FTN77,E,J,Y C IMSL ROUTINE NAME - ODNORM C C----------------------------------------------------------------------- C C COMPUTER - HP1000/SINGLE C C LATEST REVISION - JUNE 1, 1982 C C PURPOSE - MULTIVARIATE NORMAL LINEAR DISCRIMINANT C ANALYSIS AMONG SEVERAL KNOWN GROUPS C C USAGE - CALL ODNORM (X,IX,NG,NV,ND,P, C XM,IXM,S,W,IW,D,ID,IER) C C ARGUMENTS X - INPUT MATRIX OF DIMENSION NV BY THE SUM OF C ND(I) CONTAINING THE GROUP DATA. C (SEE REMARK 1). C IX - INPUT ROW DIMENSION OF MATRIX X EXACTLY AS C SPECIFIED IN THE DIMENSION STATEMENT IN THE C CALLING PROGRAM. C NG - INPUT NUMBER OF DISTINCT GROUPS. C NV - INPUT NUMBER OF DATA VARIABLES. C ND - INPUT VECTOR OF LENGTH NG. ND(I) CONTAINS C THE NUMBER OF DATA VECTORS FROM THE I-TH C GROUP IN THE DATA MATRIX X. C P - INPUT/OUTPUT VECTOR OF LENGTH NG. ON INPUT, C P(I) CONTAINS THE BAYESIAN PRIOR PROBABILITY C THAT A RANDOM OBSERVATION BELONGS TO THE C I-TH GROUP. (SEE REMARK 2). C ON OUTPUT, P CONTAINS THE CONSTANTS OF THE C NG LINEAR DISCRIMINANT FUNCTIONS. C XM - OUTPUT MATRIX OF DIMENSION NV BY NG. C THE I-TH COLUMN OF XM CONTAINS THE C MEAN VECTOR FOR THE I-TH GROUP. C IXM - INPUT ROW DIMENSION OF MATRIX XM EXACTLY AS C SPECIFIED IN THE DIMENSION STATEMENT IN THE C CALLING PROGRAM. C S - WORK VECTOR OF LENGTH ((NV+1)*NV)/2. C W - OUTPUT MATRIX OF DIMENSION NV BY NG. THE C I-TH COLUMN OF W CONTAINS THE VECTOR FOR C THE I-TH LINEAR DISCRIMINANT FUNCTION. C IW - INPUT ROW DIMENSION OF MATRIX W EXACTLY AS C SPECIFIED IN THE DIMENSION STATEMENT IN THE C CALLING PROGRAM. C D - OUTPUT PERFORMANCE MATRIX OF DIMENSION NG BY C NG. (SEE REMARK 3). C ID - INPUT ROW DIMENSION OF MATRIX D EXACTLY AS C SPECIFIED IN THE DIMENSION STATEMENT IN THE C CALLING PROGRAM. C IER - OUTPUT ERROR PARAMETER C TERMINAL ERROR C IER = 129 INDICATES THAT THE COVARIANCE C MATRIX IS SINGULAR. CHECK THE VARIABLES C FOR REDUNDANCIES. C IER = 130 INDICATES ONE OF IX,IXM,IW, OR ID C IS TOO SMALL. REDIMENSION MATRICES. C C PRECISION/HARDWARE - SINGLE AND DOUBLE/H32 C - SINGLE/H36,H48,H60 C C REQD. IMSL ROUTINES - LEQT1P,LUDECP,LUELMP,UERTST,UGETIO C C NOTATION - INFORMATION ON SPECIAL NOTATION AND C CONVENTIONS IS AVAILABLE IN THE MANUAL C INTRODUCTION OR THROUGH IMSL ROUTINE UHELP C C REMARKS 1. ON INPUT, THE MATRIX X CONTAINS THE ND(1)+ND(2)+... C ...+ND(NG) SAMPLE (COLUMN) VECTORS. THE FIRST ND(1) C COLUMNS OF MATRIX X SHOULD CONTAIN THE DATA FOR GROUP C ONE. THE NEXT ND(2) COLUMNS OF MATRIX X SHOULD CONTAIN C THE DATA FOR GROUP TWO, AND SO ON. C 2. COMMON CHOICES FOR THE BAYESIAN PRIOR PROBABILITIES C P(I) ARE 1/NG, ND(I)/(ND(1)+ND(2)+...