 661 
C     WOULD NOT USUALLY BE MADE.  IF, HOWEVER, PHI WAS NOT AVAILABLE,   WUP 662 
C     E.G., FOR THE INPUT AND OUTPUT OF A FACTOR ANALYSIS, ONE MIGHT    WUP 663 
C     WISH TO DETERMINE THIS INDEX OF PATTERN SIMILARITY.  THE SECOND   WUP 664 
C     TWO QUESTIONS, ON THE OTHER HAND, RELATE TO HOW WELL COULD ONE    WUP 665 
C     SOLUTION OF A GIVEN MATRIX BE ALSO CONSIDERED A SOLUTION TO YET   WUP 666 
C     ANOTHER MATRIX BASED UPON DIFFERENT OBSERVATIONS OF THE SAME N    WUP 667 
C     OBJECTS.  INTERPRETATIONS 3 AND 4 ARE NOT NECESSARILY SYMMETRIC,  WUP 668 
C     SINCE M MAY NOT EQUAL K OR EVEN IF M=K ONE FIT MAY BE BETTER THAN WUP 669 
C     THE OTHER FOR ITS CORRESPONDING MATRIX.  REGARDLESS OF HOW WELL A WUP 670 
C     GIVEN SOLUTION FITS ITS CORRESPONDING MATRIX WE MAY WELL BE INTER-WUP 671 
C     ESTED IN HOW WELL TWO DIFFERENT SOLUTIONS CAN BE CONSIDERED MONO- WUP 672 
C     TONIC TRANSFORMATIONS OF EACH OTHER.  AND,FINALLY,REGARDLESS OF   WUP 673 
C     WHAT KIND OF SOLUTION COULD BE OBTAINED FOR TWO MATRICES SEPARATE-WUP 674 
C     LY WE MAY WANT AN ANSWER TO THE QUESTION OF HOW CLOSE IS THE CON- WUP 675 
C     FIGURATION OF ONE MATRIX OF RELATIONS TO THAT OF ANOTHER GIVEN THEWUP 676 
C     SAME OBJECTS.  ANOTHER POSSIBLE TEST THAT MIGHT BE OF INTEREST    WUP 677 
C     WOULD BE THAT OF TESTING WHETHER A GIVEN PATTERN IS LIKE SOME HY- WUP 678 
C     POTHESIZED PATTERN,E.G.,A SIMPLEX OR A CIRCUMPLEX.                WUP 679 
C                                                                       WUP 680 
C     THIS PROGRAM FOR PATTERN MATCHING WAS WRITTEN FOR THE UNIVERSITY  WUP 681 
C     OF MICHIGAN IBM-7090 COMPUTER IN FORTRAN II.  THE GUTTMAN-LINGOES WUP 682 
C     NONMETRIC SERIES RESEARCH IS SUPPORTED IN PART BY A GRANT FROM THEWUP 683 
C     NATIONAL SCIENCE FOUNDATION (GS-929).  DATE = 2/15/67.            WUP 684 
C                                                                       WUP 685 
C     DECK SET-UP FOR G-L(CS-I) -                                       WUP 686 
C                                                                       WUP 687 
C        1.  SYSTEM ID CARD/S.                                          WUP 688 
C        2.  BINARY PROGRAM.                                            WUP 689 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 690 
C            UMNS 2-72 FOR OUTPUT LABELING).                            WUP 691 
C        4.  PARAMETER CARD (8 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 692 
C            INFORMATION SERIATUM -                                     WUP 693 
C            A) N = NUMBER OF OBJECTS (.LE. 70),                        WUP 694 
C            B) M = NUMBER OF DIMENSIONS IN FIRST COORDINATE MATRIX (IF WUP 695 
C               NOT TO BE INPUT, LEAVE FIELD BLANK) .LE. 35,            WUP 696 
C            C) K = NUMBER OF DIMENSIONS IN SECOND COORDINATE MATRIX (IFWUP 697 
C               NOT TO BE INPUT, LEAVE FIELD BLANK) .LE. 35,            WUP 698 
C            D) NC = NUMBER OF COMPARISONS TO BE MADE .LE. 6,           WUP 699 
C            E) ISIMA=1 IF SIMILARITY DATA FOR MATRIX 1, OTHERWISE ZERO,WUP 700 
C            F) ISIMB=1 IF SIMILARITY DATA FOR MATRIX 2, OTHERWISE ZERO,WUP 701 
C            G) ISIMC=1 IF MATRIX 3 REPRESENTS A SCALAR SOLUTION,E.G.,  WUP 702 
C               FROM A FACTOR ANALYSIS, AND 0 IF IT REPRESENTS A SOLU-  WUP 703 
C               TION FOR EUCLIDEAN DISTANCES AND -1 IF IT REPRESENTS A  WUP 704 
C               SOLUTION FOR CITY-BLOCK DISTANCES,                      WUP 705 
C            H) ISIMD= SAME AS G) FOR MATRIX 4, I.E., 1,0, OR -1.       WUP 706 
C        5.  PARAMETER CARD (IF NC = 6, LEAVE BLANK, OTHERWISE PUNCH IN WUP 707 
C            SUCCESSIVE 4-COLUMN FIELDS THE PAIR NUMBERS CORRESPONDING  WUP 708 
C            TO THE COMPARISONS TO BE MADE,E.G.,IF NC=3 AND MATRIX 1 IS WUP 709 
C            TO BE COMPARED WITH 2, 3 WITH 4, AND 2 WITH 3, THEN PUNCH  WUP 710 
C            1 2 3 4 2 3, WHICH WOULD REQUIRE 4 MATRICES TO BE INPUT.   WUP 711 
C            THE ORDERING WITHIN PAIRS IS MEANINGFUL,I.E.,THE ORDER TO  WUP 712 
C            BE PRESERVED REFERS TO THAT OF THE FIRST PAIR MEMBER, BUT  WUP 713 
C            THE PAIRS THEMSELVES CAN BE IN ANY ORDER,E.G., 3 4 2 3 1 2 WUP 714 
C            WOULD RESULT IN THE SAME COMPARISONS.  HOWEVER, 2 1 4 3 3 2WUP 715 
C            WOULD NOT.  WHEN NC = 6, THE COMPARISON PAIRS WILL BE 1 2, WUP 716 
C            1 3,1 4,2 3,2 4, AND 3 4, IN THAT ORDER.  THE SECOND MEMBERWUP 717 
C            OF ANY PAIR MUST HAVE A HIGHER SUBSCRIPT THAN THE FIRST,   WUP 718 
C            E.G.,2 1 IS NOT LEGITIMATE.                                WUP 719 
C        6.  FORMAT CARD FOR MATRICES 1 AND 2 (DESCRIBING IN F-NOTATION WUP 720 
C            HOW DATA HAS BEEN PUNCHED).  IF BOTH NOT INPUT,LEAVE BLANK.WUP 721 
C        7.  FORMAT CARD FOR MATRICES 3 AND 4.  IF NEITHER IS TO BE IN- WUP 722 
C            PUT,LEAVE BLANK.                                           WUP 723 
C        8.  DATA (PUNCH THE UPPER-HALF OFF-DIAGONAL MATRIX FOR MATRICESWUP 724 
C            1 AND 2 AS IN SSA-I.  THE COORDINATE MATRICES ARE PUNCHED  WUP 725 
C            SUCH THAT EACH CARD (OR SET OF CARDS IN CASE 1 CARD CANNOT WUP 726 
C            ACCOMODATE THE INFORMATION) REPRESENTS ONE ROW OF THE COOR-WUP 727 
C            DINATE MATRIX FOR AN OBJECT AND THE FIELDS CORRESPOND TO   WUP 728 
C            THE DIMENSIONS.  THE RELATION MATRICES (IF ANY) MUST PRE-  WUP 729 
C            CEDE THE COORDINATE MATRICES (IF ANY) AND THE ORDER OF THE WUP 730 
C            MATRICES SHOULD BE ISOMORPHIC TO THE COMPARISON NUMBERS.   WUP 731 
C            DATA SHOULD BE PUNCHED IN COLS. 1-72, RESERVING 73-80 FOR  WUP 732 
C            OPTIONAL ID INFORMATION.                                   WUP 733 
C        9.  FOR ADDITIONAL RUNS REPEAT ITEMS 3-8.                      WUP 734 
C                                                                       WUP 735 
C     *** REFERENCES - LINGOES, J.C.  AN IBM-7090 PROGRAM FOR GUTTMAN-  WUP 736 
C                        LINGOES CONFIGURATIONAL SIMILARITY - I.  BEHAV.WUP 737 
C                        SCI.,1967,12,502-503.                          WUP 738 
C     SSA1                                                              SA1   1 
C     A GENERAL NONMETRIC TECHNIQUE FOR FINDING THE SMALLEST EUCLIDEAN  SA1   2 
C     SPACE FOR A CONFIGURATION OF POINTS.  (L.GUTTMAN AND J.C.LINGOES).SA1   3 
C     PROGRAMMED IN FORTRAN II FOR THE UNIV. OF MICHIGAN IBM-7090 BY    SA1   4 
C     J.C.LINGOES (9/21/64).  MAJOR CHANGES IN THE PRESENT VERSION IN-  SA1   5 
C     CLUDE OPTIONS FOR:  1) ANALYZING AN INDEFINITE NUMBER OF VARIABLESSA1   6 
C     GIVEN A FIXED CONFIGURATION, 2) MINIMIZING KRUSKAL'S STRESS, AND  SA1   7 
C     3) INPUT OF A CONFIGURATION OF ONE'S CHOICE.  ALGORITHMS EMPLOYED:SA1   8 
C     G-L "SOFT-SQUEEZE", DOUBLE-PHASE FOLLOWED BY SINGLE-PHASE (RANK-  SA1   9 
C     IMAGES) FOR SEMI-STRONG MONOTONICITY, WHICH IS OPTIONALLY FOLLOWEDSA1  10 
C     BY G-L "SOFT-SQUEEZE", SINGLE-PHASE (KRUSKAL'S MONOTONE REGRESSIONSA1  11 
C     VALUES) FOR WEAK MONOTONICITY.                                    SA1  12 
C                                                                       SA1  13 
C     ==================================================================SA1  14 
C     *                                                                *SA1  15 
C     *              - REVISED GUTTMAN-LINGOES PROGRAMS -              *SA1  16 
C     *                                                                *SA1  17 
C     *              FORTRAN IV (LEVEL G) VERSION - 1/1/69             *SA1  18 
C     *                         EDITED BY TIDY*                        *SA1  19 
C     *                                                                *SA1  20 
C     *                                                                *SA1  21 
C     *    *H. M. MURPHY, TIDY, A COMPUTER CODE FOR RENUMBERING AND    *SA1  22 
C     *         EDITING FORTRAN SOURCE PROGRAMS.  AD-642-099,          *SA1  23 
C     *             CLEARINGHOUSE, U.S. DEPT. OF COMMERCE,             *SA1  24 
C     *                  SPRINGFIELD, VIRGINIA 22151                   *SA1  25 
C     *                                                                *SA1  26 
C     ==================================================================SA1  27 
C                                                                       SA1  28 
C     DECK SET-UP FOR G-L(SSA-I) -                                      SA1  29 
C                                                                       SA1  30 
C        1.   SYSTEM ID CARD/S.                                         SA1  31 
C        2.   BINARY PROGRAM.                                           SA1  32 
C        3.   TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COLSA1  33 
C             -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF SA1  34 
C             OUTPUT).                                                  SA1  35 
C        4.   PARAMETER CARD, 11 4-COLUMN FIELDS CONTAINING THE FOLLOW- SA1  36 
C             ING INFORMATION SERIATUM -                                SA1  37 
C             A)  NR=THE NUMBER OF VARIABLES .LE. 100 AND .GE. 3,       SA1  38 
C             B)  MIND=0 OR BLANK IF THE PROGRAM IS TO DETERMINE THE MINSA1  39 
C                 -IMUM NUMBER OF DIMENSIONS FOR THE PROBLEM, OTHERWISE SA1  40 
C                 ANY NUMBER BETWEEN 1 AND 10 PROVIDED MIND .LE. MAXD,  SA1  41 
C                 IN WHICH CASE ALL SOLUTIONS FROM MIND TO MAXD WILL BE SA1  42 
C                 PRINTED OUT, UNLESS K OR STRESS BECOMES .LE. .0001    SA1  43 
C                 FOR A GIVEN M, THE NUMBER OF DIMENSIONS.  UNLESS YOU  SA1  44 
C                 KNOW M, SET MIND=0, IN GENERAL,                       SA1  45 
C             C)  MAXD=THE LARGEST NUMBER OF DIMENSIONS DESIRED .LE.    SA1  46 
C                 (NV-1,10)MIN BUT .GE. 1,                              SA1  47 
C             D)  ISIM=0 OR BLANK FOR DISTANCE COEFFICIENTS OR DISSIMI- SA1  48 
C                 LARITY DATA AND 1 IF SIMILARITY DATA, E.G., CORRELA-  SA1  49 
C                 TIONS,                                                SA1  50 
C             E)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR    SA1  51 
C                 MORE DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,SA1  52 
C             F)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE  SA1  53 
C                 DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK.     SA1  54 
C                 CARDS WILL BE AUTOMATICALLY PUNCHED IF MORE THAN 100  SA1  55 
C                 ITERATIONS ARE REQUIRED FOR CONVERGENCE OF 2 OR MORE  SA1  56 
C                 DIMENSIONS.  THESE CARDS CAN BE USED FOR SUBSEQUENT   SA1  57 
C                 INPUT TO CONTINUE THE ITERATIONS,                     SA1  58 
C             G)  IFGLK=1 IF KRUSKAL'S STRESS IS TO BE MINIMIZED, OTHER-SA1  59 
C                 WISE SET TO ZERO OR LEAVE BLANK,                      SA1  60 
C             H)  IFCONF=1 IF A CONFIGURATION IS TO BE INPUT FOR CON-   SA1  61 
C                 TINUED ITERATIONS OR FOR ADDING POINTS TO A FIXED CON-SA1  62 
C                 FIGURATION, OTHERWISE LEAVE BLANK OR SET TO ZERO.     SA1  63 
C                 MAXD MUST BE THE NUMBER OF DIMENSIONS INPUT,          SA1  64 
C             I)  IFFIX=1 IF INPUT CONFIGURATION IS TO REMAIN FIXED AND SA1  65 
C                 ADDITIONAL POINTS ARE TO BE FITTED TO THIS SPACE,     SA1  66 
C                 OTHERWISE LEAVE BLANK OR SET TO ZERO.  MIND=MAXD.     SA1  67 
C                 TO ACCOMPLISH ANALYSIS OF MORE VARIABLES THAN 100:  1)SA1  68 
C                 ANALYZE SOME REPRESENTATIVE SAMPLE OF VARIABLES (S'S),SA1  69 
C                 SPECIFYING IFC=1;  2) USE THE OUTPUT SOLUTION AS IN-  SA1  70 
C                 PUT FOR IFFIX=1.  NR IS THE ORIGINAL NUMBER OF VARIA- SA1  71 
C                 BLES.  ITEMS E) THROUGH G) ARE DISABLED WHEN IFFIX=1. SA1  72 
C                 A CONDITIONAL APPROACH IS MADE TO PRESERVE THE ORDER  SA1  73 
C                 FOR JUST THE ARRAY OF VALUES INPUT FOR EACH VARIABLE. SA1  74 
C                 THE COEFFICIENT OF FIT APPLIES ONLY TO THESE VALUES   SA1  75 
C                 VIS-A-VIS THE ORIGINAL SET OF POINTS,                 SA1  76 
C             J)  IFSR=1 IF EITHER ITEM 7. OR 8. IS TO BE GENERATED BY ASA1  77 
C                 SUBROUTINE (WHICH THE USER SUBSTITUTES FOR THE DUMMY  SA1  78 
C                 SUBROUTINES PROVIDED), OTHERWISE SET TO ZERO OR LEAVE SA1  79 
C                 BLANK,                                                SA1  80 
C             K)  EPS=0 OR BLANK IF TIED BLOCKS ARE NOT TO BE FORMED,   SA1  81 
C                 OTHERWISE INSERT IN F-NOTATION (WITH DECIMAL POINT    SA1  82 
C                 PUNCHED) THE CATEGORY WIDTH FOR COEFFICIENTS WHICH ARESA1  83 
C                 TO BE TIED.                                           SA1  84 
C        5.   FORMAT CARD (DESCRIBING IN F-NOTATION WHERE THE DATA      SA1  85 
C             APPEARS ON THE CARDS).                                    SA1  86 
C        6.   IF IFCONF=1, PUNCH CONFIGURATION TO BE INPUT (OR USE OUT- SA1  87 
C             PUT CONFIGURATION) ACCORDING TO FORMAT: 10F8.3.  THERE    SA1  88 
C             SHOULD BE NR SETS OF CARDS, EACH SET OF WHICH SHOULD HAVE SA1  89 
C             MAXD COORDINATES, OTHERWISE OMIT THIS SET WHEN IFCONF=0.  SA1  90 
C        7.   DATA (PUNCH LOWER-HALF OF THE SQUARE-SYMMETRIC MATRIX WITHSA1  91 
C             -OUT THE DIAGONAL ELEMENTS, STARTING A NEW ROW ON A NEW   SA1  92 
C             CARD.  IN TOTAL YOU SHOULD HAVE NR-1 SETS OF CARDS WITH   SA1  93 
C             1 ELEMENT IN THE FIRST SET FOR THE SECOND ROW, 2 ELEMENTS SA1  94 
C             IN THE SECOND SET FOR THE THIRD ROW, ... , AND NR-1 COEF- SA1  95 
C             FICIENTS IN THE LAST OR NR-1'ST SET).  ALL ROWS MUST BE   SA1  96 
C             LEFT-ADJUSTED.  OMIT WHEN IFFIX=1.                        SA1  97 
C        8.   FOR EACH VARIABLE TO BE ADDED (WHEN IFFFIX=1) PUNCH NR    SA1  98 
C             COEFFICIENTS ON AS MANY CARDS AS NECESSARY TO SATISFY NR, SA1  99 
C             ACCORDING TO THE SAME FORMAT AS IN ITEM 5.  WHEN IFFIX=0, SA1 100 
C             OMIT THIS SET OF CARDS.                                   SA1 101 
C        9.   REPEAT ITEMS 3-8 FOR ADDITIONAL RUNS.  ONLY 1 RUN OF A    SA1 102 
C             FIXED CONFIGURATION CAN BE MADE AT A TIME AND THIS SHOULD SA1 103 
C             APPEAR AS THE LAST JOB RUN IN A DECK OF JOBS.             SA1 104 
C                                                                       SA1 105 
C     *** USERS OF THIS PROGRAM ARE EXPECTED TO PROPERLY CREDIT SOURCE  SA1 106 
C     FROM REFERENCES LISTED BELOW.  IF IFGLK IS SET TO 1, THEN A REFER-SA1 107 
C     ENCE TO KRUSKAL'S PAIR OF 1964 PSYCHOMETRIKA PAPERS SHOULD ALSO BESA1 108 
C     MADE. ***                                                         SA1 109 
C                                                                       SA1 110 
C     *** REFERENCES - GUTTMAN, L. A GENERAL NONMETRIC TECHNIQUE FOR    SA1 111 
C                                  FINDING THE SMALLEST COORDINATE SPACESA1 112 
C                                  FOR A CONFIGURATION OF POINTS.  PSY- SA1 113 
C                                  CHOMETRIKA, 1968, 33, 469-506.       SA1 114 
C                      LINGOES, J. C.  NEW COMPUTER DEVELOPMENTS IN PAT-SA1 115 
C                                  TERN ANALYSIS AND NONMETRIC TECH-    SA1 116 
C                                  NIQUES.  IN - USES OF COMPUTERS IN   SA1 117 
C                                  PSYCHOLOGICAL RESEARCH.  GAUTHIER-   SA1 118 
C                                  VILLARS, PARIS, 1966, 1-22.          SA1 119 
C                      LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- SA1 120 
C                                  LINGOES SMALLEST SPACE ANALYSIS - I. SA1 121 
C                                  BEHAV. SCI., 1965,10,183-184.        SA1 122 
C                      LINGOES, J.C., ROSKAM, E.E.C.I., & GUTTMAN, L.   SA1 123 
C                                  AN EMPIRICAL STUDY OF TWO MULTIDIMEN-SA1 124 
C                                  SIONAL SCALING ALGORITHMS.  MULTIV.  SA1 125 
C                                  BEHAV. RES., 1969, 4,                SA1 126 
C                                                                       SA1 127 
C     SSA2                                                              WUP 113 
C     GUTTMAN-LINGOES SMALLEST SPACE ANALYSIS FOR ASYMMETRIC            WUP 114 
C     AND/OR PARTLY-ORDERED DISTANCE MATRICES. G-L(SSA-II)              WUP 115 
C     PROGRAMMED IN FORTRAN II FOR THE U. OF M. IBM-7090                WUP 116 
C     BY J. C. LINGOES (1/21/65).                                       WUP 117 
C                                                                       WUP 118 
C     DECK SET-UP FOR G-L(SSA-II) -                                     WUP 119 
C                                                                       WUP 120 
C        1.  SYSTEM ID CARD/S.                                          WUP 121 
C        2.  BINARY PROGRAM.                                            WUP 122 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 123 
C            UMNS 2-72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF OUT- WUP 124 
C            PUT).                                                      WUP 125 
C        4.  PARAMETER CARD, 7 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 126 
C            INFORMATION SERIATUM -                                     WUP 127 
C            A)  NR=THE NUMBER OF VARIABLES .LE. 70,                    WUP 128 
C            B)  MIND (SEE G-L(SSA-I),                                  WUP 129 
C            C)  MAXD (SEE G-L(SSA-I),                                  WUP 130 
C            D)  ISIM (SEE G-L(SSA-I),                                  WUP 131 
C            E)  NSYM=1 IF FULL MATRIX IS PUNCHED AND 0 OR BLANK OTHER- WUP 132 
C                WISE FOR HALF-MATRIX AS IN G-L(SSA-I),                 WUP 133 
C            F)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR MOREWUP 134 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 135 
C            G)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE   WUP 136 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 137 
C            H)  IFCB=1 IF CITY BLOCK MODEL IS TO BE USED (N.B. IF THIS WUP 138 
C                ALTERNATIVE IS USED MIND MUST BE GREATER THAN ZERO),   WUP 139 
C                OTHERWISE SET TO ZERO OR LEAVE BLANK FOR EUCLIDEAN D'S.WUP 140 
C        5.  FORMAT CARD (DESCRIBING IN F-NOTATION HOW DATA IS PUNCHED).WUP 141 
C        6.  DATA (SEE G-L(SSA-I) FOR SYMMETRIC DATA INPUT.  FOR ASYMME-WUP 142 
C            TRIC DATA PUNCH A COMPLETE SQUARE MATRIX BY ROWS, INCLUDINGWUP 143 
C            THE DIAGONAL ELEMENTS (WHICH MAY BE ANYTHING SINCE THEY AREWUP 144 
C            NOT USED IN THE ANALYSIS), STARTING A NEW ROW ON A NEW SET WUP 145 
C            OF CARDS, YIELDING NR SETS).                               WUP 146 
C        7.  2ND TITLE CARD (IF NSYM=1 ON PREVIOUS CONTROL CARD, OTHER- WUP 147 
C            WISE REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS).  THE 1ST SSA   WUP 148 
C            OUTPUT IS BASED UPON WITHIN-COLUMN RANKINGS, WHILE THE 2ND WUP 149 
C            IS BASED UPON WITHIN-ROW RANKINGS.  EVEN IF NSYM=1 A PERSONWUP 150 
C            MAY ONLY BE INTERESTED IN ONE OF THESE TWO SOLUTIONS IN    WUP 151 
C            WHICH CASE HE SHOULD INPUT THE ASYMMETRIC MATRIX BUT       WUP 152 