+ND(NG)), OR C SUBJECTIVE ESTIMATES. THESE SHOULD SUM TO ONE. C 3. THE RESULTING BAYESIAN CLASSIFIER IS TESTED ON THE C ORIGINAL DATA X. THE OUTPUT MATRIX D SUMMARIZES THE C PERFORMANCE. D(I,J) IS THE FRACTION OF SAMPLES IN THE C I-TH GROUP THAT WERE CLASSIFIED IN THE J-TH GROUP. C D(I,I) IS FRACTION CLASSIFIED FOR GROUP I. THE ACTUAL C PERFORMANCE OF THE BAYESIAN CLASSIFIER ON UNLABELED C OBSERVATIONS WILL BE SLIGHTLY WORSE. C C COPYRIGHT - 1978 BY IMSL, INC. ALL RIGHTS RESERVED. C C WARRANTY - IMSL WARRANTS ONLY THAT IMSL TESTING HAS BEEN C APPLIED TO THIS CODE. NO OTHER WARRANTY, C EXPRESSED OR IMPLIED, IS APPLICABLE. C C----------------------------------------------------------------------- C SUBROUTINE ODNORM (X,IX,NG,NV,ND,P,XM,IXM,S,W,IW,D,ID,IER) C SPECIFICATIONS FOR ARGUMENTS INTEGER IX,NG,NV,ND(1),IXM,IW,ID,IER REAL X(IX,1),P(1),XM(IXM,1),S(1),W(IW,1),D(ID,1) C SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I,IDGT,IR,J,K,KHI,KLO,L,LMAX,N,NDI,NDJ,NMNG REAL D1,D2,XMAX,XMI,XMJ DOUBLE PRECISION DSUM,DZERO DATA DZERO/0.0D0/ C C CHECK SUFFICIENT MATRIX DIMENSIONS C C FIRST EXECUTABLE STATEMENT IER = 0 IF (IX.GE.NV.AND.IXM.GE.NV.AND.IW.GE.NV.AND.ID.GE.NG) GO TO 5 IER = 130 GO TO 9000 C COMPUTE MATRIX OF MEAN VECTORS 5 KHI = 0 DO 20 J=1,NG NDJ = ND(J) KLO = KHI+1 KHI = KLO+NDJ-1 DO 15 I=1,NV DSUM = DZERO DO 10 K=KLO,KHI DSUM = DSUM+X(I,K) 10 CONTINUE XM(I,J) = DSUM/NDJ 15 CONTINUE 20 CONTINUE N = KHI C COMPUTE POOLED COVARIANCE MATRIX NMNG = N-NG IR = 0 DO 40 I=1,NV DO 35 J=1,I DSUM = DZERO KHI = 0 DO 30 L=1,NG KLO = KHI+1 KHI = KLO+ND(L)-1 XMI = XM(I,L) XMJ = XM(J,L) DO 25 K=KLO,KHI DSUM = DSUM+(X(I,K)-XMI)*(X(J,K)-XMJ) 25 CONTINUE 30 CONTINUE IR = IR+1 S(IR) = DSUM/NMNG 35 CONTINUE 40 CONTINUE DO 50 J=1,NG DO 45 I=1,NV W(I,J) = XM(I,J) 45 CONTINUE 50 CONTINUE C SOLVE FOR DISCRIMINANT WEIGHT VECTORS IDGT = 0 CALL LEQT1P (S,NG,NV,W,IW,IDGT,D1,D2,IER) IF (IER.NE.0) GO TO 9000 C COMPUTE CONSTANT WEIGHTS FOR EACH GROUP DO 60 I=1,NG DSUM = DZERO DO 55 J=1,NV DSUM = DSUM+XM(J,I)*W(J,I) 55 CONTINUE P(I) = -DSUM/2+ALOG(P(I)) 60 CONTINUE C COMPUTE PERFORMANCE MATRIX KHI = 0 DO 90 I=1,NG NDI = ND(I) DO 65 J=1,NG D(I,J) = 0 65 CONTINUE KLO = KHI+1 KHI = KLO+NDI-1 DO 80 K=KLO,KHI XMAX = -1.E20 DO 75 L=1,NG DSUM = DZERO DO 70 J=1,NV DSUM = DSUM+W(J,L)*X(J,K) 70 CONTINUE DSUM = DSUM+P(L) IF (DSUM.LT.XMAX) GO TO 75 XMAX = DSUM LMAX = L 75 CONTINUE D(I,LMAX) = D(I,LMAX)+1 80 CONTINUE DO 85 J=1,NG D(I,J) = D(I,J)/NDI 85 CONTINUE 90 CONTINUE GO TO 9005 9000 CONTINUE CALL UERTST (IER,'ODNORM') 9005 RETURN END