C            OMIT THIS AND THE FOLLOWING CONTROL CARD.  IF THIS OPTION  WUP 153 
C            IS CHOSEN, HOWEVER, ONE CANNOT DO MULTIPLE JOB PROCESSING).WUP 154 
C        8.  2ND PARAMETER CARD (IF NSYM=1 ON 1ST CONTROL CARD, REPEAT  WUP 155 
C            ALL PARAMETERS BUT SET COLUMN 20 TO A 0 OR LEAVE BLANK. FORWUP 156 
C            MULTIPLE JOBS WHERE 2 SOLUTIONS ARE DESIRED FOR ASYMMETRIC WUP 157 
C            MATRICES, REPEAT ITEMS 3-8).                               WUP 158 
C                                                                       WUP 159 
C     *** REFERENCES - LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 160 
C                                  LINGOES SMALLEST SPACE ANALYSIS - II.WUP 161 
C                                  BEHAV. SCI., 1965, 10, 487.          WUP 162 
C     SSA3                                                              WUP 163 
C     NONMETRIC FACTOR ANALYSIS.  THIS PROGRAM STARTING WITH A MATRIX OFWUP 164 
C     COEFFICIENTS R(I,J) RESULTING FROM MM' DETERMINES A MINIMUM SET OFWUP 165 
C     ORTHOGONAL COORDINATES X(A), A=1,2,...,M SUCH THAT THE VALUES OB- WUP 166 
C     TAINED FROM XX' ARE A MONOTONIC FUNCTION OF THE ORIGINAL COEFFI-  WUP 167 
C     CIENTS.  THIS RESEARCH IS SUPPORTED IN PART BY NSF-GS-929, COPRIN-WUP 168 
C     CIPAL INVESTIGATORS - GUTTMAN, L. AND LINGOES, J.C.               WUP 169 
C     PROGRAMMED IN FORTRAN II (8/15/65).                               WUP 170 
C                                                                       WUP 171 
C     DECK SET-UP FOR G-L(SSA-III) -                                    WUP 172 
C                                                                       WUP 173 
C        1.  SYSTEM ID CARD/S.                                          WUP 174 
C        2.  BINARY PROGRAM                                             WUP 175 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 176 
C            UMNS 2-72, WHICH WILL HEAD OUTPUT).                        WUP 177 
C        4.  PARAMETER CARD, 10 4-COLUMN AND 1 8-COLUMN FIELDS CONTAIN- WUP 178 
C            ING THE FOLLOWING INFORMATION SERIATUM -                   WUP 179 
C            A)  RUN=SOME NUMERIC CODE IDENTIFYING OUTPUT .LE. 2**15,   WUP 180 
C            B)  NV=NUMBER OF VARIABLES .LE. 70,                        WUP 181 
C            C)  NFMT=NUMBER OF FORMAT CARDS .LE. 10,                   WUP 182 
C            D)  NITER=NUMBER OF ITERATIONS, IF 0 OR BLANK NITER=25,    WUP 183 
C            E)  MIND=MINIMUM NUMBER OF DIMENSIONS DESIRED.  IF BLANK ORWUP 184 
C                ZERO MIND=1,                                           WUP 185 
C            F)  NDIM=MAXIMUM NUMBER OF DIMENSIONS DESIRED.  IF BLANK ORWUP 186 
C                ZERO PROGRAM WILL DETERMINE,                           WUP 187 
C            G)  IFT=1 IF THETA COEFFICIENTS ARE TO BE PRINTED FOR 2 OR WUP 188 
C                MORE DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK, WUP 189 
C            H)  IFC=1 IF COORDINATES FOR 2 OR MORE DIMENSIONS ARE TO BEWUP 190 
C                PUNCHED, OTHERWISE SET TO ZERO OR LEAVE BLANK,         WUP 191 
C            I)  IFCOV=1 IF NORMALIZED (ON LARGEST VARIANCE) COVARIANCESWUP 192 
C                RATHER THAN CORRELATIONS ARE DESIRED, OTHERWISE LEAVE  WUP 193 
C                BLANK OR SET TO ZERO FOR CORRELATIONS,                 WUP 194 
C            J)  IFMISS=1 IF MISSING DATA, BLANK OR ZERO OTHERWISE,     WUP 195 
C            K)  CODE=SOME NUMERIC CODE APPLICABLE TO ALL VARIABLES FOR WUP 196 
C                WHICH MISSING DATA EXIST.  PUNCH WITH DECIMAL POINT.   WUP 197 
C        5.  FORMAT CARD/S, (PUNCH '(I1,' AND DESCRIBE IN F-NOTATION    WUP 198 
C            WHERE DATA APPEAR ON CARDS.  TERMINATE WITH ')').          WUP 199 
C        6.  DATA CARDS - LEAVE COLUMN 1 BLANK AND PLACE DATA IN COLUMNSWUP 200 
C            2-72, RESERVING 73-80 FOR OPTIONAL ID INFORMATION.  DO NOT WUP 201 
C            SPLIT A FIELD OVER 2 CARDS.  PUNCH ALL SCORES FOR 1 S ON 1 WUP 202 
C            SET OF CARDS, FOLLOWED BY 2ND S, ETC.                      WUP 203 
C        7.  IF THERE ARE T CARD/S, T TRAILER CARDS MUST FOLLOW DATA,   WUP 204 
C            WITH A 9 PUNCHED IN COLUMN 1 OF THE FIRST TRAILER CARD.    WUP 205 
C        8.  TITLE CARD FOR SSA-III PAGE HEADINGS (SEE ITEM 3 ABOVE).   WUP 206 
C        9.  REPEAT 3-8 FOR ADDITONAL RUNS.                             WUP 207 
C                                                                       WUP 208 
C     *** REFERENCES - LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 209 
C                        LINGOES SMALLEST SPACE ANALYSIS - III.  BEHAV. WUP 210 
C                        SCI., 1966,11,75-76.                           WUP 211 
C                      LINGOES, J. C. AND GUTTMAN, L.  NONMETRIC FACTOR WUP 212 
C                        ANALYSIS - A RANK REDUCING ALTERNATIVE TO      WUP 213 
C                        LINEAR FACTOR ANALYSIS.  MULT. BEHAV. RES.,    WUP 214 
C                        1967,2,485-505.                                WUP 215 
C     SSA3A                                                             WUP 216 
C     SSA-IIIA - COEFFICIENT INPUT.  CORE 1.                            WUP 217 
C                                                                       WUP 218 
C     DECK SET-UP FOR G-L(SSA-IIIA) -                                   WUP 219 
C                                                                       WUP 220 
C        1.  SYSTEM ID CARDS.                                           WUP 221 
C        2.  BINARY PROGRAM.                                            WUP 222 
C        3.  PARAMETER CARD, 8 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 223 
C            INFORMATION SERIATUM -                                     WUP 224 
C            A)  NV=NUMBER OF VARIABLES, .LE. 70,                       WUP 225 
C            B)  NFMT=NUMBER OF FORMAT CARDS, .LE. 10,                  WUP 226 
C            C)  NITER=NUMBER OF ITERATIONS (SEE SSA-III),              WUP 227 
C            D)  MIND=MINIMUM NUMBER OF DIMENSIONS (SEE SSA-III),       WUP 228 
C            E)  NDIM=MAXIMUM NUMBER OF DIMENSIONS (SEE SSA-III),       WUP 229 
C            F)  IFNOM=1 IF MEAN OF INPUT VALUES IS NOT TO BE PRESERVED,WUP 230 
C                OTHERWISE SET TO ZERO OR LEAVE BLANK,                  WUP 231 
C            G)  IFT=1 IF THETA COEFFICIENTS ARE TO BE PRINTED FOR 2 OR WUP 232 
C                MORE DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK, WUP 233 
C            H)  IFC=1 IF COORDINATES FOR 2 OR MORE DIMENSIONS ARE TO BEWUP 234 
C                PUNCHED, OTHERWISE SET TO ZERO OR LEAVE BLANK.         WUP 235 
C        4.  FORMAT CARD/S (SEE SSA-I).                                 WUP 236 
C        5.  DATA CARDS (SAME AS SSA-I).                                WUP 237 
C        6.  TITLE CARD FOR SSA-IIIA OUTPUT.                            WUP 238 
C        7.  REPEAT ITEMS 3-6 FOR ADDITONAL RUNS.                       WUP 239 
C     SSA3B                                                             WUP 240 
C     PROGRAM TO COMPUTE NORMALIZED SCALAR PRODUCTS FOR SSA-III. CORE 2.WUP 241 
C                                                                       WUP 242 
C     SSA4                                                              WUP 264 
C     SMALLEST SPACE ANALYSIS WITH UNKNOWN COMMUNALITIES - G-L(SSA-IV). WUP 265 
C     PROGRAMMED IN FORTRAN II BY J. C. LINGOES - 2/15/66.  NSF-GS-929. WUP 266 
C     IN GENERAL THIS PROGRAM SHOULD BE RESTRICTED TO PROXIMITY MEASURESWUP 267 
C     AND MORE SPECIFICALLY CORRELATIONS OR COVARIANCES.                WUP 268 
C                                                                       WUP 269 
C     DECK SET-UP FOR G-L(SSA-IV) -                                     WUP 270 
C                                                                       WUP 271 
C        1.  SYSTEM ID CARD/S.                                          WUP 272 
C        2.  BINARY PROGRAM.                                            WUP 273 
C        3.  TITLE CARD (SEE SSA-I).                                    WUP 274 
C        4.  PARAMETER CARD, 6 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 275 
C            INFORMATION SERIATUM -                                     WUP 276 
C            A)  NV= THE NUMBER OF VARIABLES (.LE. 60),                 WUP 277 
C            B)  M=THE MINIMUM NUMBER OF DIMENSIONS DESIRED (1 TO MAXD),WUP 278 
C            C)  MAXD= THE MAXIMUM NUMBER OF DIMENSIONS DESIRED .LE.    WUP 279 
C                (NV,10)MIN,                                            WUP 280 
C            D)  ITER=NUMBER OF ITERATIONS,                             WUP 281 
C            E)  IFC=1 IF COORDINATES FOR 2 OR MORE DIMENSIONS ARE TO BEWUP 282 
C                PUNCHED, OTHERWISE SET TO ZERO OR LEAVE BLANK,         WUP 283 
C            F)  CMON=CUT-OUT FOR COEFFICIENT OF MONOTONICITY (.G. 0 BUTWUP 284 
C                .LE. 1.00), WHICH MUST INCLUDE DECIMAL POINT.          WUP 285 
C        5.  FORMAT CARD.                                               WUP 286 
C        6.  DATA (SAME AS FOR SSA-I, Q.V.).                            WUP 287 
C        7.  REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                      WUP 288 
C                                                                       WUP 289 
C     *** REFERENCES - LINGOES,J.C.  AN IBM-7090 PROGRAM FOR GUTTMAN-   WUP 290 
C                                  LINGOES SMALLEST SPACE ANALYSIS - IV.WUP 291 
C                                  BEHAV. SCI.,1966,11,407.             WUP 292 
C     SSAR1                                                             WUP 293 
C     A GENERAL NONMETRIC TECHNIQUE FOR FINDING THE SMALLEST EUCLIDEAN  WUP 294 
C     SPACE FOR A CONFIGURATION OF POINTS.  SOLUTION FOR THE CASE IN-   WUP 295 
C     VOLVING TWO SETS OF POINTS WITH THE BETWEEN SET DISTANCES DEFINED WUP 296 
C     BUT THE WITHIN SET DISTANCES UNKNOWN.  DETERMINE THE SMALLEST     WUP 297 
C     SPACE FOR WHICH THE BETWEEN DISTANCES ARE MONOTONIC WITH ORIGINAL WUP 298 
C     DISTANCES.  NONMETRIC PROGRAM FOR MULTIFACET DESIGNS.  THIS RE-   WUP 299 
C     SEARCH IN NONMETRIC METHODS SUPPORTED IN PART BY A GRANT TO L.    WUP 300 
C     GUTTMAN AND J. C. LINGOES FROM NSF (GS-929).  PROGRAMMED IN FOR-  WUP 301 
C     TRAN II FOR THE UNIV. OF MICHIGAN IBM-7090 BY J.C.LINGOES(1/15/66)WUP 302 
C                                                                       WUP 303 
C     DECK SET-UP FOR G-L(SSAR-I) -                                     WUP 304 
C                                                                       WUP 305 
C        1.   SYSTEM ID CARD/S.                                         WUP 306 
C        2.   BINARY PROGRAM.                                           WUP 307 
C        3.   TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COLWUP 308 
C             -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF WUP 309 
C             OUTPUT).                                                  WUP 310 
C        4.   PARAMETER CARD, 8 4-COLUMN FIELDS CONTAINING THE FOLLOW-  WUP 311 
C             ING INFORMATION SERIATUM -                                WUP 312 
C             A)  NS=THE NUMBER OF ROWS .LE. 50,                        WUP 313 
C             B)  NV=THE NUMBER OF COLUMNS .LE. 30, BUT SINCE ROW AND   WUP 314 
C                 COLUMN DESIGNATIONS ARE ARBITRARY,IF ONE HAS MORE COL-WUP 315 
C                 UMNS THAN ROWS THEY CAN BE INTERCHANGED,              WUP 316 
C             C)  MIND=0 OR BLANK IF THE PROGRAM IS TO DETERMINE THE MINWUP 317 
C                 -IMUM NUMBER OF DIMENSIONS FOR THE PROBLEM, OTHERWISE WUP 318 
C                 ANY NUMBER BETWEEN 1 AND 10 PROVIDED MIND .LE. MAXD,  WUP 319 
C                 IN WHICH CASE ALL SOLUTIONS FROM MIND TO MAXD WILL BE WUP 320 
C                 PRINTED OUT UNLESS THE NORMALIZED PHI GETS TO BE .LE. WUP 321 
C                 .000001 FOR A GIVEN M, THE NUMBER OF DIMENSIONS,      WUP 322 
C             D)  MAXD=THE LARGEST NUMBER OF DIMENSIONS DESIRED .LE.    WUP 323 
C                 (NV-1,10)MIN,                                         WUP 324 
C             E)  ISIM=0 OR BLANK FOR DISTANCE COEFFICIENTS OR DISSIMI- WUP 325 
C                 LARITY DATA AND 1 IF SIMILARITY DATA, E.G., CORRELA-  WUP 326 
C                 TIONS,                                                WUP 327 
C             F)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR    WUP 328 
C                 MORE DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,WUP 329 
C             G)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE  WUP 330 
C                 DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,     WUP 331 
C             H)  IFCB=1 IF CITY-BLOCK MODEL IS TO BE USED (N.B. IF THISWUP 332 
C                 ALTERNATIVE IS USED MIND MUST BE .G. 0), OTHERWISE SETWUP 333 
C                 TO ZERO OR LEAVE BLANK FOR EUCLIDEAN MODEL.           WUP 334 
C        5.   FORMAT CARD (DESCRIBING IN F-NOTATION WHERE THE DATA      WUP 335 
C             APPEARS ON THE CARDS).                                    WUP 336 
C        6.   DATA (PUNCH EACH ROW ON 1 SET OF CARDS, YIELDING NS SETS  WUP 337 
C             WITH NV ELEMENTS (COLUMN FIELDS) IN EACH SET).            WUP 338 
C        7.   REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                     WUP 339 
C                                                                       WUP 340 
C     *** REFERENCES - GUTTMAN, L. A GENERAL NONMETRIC TECHNIQUE FOR    WUP 341 
C                                  FINDING THE SMALLEST EUCLIDEAN SPACE WUP 342 
C                                  FOR A CONFIGURATION OF POINTS.  PSY- WUP 343 
C                                  CHOMETRIKA,  1968,                   WUP 344 
C                      LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 345 
C                                  LINGOES SMALLEST SPACE ANALYSIS - I. WUP 346 
C                                  BEHAV. SCI., 1965,10,183-184.        WUP 347 
C                      LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 348 
C                                  LINGOES SMALLEST SPACE ANALYSIS - RI.WUP 349 
C                                  BEHAV. SCI., 1966,11, 322.           WUP 350 
C                      LINGOES, J. C. AND VANDENBERG, S. G.  A NONMETRICWUP 351 
C                                  ANALYSIS OF TWIN DATA BASED ON A MUL-WUP 352 
C                                  TIFACETED DESIGN.  RES. RPT.,1966,   WUP 353 
C                                  17, 1-19.                            WUP 354 
C     SSAR2                                                             WUP 355 
C     SMALLEST SPACE ANALYSIS-RECTANGULAR - II, A NONMETRIC METHOD FOR  WUP 356 
C     SOLVING FOR TWO SETS OF POINTS GIVEN THE INTER-SET DISTANCES/SIM- WUP 357 
C     ILARITIES.  USEFUL FOR THE STUDY OF REGRESSION CURVES AND MULTIDI-WUP 358 
C     MENSIONAL UNFOLDING (COOMBS) OF PREFERENCE DATA.  THIS            WUP 359 
C     RESEARCH IN NONMETRIC METHODS IS SUPPORTED IN PART BY A NSF GRANT WUP 360 
C     (GS-929) TO L. GUTTMAN AND J. C. LINGOES.  PROGRAMMED IN FORTRAN  WUP 361 
C     II BY LINGOES 12/15/65.                                           WUP 362 
C                                                                       WUP 363 
C     DECK SET-UP FOR G-L(SSAR-II) -                                    WUP 364 
C                                                                       WUP 365 
C        1.  SYSTEM ID CARD/S.                                          WUP 366 
C        2.  BINARY PROGRAM.                                            WUP 367 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 368 
C            UMNS 2-72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF OUT- WUP 369 
C            PUT).                                                      WUP 370 
C        4.  PARAMETER CARD, 9 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 371 
C            INFORMATION SERIATUM -                                     WUP 372 
C            A)  NS=THE NUMBER OF ROWS OF RECTANGULAR MATRIX (.LE.39),  WUP 373 
C            B)  NV=THE NUMBER OF COLUMNS OF MATRIX (.LE.39),           WUP 374 
C            C)  MIND=MINIMUM NUMBER OF DIMENSIONS DESIRED.  IF ZERO OR WUP 375 
C                BLANK PROGRAM WILL DETERMINE,                          WUP 376 
C            D)  MAXD=MAXIMUM NUMBER OF DIMENSIONS DESIRED (.LE. 5 OR   WUP 377 
C                THE ROW OR COLUMN ORDER OF SUBMATRIX, WHICHEVER IS     WUP 378 
C                SMALLER),                                              WUP 379 
C            E)  ISIM=ZERO OR BLANK IF DISTANCES/DISSIMILARITIES AND 1  WUP 380 
C                IF SIMILARITIES/PROXIMITIES,                           WUP 381 
C            F)  MU=0 OR BLANK IF BOTH A ROW AND A COLUMN SOLUTION IS   WUP 382 
C                DESIRED AND MU=1 IF ONLY A ROW SOLUTION IS NEEDED,     WUP 383 
C            G)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR MOREWUP 384 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 385 
C            H)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE   WUP 386 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 387 
C            I)  IFCB=1 IF CITY-BLOCK MODEL IS TO BE USED (N. B. IF THISWUP 388 
C                ALTERNATIVE IS USED MIND MUST BE .G. 0), OTHERWISE SET WUP 389 
C                TO ZERO OR LEAVE BLANK FOR EUCLIDEAN MODEL.            WUP 390 
C        5.  FORMAT CARD (DESCRIBING IN F-NOTATION HOW DATA IS PUNCHED).WUP 391 
C        6.  DATA - EACH SET OF CARDS CONTAINS ALL THE DATA FOR ONE ROW WUP 392 
C            OF SUBMATRIX.  NS SETS WILL BE INPUT.                      WUP 393 
C        7.  REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                      WUP 394 
C                                                                       WUP 395 
C     *** REFERENCES - LINGOES, J. C.  AN IBM 7090 PROGRAM FOR GUTTMAN- WUP 396 
C                                  LINGOES SMALLEST SPACE ANALYSIS-RII. WUP 397 
C                                  BEHAV. SCI., 1966,11, 322.           WUP 398 
C     SSAR3                                                             WUP 399 
C     SMALLEST SPACE ANALYSIS-R3, A NONMETRIC METHOD FOR OFF-DIAGONAL   WUP 400 
C     SUBMATRICES AND FOR MULTIDIMENSIONAL UNFOLDING.  THIS             WUP 401 
C     RESEARCH IN NONMETRIC METHODS IS SUPPORTED IN PART BY A NSF GRANT WUP 402 
C     (GS-929) TO L. GUTTMAN AND J. C. LINGOES.  PROGRAMMED IN FORTRAN  WUP 403 
C     II BY LINGOES 12/15/65.                                           WUP 404 
C                                                                       WUP 405 
C     DECK SET-UP FOR G-L(SSAR-III) -                                   WUP 406 
C                                                                       WUP 407 
C        1.  SYSTEM ID CARD/S.                                          WUP 408 
C        2.  BINARY PROGRAM.                                            WUP 409 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 410 
C            UMNS 2-72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF OUT- WUP 411 
C            PUT).                                                      WUP 412 
C        4.  PARAMETER CARD, 9 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 413 
C            INFORMATION SERIATUM -                                     WUP 414 
C            A)  NS= THE NUMBER OF I-SCALES OR ROWS OF OFF-DIAGONAL SUB-WUP 415 
C                MATRIX, (.LE. 33),                                     WUP 416 
C            B)  NV=THE NUMBER OF STIMULI OR THE NUMBER OF COLUMNS IN   WUP 417 
C                THE OFF-DIAGONAL SUBMATRIX (.LE.33),                   WUP 418 
C            C)  MIND=MINIMUM NUMBER OF DIMENSIONS DESIRED.  IF ZERO OR WUP 419 
C                BLANK PROGRAM WILL DETERMINE,                          WUP 420 
C            D)  MAXD=MAXIMUM NUMBER OF DIMENSIONS DESIRED (.LE. 8 OR   WUP 421 
C                THE ROW OR COLUMN ORDER OF SUBMATRIX, WHICHEVER IS     WUP 422 
C                SMALLER),                                              WUP 423 
C            E)  ISIM=ZERO OR BLANK IF DISTANCES/DISSIMILARITIES AND 1  WUP 424 
C                IF SIMILARITIES/PROXIMITIES,                           WUP 425 
C            F)  MU=0 OR BLANK IF RANKS ARE TO BE MAINTAINED OVER ROWS  WUP 426 
C                AND COLUMNS,  MU=1 IF RANKS MAINTAINED OVER ROWS ONLY  WUP 427 
C                AS IN COOMBS' MULTIDIMENSIONAL UNFOLDING ANALYSIS,     WUP 428 
C            G)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR MOREWUP 429 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 430 
C            H)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE   WUP 431 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 432 
C            I)  IFCB=1 IF CITY-BLOCK MODEL IS TO BE USED (N. B.  IF    WUP 433 
C                THIS ALTERNATIVE IS USED MIND MUST BE .G. 0), OTHERWISEWUP 434 
C                SET TO ZERO OR LEAVE BLANK FOR EUCLIDEAN MODEL.        WUP 435 
C        5.  FORMAT CARD (DESCRIBING IN F-NOTATION HOW DATA IS PUNCHED).WUP 436 
C        6.  DATA - EACH SET OF CARDS CONTAINS ALL THE DATA FOR ONE ROW WUP 437 
C            OF SUBMATRIX.  NS SETS WILL BE INPUT.                      WUP 438 
C        7.  REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                      WUP 439 
C                                                                       WUP 440 
C     *** REFERENCES - LINGOES, J. C.  AN IBM 7090 PROGRAM FOR GUTTMAN- WUP 441 
C                                  LINGOES SMALLEST SPACE ANALYSIS-RIII.WUP 442 
C                                  BEHAV. SCI., 1966,11, 323.           WUP 443 
C     SSAR4                                                             WUP 444 
C     SMALLEST SPACE ANALYSIS-RECTANGULAR - IV, A NONMETRIC METHOD FOR  WUP 445 
C     SOLVING FOR TWO SETS OF POINTS GIVEN THE INTER-SET DISTANCES/SIM- WUP 446 
C     ILARITIES FOR SQUARE MATRICES WITH DIAGONAL ELEMENTS MISSING, DIS-WUP 447 
C     TANCES FOR WHICH ARE TO BE DERIVED.  AN SSA-II ANALYSIS IN A JOINTWUP 448 
C     SPACE.  USEFUL FOR MULTIDIMENSIONAL UNFOLDING (COOMBS).  THIS     WUP 449 
C     RESEARCH IN NONMETRIC METHODS IS SUPPORTED IN PART BY A NSF GRANT WUP 450 
C     (GS-929) TO L. GUTTMAN AND J. C. LINGOES.  PROGRAMMED IN FORTRAN  WUP 451 
C     II BY LINGOES - 5/15/66.                                          WUP 452 
C                                                                       WUP 453 
C     DECK SET-UP FOR G-L(SSAR-IV) -                                    WUP 454 
C                                                                       WUP 455 
C        1.  SYSTEM ID CARD/S.                                          WUP 456 
C        2.  BINARY PROGRAM.                                            WUP 457 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 458 
C            UMNS 2-72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF OUT- WUP 459 
C            PUT).                                                      WUP 460 
C        4.  PARAMETER CARD, 8 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 461 
C            INFORMATION SERIATUM -                                     WUP 462 
C            A)  NS=ORDER OF MATRIX (.LE. 38),                          WUP 463 
C            B)  MIND=MINIMUM NUMBER OF DIMENSIONS DESIRED.  IF ZERO OR WUP 464 
C                BLANK PROGRAM WILL DETERMINE,                          WUP 465 
C            C)  MAXD=MAXIMUM NUMBER OF DIMENSIONS DESIRED .LE.         WUP 466 
C                (NS-1,10)MIN,                                          WUP 467 
C            D)  ISIM=ZERO OR BLANK IF DISTANCES/DISSIMILARITIES AND 1  WUP 468 
C                IF SIMILARITIES/PROXIMITIES,                           WUP 469 
C            E)  MU=0 OR BLANK IF BOTH A ROW AND A COLUMN SOLUTION IS   WUP 470 
C                DESIRED AND MU=1 IF ONLY A ROW SOLUTION IS NEEDED,     WUP 471 
C            F)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR MOREWUP 472 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 473 
C            G)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE   WUP 474 
C                DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,      WUP 475 
C            H)  IFCB=1 IF CITY-BLOCK MODEL IS TO BE USED (N.B.  IF THISWUP 476 
C                MODEL IS USED MIND MUST BE .G. 0), OTHERWISE SET TO    WUP 477 
C                ZERO OR LEAVE BLANK FOR EUCLIDEAN MODEL.               WUP 478 
C        5.  FORMAT CARD (DESCRIBING IN F-NOTATION HOW DATA IS PUNCHED).WUP 479 
C        6.  DATA - EACH SET OF CARDS CONTAINS ALL THE DATA FOR ONE ROW WUP 480 
C            OF SUBMATRIX.  NS SETS WILL BE INPUT (SEE SSA-II).         WUP 481 
C        7.  REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                      WUP 482 
C                                                                       WUP 483 
C     *** REFERENCES - LINGOES, J. C.  AN IBM 7090 PROGRAM FOR GUTTMAN- WUP 484 
C                                  LINGOES SMALLEST SPACE ANALYSIS-RII. WUP 485 
C                                  BEHAV. SCI., 1966,11,322.            WUP 486 
C                      LINGOES, J. C.  AN IBM 7090 PROGRAM FOR GUTTMAN- WUP 487 
C                                  LINGOES SMALLEST SPACE ANALYSIS-RIV. WUP 488 
C                                  BEHAV. SCI., 1967,12,74-75.          WUP 489 
C                      LINGOES, J. C.  RECENT COMPUTATIONAL ADVANCES IN WUP 490 
C                                  NONMETRIC METHODOLOGY FOR THE BEHAV- WUP 491 
C                                  IORAL SCIENCES.  PROCEEDINGS OF THE  WUP 492 
C                                  INTERNATIONAL SYMPOSIUM ON MATHEMAT- WUP 493 
C                                  ICAL AND COMPUTATIONAL METHODS IN SO-WUP 494 
C                                  CIAL SCIENCES, ROME, ITALY, 1966.    WUP 495 
C     SSAP1                                                             SP1   1 
C     A GENERAL NONMETRIC TECHNIQUE FOR FINDING THE SMALLEST EUCLIDEAN  SP1   2 
C     SPACE FOR A CONFIGURATION OF POINTS IN A JOINT SPACE, WHERE THE   SP1   3 
C     MATRIX IS PARTITIONED INTO TWO DIAGONAL SYMMETRIC SUBMATRICES     SP1   4 
C     (CORRESPONDING TO THE ASSOCIATIONS AMONG OBJECTS AND VARIABLES/   SP1   5 
C     CATEGORIES, RESPECTIVELY) AND AN OFF-DIAGONAL SUBMATRIX CONTAININGSP1   6 
C     THE RELATIONSHIPS BETWEEN A SET OF OBJECTS AND A SET OF VARIABLES/SP1   7 
C     CATEGORIES.  ORDINAL INFORMATION IS ASSUMED TO EXIST WITHIN EACH  SP1   8 
C     PARTITION SEPARATELY AND OVER ALL ELEMENTS IN THAT PARTITION.     SP1   9 
C     PROGRAMMED IN FORTRAN IV FOR THE UNIV. OF MICHIGAN IBM-360/67 BY  SP1  10 
C     J.C.LINGOES (1/15/69).  THE PRESENT PROGRAM INCLUDES OPTIONS FOR: SP1  11 
C     1) ANALYZING AN INDEFINITE NUMBER OF SUBJECTS OR VARIABLES/CATE-  SP1  12 
C     GORIES GIVEN A FIXED CONFIGURATION AND, 2) INPUT OF A CONFIGURA-  SP1  13 
C     TION OF ONE'S CHOICE.  ALGORITHMS EMPLOYED:  G-L "SOFT-SQUEEZE",  SP1  14 
C     DOUBLE-PHASE FOLLOWED BY SINGLE-PHASE (RANK-IMAGES) FOR SEMI-     SP1  15 
C     STRONG MONOTONICITY.                                              SP1  16 
C                                                                       SP1  17 
C     DECK SET-UP FOR G-L(SSAP-I):                                      SP1  18 
C                                                                       SP1  19 
C        1.   SYSTEM ID CARD/S.                                         SP1  20 
C        2.   BINARY PROGRAM.                                           SP1  21 
C        3.   TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COLSP1  22 
C             -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF SP1  23 
C             OUTPUT).                                                  SP1  24 
C        4.   PARAMETER CARD, 10 4-COLUMN FIELDS CONTAINING THE FOLLOW- SP1  25 
C             ING INFORMATION SERIATUM:                                 SP1  26 
C             A)  NS=THE NUMBER OF OBJECTS (V.I., RE CAPACITY),         SP1  27 
C             B)  NR=THE NUMBER OF VARIABLES/CATEGORIES.  NS+NR .LE. 100SP1  28 
C             C)  MIND=0 OR BLANK IF THE PROGRAM IS TO DETERMINE THE MINSP1  29 
C                 -IMUM NUMBER OF DIMENSIONS FOR THE PROBLEM, OTHERWISE SP1  30 
C                 ANY NUMBER BETWEEN 1 AND 10 PROVIDED MIND .LE. MAXD,  SP1  31 
C                 IN WHICH CASE ALL SOLUTIONS FROM MIND TO MAXD WILL BE SP1  32 
C                 PRINTED OUT, UNLESS COEFFICIENT OF ALIENATION < .0001 SP1  33 
C                 FOR A GIVEN M, THE NUMBER OF DIMENSIONS.  UNLESS YOU  SP1  34 
C                 KNOW M, SET MIND=0, IN GENERAL,                       SP1  35 
C             D)  MAXD=THE LARGEST NUMBER OF DIMENSIONS DESIRED .LE.    SP1  36 
C                 (NV-1,10)MIN BUT .GE. 1,                              SP1  37 
C             E)  ISIM=0 OR BLANK FOR DISTANCE COEFFICIENTS OR DISSIMI- SP1  38 
C                 LARITY DATA AND 1 IF SIMILARITY DATA, E.G., CORRELA-  SP1  39 
C                 TIONS.  ALL ELEMENTS ARE ASSUMED TO BE IN SAME ORDER, SP1  40 
C             F)  IFD=1 IF DISTANCE MATRIX IS TO BE PRINTED FOR 2 OR    SP1  41 
C                 MORE DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK,SP1  42 
C             G)  IFC=1 IF COORDINATES ARE TO BE PUNCHED FOR 2 OR MORE  SP1  43 
C                 DIMENSIONS, OTHERWISE SET TO ZERO OR LEAVE BLANK.     SP1  44 
C                 CARDS WILL BE AUTOMATICALLY PUNCHED IF MORE THAN 100  SP1  45 
C                 ITERATIONS ARE REQUIRED FOR CONVERGENCE OF 2 OR MORE  SP1  46 
C                 DIMENSIONS.  THESE CARDS CAN BE USED FOR SUBSEQUENT   SP1  47 
C                 INPUT TO CONTINUE THE ITERATIONS,                     SP1  48 
C             H)  IFCONF=1 IF A CONFIGURATION IS TO BE INPUT FOR CON-   SP1  49 
C                 TINUED ITERATIONS OR FOR ADDING POINTS TO A FIXED CON-SP1  50 
C                 FIGURATION, OTHERWISE LEAVE BLANK OR SET TO ZERO.     SP1  51 
C                 MAXD MUST BE THE NUMBER OF DIMENSIONS INPUT,          SP1  52 
C             I)  IFFIX=1 IF INPUT CONFIGURATION IS TO REMAIN FIXED AND SP1  53 
C                 ADDITIONAL POINTS ARE TO BE FITTED TO THIS SPACE,     SP1  54 
C                 OTHERWISE LEAVE BLANK OR SET TO ZERO.  MIND=MAXD.     SP1  55 
C                 TO ACCOMPLISH ANALYSIS OF NS+NR > 100: 1) ANALYZE SOMESP1  56 
C                 REPRESENTATIVE SAMPLE OF OBJECTS OR VARIABLES, SPECI- SP1  57 
C                 FYING IFC=1;  2) USE THE OUTPUT SOLUTION AS INPUT FOR SP1  58 
C                 IFFIX=1.  NS(ASSOCIATION COEFFICIENTS) + NR(VARIABLE/ SP1  59 
C                 CATEGORY SCORES) IS THE ORIGINAL NUMBER OF OBJECTS    SP1  60 
C                 PLUS VARIABLES/CATEGORIES.  ITEMS F) AND G) ABOVE ARE SP1  61 
C                 DISABLED WHEN IFFIX=1.  A CONDITIONAL APPROACH IS IN- SP1  62 
C                 VOKED FOR PRESERVING ORDER WITHIN THE SET OF NS AND   SP1  63 
C                 NR ELEMENTS SEPARATELY VIS-A-VIS THE ORIGINAL SET OF  SP1  64 
C                 NS OBJECT POINTS AND NR VARIABLE OR CATEGORY POINTS.  SP1  65 
C                 IF VARIABLES/CATEGORIES, RATHER THAN OBJECTS, ARE TO  SP1  66 
C                 BE ADDED, THEN NS SHOULD BE THE NUMBER OF VARIABLES/  SP1  67 
C                 CATEGORIES AND NR, THE NUMBER OF OBJECTS.  ONE INPUTS SP1  68 
C                 A NS+NR VECTOR OF VALUES IN ANY EVENT,                SP1  69 
C             J)  IFSR=1 IF EITHER ITEM 7. OR 8. IS TO BE GENERATED BY ASP1  70 
C                 SUBROUTINE (WHICH THE USER SUBSTITUTES FOR THE DUMMY  SP1  71 
C                 SUBROUTINES PROVIDED), OTHERWISE SET TO ZERO OR LEAVE SP1  72 
C                 BLANK.                                                SP1  73 
C        5.   FORMAT CARD (DESCRIBING IN F-NOTATION WHERE THE DATA      SP1  74 
C             APPEARS ON THE CARDS).                                    SP1  75 
C        6.   IF IFCONF=1, PUNCH CONFIGURATION TO BE INPUT (OR USE OUT- SP1  76 
C             PUT CONFIGURATION) ACCORDING TO FORMAT: 10F8.3.  THERE    SP1  77 
C             MUST BE NS+NR SETS OF CARDS, EACH SET OF WHICH SHOULD HAVESP1  78 
C             MAXD COORDINATES, OTHERWISE OMIT THIS SET WHEN IFCONF=0.  SP1  79 
C        7.   DATA (PUNCH LOWER-HALF OF THE SQUARE-SYMMETRIC MATRIX WITHSP1  80 
C             -OUT THE DIAGONAL ELEMENTS, STARTING A NEW ROW ON A NEW   SP1  81 
C             CARD.  IN TOTAL YOU SHOULD HAVE NS+NR-1 SETS OF CARDS WITHSP1  82 
C             1 ELEMENT IN THE FIRST SET FOR THE SECOND ROW, 2 ELEMENTS SP1  83 
C             IN THE SECOND SET FOR THE THIRD ROW,..., AND NS+NR-1 COEF-SP1  84 
C             FICIENTS IN THE LAST OR NS+NR-1'ST SET).  ALL ROWS MUST BESP1  85 
C             LEFT-ADJUSTED.  OMIT WHEN IFFIX=1.                        SP1  86 
C        8.   FOR EACH VARIABLE TO BE ADDED (WHEN IFFFIX=1) PUNCH NS+NR SP1  87 
C             COEFFICIENTS ON AS MANY CARDS AS NECESSARY TO SATISFY NS+ SP1  88 
C             NR ACCORDING TO THE FORMAT IN ITEM 5.  WHEN IFFIX=0, OMIT SP1  89 
C             THIS SET OF CARDS.                                        SP1  90 
C        9.   REPEAT ITEMS 3-8 FOR ADDITIONAL RUNS.  ONLY 1 RUN OF A    SP1  91 
C             FIXED CONFIGURATION CAN BE MADE AT A TIME AND THIS SHOULD SP1  92 
C             APPEAR AS THE LAST JOB RUN IN A DECK OF JOBS.             SP1  93 
C                                                                       SP1  94 
C     *** USERS OF THIS PROGRAM ARE EXPECTED TO PROPERLY CREDIT SOURCE  SP1  95 
C     FROM REFERENCES LISTED BELOW. ***                                 SP1  96 
C                                                                       SP1  97 
C     *** REFERENCES - GUTTMAN, L. A GENERAL NONMETRIC TECHNIQUE FOR    SP1  98 
C                                  FINDING THE SMALLEST COORDINATE SPACESP1  99 
C                                  FOR A CONFIGURATION OF POINTS.  PSY- SP1 100 
C                                  CHOMETRIKA, 1968, 33, 469-506.       SP1 101 
C                      LINGOES, J. C. A GENERAL NONPARAMETRIC MODEL FOR SP1 102 
C                                  REPRESENTING OBJECTS AND ATTRIBUTES  SP1 103 
C                                  IN A JOINT METRIC SPACE.  MULTIV.    SP1 104 
C                                  BEHAV. RES.,1969, 4,                 SP1 105 
C                      LINGOES, J. C.  AN IBM 360/67 PROGRAM FOR GUTTMANSP1 106 
C                                  -LINGOES SMALLEST SPACE ANALYSIS - PISP1 107 
C                                  BEHAV. SCI., 1969, 14,               SP1 108 
C                      LINGOES, J.C., ROSKAM, E.E.C.I., & GUTTMAN, L.   SP1 109 
C                                  AN EMPIRICAL STUDY OF TWO MULTIDIMEN-SP1 110 
C                                  SIONAL SCALING ALGORITHMS.  MULTIV.  SP1 111 
C                                  BEHAV. RES., 1969, 4,                SP1 112 
C                                                                       SP1 113 
C     MSA1                                                              WUP 496 
C     LINGOES MULTIVARIATE ANALYSIS OF CONTINGENCIES - CORE 1 (3/15/63).WUP 497 
C                                                                       WUP 498 
C     DECK SET-UP FOR G-L(MSA-I) -                                      WUP 499 
C                                                                       WUP 500 
C        1.  SYSTEM ID CARD/S.                                          WUP 501 
C        2.  BINARY PROGRAM.                                            WUP 502 
C        3.  TITLE CARD  (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COLWUP 503 
C            -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF  WUP 504 
C            OUTPUT).                                                   WUP 505 
C        4.  CONTROL CARD 1, 7 4-COLUMN FIELDS AND 1 8-COLUMN FIELD CON WUP 506 
C            -TAINING THE FOLLOWING INFORMATION SERIATUM -              WUP 507 
C            A)  NV=NUMBER OF VARIABLES OR ITEMS .LE. 50,               WUP 508 
C            B)  NS=NUMBER OF SUBJECTS .LE. 100 OR TYPES .LE. 60,       WUP 509 
C            C)  IFCODE=1, IF DATA HAS BEEN PRECODED, I.E., ALL VALUES  WUP 510 
C                MUST BE INTEGERS IN THE RANGE 1-20, OTHERWISE LEAVE    WUP 511 
C                BLANK OR SET TO 0,                                     WUP 512 
C            D)  MAX=THE NUMBER OF EQUAL INTERVALS INTO WHICH THE DATA  WUP 513 
C                IS TO BE CODED, ASSUMING THAT COLUMN 12 HAS BEEN LEFT  WUP 514 
C                BLANK.  IF THE DATA IS PRECODED LEAVE THESE COLUMNS    WUP 515 
C                BLANK OR SET TO 0.  MAX .LE. 20 BUT .G. 1,             WUP 516 
C            E)  NCAT=THE SMALLEST FREQUENCY .G. 1 TO BE PERMITTED IN   WUP 517 
C                ANY CATEGORY AFTER CODING.  IF NO LOWER LIMITS ARE DE- WUP 518 
C                SIRED SET TO 0 OR LEAVE BLANK,                         WUP 519 
C            F)  IFCDS=1, IF CARD OUTPUT OF THE CODED DATA IS DESIRED,  WUP 520 
C                OTHERWISE SET TO ZERO OR LEAVE BLANK,                  WUP 521 
C            G)  IFT=NUMBER OF TYPES IF NON-REDUNDANT PROFILES ARE TO BEWUP 522 
C                INPUT .LE. 60, OTHERWISE SET TO ZERO OR LEAVE BLANK IF WUP 523 
C                PROGRAM IS TO DETERMINE REDUNDANCIES AMONG THE NS SUB- WUP 524 
C                JECTS.  IF IFT .G. 0 THEN SET NS=IFT,                  WUP 525 
C            H)  CODE=A NUMERIC VALUE WHICH IS CONSTANT FOR ALL VARIA-  WUP 526 
C                BLES HAVING MISSING INFORMATION FOR WHICH IT IS REASON-WUP 527 
C                ABLE TO SUBSTITUTE A MEAN.  DO NOT USE A VALUE WHICH   WUP 528 
C                REPRESENTS A LEGITIMATE SCORE FOR ANY VARIABLE.  WHEN  WUP 529 
C                THERE IS NO MISSING DATA OR WHEN THE DATA HAS BEEN PRE-WUP 530 
C                CODED, LEAVE THESE COLUMNS BLANK OR SET TO 0.  A DECI- WUP 531 
C                MAL POINT MUST BE PUNCHED AND THE FIELD WIDTHS FOR THE WUP 532 
C                DATA MUST BE ABLE TO ACCOMODATE THE VALUE FOR CODE.    WUP 533 
C        5.  IF IFT .G. 0, PUNCH THE FREQUENCY (.G. 0) FOR EACH OF THE  WUP 534 
C            IFT TYPES IN 2 COLUMN FIELDS (1 TO 72).  IF THERE ARE MORE WUP 535 
C            THAN 36 TYPES, CONTINUE ONTO A SECOND CARD.                WUP 536 
C        6.  FORMAT CARD  (DESCRIBING IN F-NOTATION FOR UNCODED DATA ANDWUP 537 
C            IN I-NOTATION FOR PRECODED DATA WHERE THE DATA APPEARS).   WUP 538 
C        7.  DATA  (PUNCH IN COLUMNS 1-72, RESERVING 73-80 FOR IDENTIFI-WUP 539 
C            CATION (IF DESIRED),  ALL MEASUREMENTS FOR ONE OBSERVATION,WUP 540 
C            CONTINUING ONTO AS MANY CARDS AS NECESSARY,  WITHOUT SPLIT-WUP 541 
C            TING A FIELD FOR A VARIABLE OVER 2 CARDS.  EACH OBSERVATIONWUP 542 
C            BEGINS ON A NEW CARD.  SINCE THE CODING PROCEDURE IS LINEARWUP 543 
C            ONE SHOULD AVOID HAVING OBSERVATIONS REPRESENTING EXTREME  WUP 544 
C            DEVIATIONS FROM THE MAJORITY,  OTHERWISE IN THE LIMIT ONE  WUP 545 
C            WILL GET ALL OBSERVATIONS IN A SINGLE CATEGORY).           WUP 546 
C        8.  TITLE CARD FOR G-L(MSA-I) OUTPUT HEADING.  PUNCH 1 IN COL- WUP 547 
C            UMN 1 AND ANY BCD TITLE IN 2 TO 72.                        WUP 548 
C        9.  CONTROL CARD 2, 5 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 549 
C            INFORMATION -                                              WUP 550 
C            A)  MIND= 2-4 FOR NUMBER OF DIMENSIONS DESIRED ,  IF LEFT  WUP 551 
C                BLANK OR SET TO 0 MIND=1,                              WUP 552 
C            B)  MAXD = MAXIMUM NUMBER OF DIMENSIONS DESIRED (MAXD .GE. WUP 553 
C                MIND),                                                 WUP 554 
C            C)  NIT=NUMBER OF ITERATIONS, IF BLANK OR ZERO NIT=25,     WUP 555 
C            D)  IFP=1 IF ITEM PLOTS ARE TO BE PRINTED FOR EACH ITEM,   WUP 556 
C                OTHERWISE SET TO ZERO OR LEAVE BLANK,                  WUP 557 
C            E)  CCON=CUT-OUT CRITERION FOR COEFFICIENT OF CONTIGUITY   WUP 558 
C                (.G.0 BUT .LE. 1.00), WHICH MUST INCLUDE DECIMAL POINT.WUP 559 
C       10.  REPEAT 3-9 FOR ADDITIONAL RUNS.                            WUP 560 
C                                                                       WUP 561 
C     *** REFERENCES - GUTTMAN, L. A GENERAL NONMETRIC TECHNIQUE FOR    WUP 562 
C                                  FINDING THE SMALLEST EUCLIDEAN SPACE WUP 563 
C                                  FOR A CONFIGURATION OF POINTS.  PSY- WUP 564 
C                                  CHOMETRIKA,  1968,                   WUP 565 
C                      LINGOES, J. C.  MULTIVARIATE ANALYSIS OF CONTIN- WUP 566 
C                                  GENCIES - AN IBM 7090 PROGRAM FOR AN-WUP 567 
C                                  ALYZING METRIC/NONMETRIC OR LINEAR/  WUP 568 
C                                  NONLINEAR DATA.  COMP. RPT., 1963,2, WUP 569 
C                                  1-24.  (A DITTO COPY IS AVAILABLE    WUP 570 
C                                  FROM AUTHOR UPON WRITTEN REQUEST).   WUP 571 
C                      LINGOES, J. C.  SIMULTANEOUS LINEAR REGRESSIONS -WUP 572 
C                                  AN IBM 7090 PROGRAM FOR ANALYZING    WUP 573 
C                                  METRIC/NONMETRIC OR LINEAR/NONLINEAR WUP 574 
C                                  DATA.  BEHAV. SCI., 1964,9, 87-88.   WUP 575 
C                      LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 576 
C                                  LINGOES SMALLEST SPACE ANALYSIS - I. WUP 577 
C                                  BEHAV. SCI., 1965,10,183-184.        WUP 578 
C                      LINGOES, J. C.  AN IBM-7090 PROGRAM FOR GUTTMAN- WUP 579 
C                                  LINGOES MULTIDIMENSIONAL SCALOGRAM   WUP 580 
C                                  ANALYSIS - I.  BEHAV. SCI., 1966, 11,WUP 581 
C                                  76-78.                               WUP 582 
C                      LINGOES, J. C.  NEW COMPUTER DEVELOPMENTS IN PAT-WUP 583 
C                                  TERN ANALYSIS AND NONMETRIC TECH-    WUP 584 
C                                  NIQUES. IN - USES OF COMPUTERS IN    WUP 585 
C                                  PSYCHOLOGICAL RESEARCH. GAUTHIER-    WUP 586 
C                                  VILLARS, PARIS, 1966,1-22.           WUP 587 
C                      LINGOES, J. C.  THE MULTIVARIATE ANALYSIS OF     WUP 588 
C                                  QUALITATIVE DATA.  MULT.BEHAV.RES.,  WUP 589 
C                                  1968,                                WUP 590 
C     MSA2                                                              WUP 591 
C     A GENERAL NONMETRIC TECHNIQUE FOR MULTIDIMENSIONAL SCALOGRAM ANAL-WUP 592 
C     YSIS WITH SPHERICAL BOUNDARIES.  THIS RESEARCH IN NONMETRIC METH- WUP 593 
C     ODS IS SUPPORTED IN PART BY A GRANT TO L. GUTTMAN AND J.C. LINGOESWUP 594 
C     FROM THE NATIONAL SCIENCE FOUNDATION (GS-929).  PROGRAMMED FOR THEWUP 595 
C     UNIVERSITY OF MICHIGAN IBM-7090 COMPUTER IN FORTRAN-II BY LINGOES WUP 596 
C     (11/15/66).                                                       WUP 597 
C                                                                       WUP 598 
C     DECK SET-UP FOR G-L(MSA-II) -                                     WUP 599 
C                                                                       WUP 600 
C        1.   SYSTEM ID CARD/S.                                         WUP 601 
C        2.   BINARY PROGRAM.                                           WUP 602 
C        3.   TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COLWUP 603 
C             -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF WUP 604 
C             OUTPUT).                                                  WUP 605 
C        4.   PARAMETER CARD, 6 4-COLUMN FIELDS CONTAINING THE FOLLOW-  WUP 606 
C             ING INFORMATION SERIATUM -                                WUP 607 
C             A)  NS=NUMBER OF SUBJECTS,I.E.,ROWS OF MATRIX,            WUP 608 
C             B)  NV=NUMBER OF VARIABLES,I.E.,COLUMNS OF MATRIX,        WUP 609 
C             C)  NC=TOTAL NUMBER OF CATEGORIES OVER ALL VARIABLES      WUP 610 
C                 NC+NS .LE. 80,                                        WUP 611 
C             D)  MIND=0 IF PROGRAM IS TO DETERMINE MINIMUM DIMENSIONAL-WUP 612 
C                 ITY OF PROBLEM, OTHERWISE MIND=MINIMUM NUMBER OF DI-  WUP 613 
C                 MENSIONS DESIRED .LE. MAXD (V.I.),                    WUP 614 
C             E)  MAXD=MAXIMUM NUMBER OF DIMENSIONS DESIRED .LE. 10,    WUP 615 
C             F)  IT=0 IF NUMBER OF ITERATIONS BETWEEN COMPUTATIONS OF  WUP 616 
C                 LOSS FUNCTION =5, OTHERWISE SET TO DESIRED NUMBER (THEWUP 617 
C                 LARGER THE PROBLEM THE SMALLER IT SHOULD BE).         WUP 618 
C        5.   FORMAT CARD (DESCRIBING IN I-NOTATION WHERE DATA APPEARS  WUP 619 
C             ON THE CARDS).                                            WUP 620 
C        6.   DATA (PUNCH THE CATEGORY NUMERIC CODE CORRESPONDING TO THEWUP 621 
C             CATEGORY IN WHICH THE S FALLS. A SET OF CARDS REPRESENTS  WUP 622 
C             ONE ROW AND FIELDS ON THE CARD/S REPRESENT COLUMNS OF     WUP 623 
C             DATA MATRIX. AT LEAST ONE SUBJECT MUST FALL IN EVERY CATE-WUP 624 
C             GORY. ONLY INTEGERS (.GE.1) ARE TO BE USED).              WUP 625 
C        7.   REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                     WUP 626 
C                                                                       WUP 627 
C     *** REFERENCES - LINGOES, J.C.  AN IBM-7090 PROGRAM FOR GUTTMAN-  WUP 628 
C                        LINGOES MULTIDIMENSIONAL SCALOGRAM ANALYSIS    WUP 629 
C                        - II.  BEHAV.SCI.,1967,12,268-270.             WUP 630 
C                      LINGOES, J.C.  THE MULTIVARIATE ANALYSIS OF QUAL-WUP 631 
C                                                                               
C     MSA3                                                                      
C     A GENERAL NONMETRIC TECHNIQUE FOR MULTIDIMENSIONAL SCALOGRAM ANAL-        
C     YSIS WITH PARALLEL STRAIGHT LINE BOUNDARIES.  THIS RESEARCH IN            
C     NONMETRIC METHODS IS SUPPORTED IN PART BY A GRANT TO L. GUTTMAN           
C     AND J. C. LINGOES FROM THE NATIONAL SCIENCE FOUNDATION (GS-929).          
C     PROGRAMMED FOR THE UNIVERSITY OF MICHIGAN IBM 360/67 COMPUTER IN          
C     FORTRAN IV BY LINGOES (12/15/67).                                         
C                                                                               
C     DECK SET-UP FOR G-L(MSA-III) -                                            
C                                                                               
C        1.   SYSTEM ID CARD/S.                                                 
C        2.   BINARY PROGRAM.                                                   
C        3.   TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL        
C             -UMNS 2 TO 72, WHICH WILL BE PRINTED OUT FOR EACH PAGE OF         
C             OUTPUT).                                                          
C        4.   PARAMETER CARD, 5 4-COLUMN FIELDS CONTAINING THE FOLLOW-          
C             ING INFORMATION SERIATUM -                                        
C             A)  NS=NUMBER OF SUBJECTS,I.E.,ROWS OF MATRIX,                    
C             B)  NV=NUMBER OF VARIABLES,I.E.,COLUMNS OF MATRIX,                
C             C)  NC=TOTAL NUMBER OF CATEGORIES OVER ALL VARIABLES              
C                 NC+NS .LE. 80,                                                
C             D)  MIND=0 IF PROGRAM IS TO DETERMINE MINIMUM DIMENSIONAL-        
C                 ITY OF PROBLEM, OTHERWISE MIND=MINIMUM NUMBER OF DI-          
C                 MENSIONS DESIRED .LE. MAXD (V.I.),                            
C             E)  MAXD=MAXIMUM NUMBER OF DIMENSIONS DESIRED .LE. 10.            
C        5.   FORMAT CARD (DESCRIBING IN I-NOTATION WHERE DATA APPEARS          
C             ON THE CARDS).                                                    
C        6.   DATA (PUNCH THE CATEGORY NUMERIC CODE CORRESPONDING TO THE        
C             CATEGORY IN WHICH THE S FALLS. A SET OF CARDS REPRESENTS          
C             ONE ROW AND FIELDS ON THE CARD/S REPRESENT COLUMNS OF             
C             DATA MATRIX. AT LEAST ONE SUBJECT MUST FALL IN EVERY CATE-        
C             GORY. ONLY INTEGERS (.GE.1) ARE TO BE USED).                      
C        7.   REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                             
C                                                                               
C     *** REFERENCES - LINGOES, J.C.  AN IBM-7090 PROGRAM FOR GUTTMAN-          
C                        LINGOES MULTIDIMENSIONAL SCALOGRAM ANALYSIS            
C                        - II.  BEHAV.SCI.,1967,12,268-270.                     
C                      LINGOES, J.C.  THE MULTIVARIATE ANALYSIS OF QUAL-        
C                        ITATIVE DATA.  MULT. BEHAV. RES., 1968,                
C                      LINGOES, J. C.  AN IBM 360/67 PROGRAM FOR GUTTMAN        
C                        -LINGOES MULTIDIMENSIONAL SCALOGRAM ANALYSIS -         
C                        III.  BEHAV. SCI., 1968, 13,                           
C                        ITATIVE DATA.  MULT. BEHAV. RES., 1968,        WUP 632 
C                                                                       WUP 633 
C     CM-1                                                              WUP 739 
C     GIVEN AN RXC MATRIX OF REAL NUMBERS Y(I,J) DETERMINE A SET OF ROW WUP 740 
C     VALUES R(I) AND A SET OF COLUMN VALUES C(J) SUCH THAT X(I,J) =    WUP 741 
C     F(R(I),C(J)) AND X(I,J) IS MONOTONIC WITH Y(I,J) FOR NORMALIZED   WUP 742 
C     PHI, A MINIMUM.  THIS PROGRAM FOR CONJOINT MEASUREMENT WAS WRITTENWUP 743 
C     IN FORTRAN II BY J. C. LINGOES FOR THE UNIVERSITY OF MICHIGAN     WUP 744 
C     IBM-7090 COMPUTER.  THE GUTTMAN-LINGOES NONMETRIC SERIES RESEARCH WUP 745 
C     IS SUPPORTED IN PART BY A GRANT FROM THE NATIONAL SCIENCE FOUNDA- WUP 746 
C     TION (GS-929).  DATE = 1/15/67.                                   WUP 747 
C                                                                       WUP 748 
C     DECK SET-UP FOR G-L(CM-I) -                                       WUP 749 
C                                                                       WUP 750 
C        1.  SYSTEM ID CARD/S.                                          WUP 751 
C        2.  BINARY PROGRAM.                                            WUP 752 
C        3.  TITLE CARD (PUNCH A 1 IN COLUMN 1 AND ANY BCD TITLE IN COL-WUP 753 
C            UMNS 2-72 FOR OUTPUT LABELING).                            WUP 754 
C        4.  PARAMETER CARD, 3 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 755 
C            INFORMATION SERIATUM-                                      WUP 756 
C            A)  NR=NUMBER OF ROWS OF INPUT MATRIX (NR .LE. 50),        WUP 757 
C            B)  NC=NUMBER OF COLUMNS (NC .LE. 50),                     WUP 758 
C            C)  M=1 IF ADDITIVE MODEL DESIRED, OR                      WUP 759 
C                M=2 IF SUBTRACTIVE MODEL, OR                           WUP 760 
C                M=3 IF QUADRATIC-ADDITIVE, OR                          WUP 761 
C                M=4 IF CUBIC-ADDITIVE,OR                               WUP 762 
C                M=5 IF COMPLEX MODEL (SUPPLIED BY A USER'S MODIFICATIONWUP 763 
C                    OF THE FUNCTION SUBROUTINE), OR                    WUP 764 
C                M=0 IF MODELS 1-4 ARE TO BE TRIED IN SEQUENCE.         WUP 765 
C        5.  FORMAT CARD (DESCRIBING IN F-NOTATION HOW DATA HAS BEEN    WUP 766 
C            PUNCHED).                                                  WUP 767 
C        6.  DATA (PUNCH VALUES OF Y, WHERE EACH SET OF CARDS REPRESENTSWUP 768 
C            A ROW OF MATRIX AND THE FIELDS REPRESENT COLUMNAR ENTRIES).WUP 769 
C        7.  REPEAT ITEMS 3-6 FOR ADDITIONAL RUNS.                      WUP 770 
C                                                                       WUP 771 
C        *** REFERENCES - LINGOES, J.C.  AN IBM-7090 PROGRAM FOR GUTTMANWUP 772 
C                           -LINGOES CONJOINT MEASUREMENT - I.  BEHAV.  WUP 773 
C                           SCI.,1967,12,501-502.                       WUP 774 
C                                                                       WUP 775 
C     CM-2                                                              WUP 776 
C     GIVEN A DEPENDENT VARIABLE Y AND A MATRIX OF INDEPENDENT VARIABLESWUP 777 
C     X, DETERMINE A SET OF WEIGHTS (1 FOR EACH OBSERVATION), SUCH THAT WUP 778 
C     MEAN R(W*,X*) IS A MAXIMUM SUBJECT TO THE CONSTRAINTS THAT W* IS AWUP 779 
C     MONOTONE TRANSFORMATION OF Y AND X* IS MONOTONICALLY RELATED TO X,WUP 780 
C     FOR EACH VARIABLE SEPARATELY FOR R(W,W*) A MAXIMUM.  THIS PROGRAM WUP 781 
C     IS DESIGNED FOR NONMETRIC GENERALIZED MULTIPLE REGRESSION ANALYSISWUP 782 
C     AND WAS PROGRAMMED IN FORTRAN II BY J.C. LINGOES FOR THE UNIVERSI-WUP 783 
C     TY OF MICHIGAN IBM-7090 COMPUTER.  THE GUTTMAN-LINGOES NONMETRIC  WUP 784 
C     SERIES RESEARCH IS SUPPORTED IN PART BY A GRANT FROM THE NATIONAL WUP 785 
C     SCIENCE FOUNDATION (GS-929).  DATE = 5/1/67.                      WUP 786 
C                                                                       WUP 787 
C     DECK SET-UP FOR G-L(CM-II) -                                      WUP 788 
C                                                                       WUP 789 
C        1.  SYSTEM ID CARD/S.                                          WUP 790 
C        2.  BINARY PROGRAM.                                            WUP 791 
C        3.  TITLE CARD FOR HEADING (PUNCH A 1 IN COL. 1 AND ANY BCD    WUP 792 
C            TITLE IN COLS. 2-72).                                      WUP 793 
C        4.  PARAMETER CARD, 7 4-COLUMN FIELDS CONTAINING THE FOLLOWING WUP 794 
C            INFORMATION SERIATUM -                                     WUP 795 
C            A)  NS=NUMBER OF OBSERVATIONS (NS .LE. 200),               WUP 796 
C            B)  NV=NUMBER OF VARIABLES INCLUDING Y (NV  .LE.  25),     WUP 797 
C            C)  ICARDS=1 IF CARD OUTPUT DESIRED AND ZERO OR BLANK,     WUP 798 
C                OTHERWISE.  S SEQUENCE NUMBER IS FUNCHED FIRST, THEN X*WUP 799 
C                AND FINALLY, Y* FOR EACH OBSERVATION,                  WUP 800 
C            D)  MISS=1 IF MISSING DATA EXISTS FOR 1 OR MORE INDEPENDENTWUP 801 
C                VARIABLES, OTHERWISE SET TO ZERO OR LEAVE BLANK.  IF   WUP 802 
C                MISSING DATA EXISTS FOR THE DEPENDENT VARIABLE, HOWEVERWUP 803 
C                , THOSE OBSERVATIONS MUST BE DELETED,                  WUP 804 
C            E)  CODE=SOME NUMERIC VALUE THAT IS UNIFORM FOR ALL VARIA- WUP 805 
C                BLES AND OBSERVATIONS DENOTING AN UNKNOWN SCORE (DO    WUP 806 
C                NOT USE A VALUE REPRESENTING A LEGITIMATE SCORE.  DECI-WUP 807 
C                MAL POINT MUST BE PUNCHED.)  IF NO MISSING DATA, LEAVE WUP 808 
C                BLANK,                                                 WUP 809 
C            F)  CK=MINIMUM VALUE DESIRED FOR K=SQRT(1-R**2(W,W*)), THE WUP 810 
C                G-L COEFFICIENT OF ALIENATION ACCORDING TO FORMAT F4.4,WUP 811 
C                (DO NOT PUNCH DECIMAL POINT.),                         WUP 812 
C            G)  Z=MAXIMUM CONTRIBUTION THAT ANY ONE S CAN CONTRIBUTE TOWUP 813 
C                ANY CORRELATION ACCORDING TO FORMAT F4.4 (DO NOT PUNCH WUP 814 
C                DECIMAL POINT).  IF FIELD LEFT BLANK Z=.5000.  RECOM-  WUP 815 
C                MENDED VALUE FOR Z, IN GENERAL, IS 5/NS IF COMMENT IS  WUP 816 
C                PRINTED OUT THAT SOME OBSERVATION IS AN OUTLIER.       WUP 817 
C        5.  FORMAT (DESCRIBING IN F-FORMAT HOW DATA HAS BEEN PUNCHED). WUP 818 
C        6.  DATA (PUNCH Y THEN X'S FOR EACH S, WHERE EACH CARD OR SET  WUP 819 
C            OF CARDS REPRESENTS 1 S AND EACH FIELD A VARIABLE IN COLS. WUP 820 
C            1-72.  73-80 MAY OPTIONALLY BE USED FOR ID INFORMATION).   WUP 821 
C        7.  REPEAT ITEMS 3-6 FOR ADDITONAL RUNS.                       WUP 822 
C                                                                       WUP 823 
C     *** REFERENCES - LINGOES, J.C.,  AN IBM-7090 PROGRAM FOR          WUP 824 
C                          GUTTMAN-LINGOES CONJOINT MEASUREMENT - II.   WUP 825 
C                          BEHAV. SCI., 1968, 13,                       WUP 826 
C                                                                               
C     CM-3 (CORE 1)                                                     CM3   1 
C     GIVEN A MATRIX OF VARIABLES X, DETERMINE Z*(I,J) = F(X(I,J)), SUCHCM3   2 
C     THAT WHENEVER X(I,J) .GT. X(K,J) THEN Z*(I,J) .GT. Z*(K,J). THIS  CM3   3 
C     PROGRAM WILL MAXIMIZE THE AVERAGE CORRELATION AMONG THE SET OF    CM3   4 
C     VARIABLES SUBJECT ONLY TO THE ABOVE MONOTONE RESTRICTION. AN OP-  CM3   5 
C     TION IS INCLUDED FOR A NOMETRIC FACTOR ANALYSIS OF THE CORRELA-   CM3   6 
C     TIONS GENERATED FROM THE OPTIMALLY SCALED VARIABLES, THUS ACHIEV- CM3   7 
C     ING AN ECONOMY OF DESCRIPTION GREATER THAN THAT REALIZABLE FROM A CM3   8 
C     NONMETRIC FACTOR ANALYSIS ON THE UNSCALED SCORES. THIS PROGRAM IS CM3   9 
C     USEFUL IN THOSE CASES WHERE MODERATELY NONLINEAR RELATIONS MAY BE CM3  10 
C     PRESENT. WRITTEN IN FORTRAN IV (LEVEL G) BY LINGOES FOR THE U. OF CM3  11 
C     M. IBM 360/67 COMPUTER. THE GUTTMAN-LINGOES NONMETRIC SERIES RE-  CM3  12 
C     SEARCH IS SUPPORTED IN PART BY A GRANT FROM THE NATIONAL SCIENCE  CM3  13 
C     FOUNDATION (GS-929).  DATE = 2/15/68.                             CM3  14 
C                                                                       CM3  15 
C     DECK SET-UP FOR G-L(CM-III) -                                     CM3  16 
C                                                                       CM3  17 
C     1.  SYSTEM ID CARD/S.                                             CM3  18 
C     2.  BINARY PROGRAM.                                               CM3  19 
C     3.  TITLE CARD FOR HEADING (PUNCH A 1 IN COLUMN 1 AND ANY BCD     CM3  20 
C         TITLE IN COLUMNS 2-72).                                       CM3  21 
C     4.  PARAMETER CARD, 6 4-COLUMN FIELDS CONTAINING THE FOLLOWING    CM3  22 
C         INFORMATION SERIATUM -                                        CM3  23 
C         A)  NS=NUMBER OF OBSERVATIONS (NS .LE. 200),                  CM3  24 
C         B)  NV=NUMBER OF VARIABLES (NV .LE. 70),                      CM3  25 
C         C)  MISS=1 IF MISSING DATA EXISTS FOR 1 OR MORE VARIABLES,    CM3  26 
C             OTHERWISE SET TO ZERO OR LEAVE BLANK,                     CM3  27 
C         D)  CODE=SOME NUMERIC VALUE THAT IS UNIFORM FOR ALL VARIABLES CM3  28 
C             AND OBSERVATIONS DENOTING AN UNKNOWN SCORE (DO NOT USE A  CM3  29 
C             VALUE REPRESENTING A LEGITIMATE SCORE.  DECIMAL POINT MUSTCM3  30 
C             BE PUNCHED), IF NO MISSING INFORMATION, LEAVE BLANK,      CM3  31 
C         E)  Z=MAXIMUM CONTRIBUTION THAT ANY ONE S CAN CONTRIBUTE TO   CM3  32 
C             ANY CORRELATION ACCORDING TO FORMAT F4.4 (DO NOT PUNCH    CM3  33 
C             DECIMAL POINT).  IF FIELD LEFT BLANK Z=.5000.  RECOM-     CM3  34 
C             MENDED VALUE FOR Z,IN GENERAL,IS 5/NS IF COMMENT IS       CM3  35 
C             PRINTED OUT THAT SOME OBSERVATION IS AN OUTLIER.          CM3  36 
C         F)  NMFA=0 OR BLANK IF A NONMETRIC FACTORING IS TO BE DONE ON CM3  37 
C             THE TRANSFORMED X'S, 1 IF NOT DESIRED.                    CM3  38 
C     5.  FORMAT (DESCRIBING IN F-FORMAT HOW DATA HAS BEEN PUNCHED).    CM3  39 
C     6.  DATA (PUNCH X VALUES, WHERE EACH CARD OR SET OF CARDS REPRE-  CM3  40 
C         SENTS ONE OBSERVATION AND THE COLUMNS REPRESENT THE X'S, IN   CM3  41 
C         COLS. 1-72. 73-80 MAY OPTIONALLY BE USED FOR ID INFORMATION). CM3  42 
C     7.  TITLE CARD FOR SSA-III OUTPUT IF NMFA=0, OTHERWISE OMIT.      CM3  43 
C     8.  REPEAT ITEMS 3-6/7 FOR ADDITIONAL RUNS.                       CM3  44 
C                                                                       CM3  45 
C     *** REFERENCES - LINGOES, J. C. AND GUTTMAN, L., NOMETRIC FACTOR  CM3  46 
C                        ANALYSIS - A RANK REDUCING ALTERNATIVE TO LIN- CM3  47 
C                        EAR FACTOR ANALYSIS. MULT. BEHAV. RES., 1967,  CM3  48 
C                        2, 485-505.                                    CM3  49 
C                      LINGOES, J. C., AN IBM 360/67 PROGRAM FOR GUTTMANCM3  50 
C                        -LINGOES CONJOINT MEASUREMENT - III. BEHAV.    CM3  51 
C                        SCI., 1968, 13,                                CM3  52 
      END                                                               WUP 827-
