C TRAC 10
C ..................................................................TRAC 20
C TRAC 30
C SUBROUTINE TRACE TRAC 40
C TRAC 50
C PURPOSE TRAC 60
C COMPUTE CUMULATIVE PERCENTAGE OF EIGENVALUES GREATER THAN TRAC 70
C OR EQUAL TO A CONSTANT SPECIFIED BY THE USER. THIS SUB- TRAC 80
C ROUTINE NORMALLY OCCURS IN A SEQUENCE OF CALLS TO SUB- TRAC 90
C ROUTINES CORRE, EIGEN, TRACE, LOAD, AND VARMX IN THE PER- TRAC 100
C FORMANCE OF A FACTOR ANALYSIS. TRAC 110
C TRAC 120
C USAGE TRAC 130
C CALL TRACE (M,R,CON,K,D) TRAC 140
C TRAC 150
C DESCRIPTION OF PARAMETERS TRAC 160
C M - NUMBER OF VARIABLES. M MUST BE > OR = TO 1 TRAC 170
C R - INPUT MATRIX (SYMMETRIC AND STORED IN COMPRESSED TRAC 180
C FORM WITH ONLY UPPER TRIANGLE BY COLUMN IN CORE) TRAC 190
C CONTAINING EIGENVALUES IN DIAGONAL. EIGENVALUES ARETRAC 200
C ARRANGED IN DESCENDING ORDER. THE ORDER OF MATRIX RTRAC 210
C IS M BY M. ONLY M*(M+1)/2 ELEMENTS ARE IN STORAGE. TRAC 220
C (STORAGE MODE OF 1) TRAC 230
C CON - A CONSTANT USED TO DECIDE HOW MANY EIGENVALUES TO TRAC 240
C RETAIN. CUMULATIVE PERCENTAGE OF EIGENVALUES TRAC 250
C WHICH ARE GREATER THAN OR EQUAL TO THIS VALUE IS TRAC 260
C CALCULATED. TRAC 270
C K - OUTPUT VARIABLE CONTAINING THE NUMBER OF EIGENVALUESTRAC 280
C GREATER THAN OR EQUAL TO CON. (K IS THE NUMBER OF TRAC 290
C FACTORS.) TRAC 300
C D - OUTPUT VECTOR OF LENGTH M CONTAINING CUMULATIVE TRAC 310
C PERCENTAGE OF EIGENVALUES WHICH ARE GREATER THAN TRAC 320
C OR EQUAL TO CON. TRAC 330
C REMARKS TRAC 340
C NONE TRAC 350
C TRAC 360
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED TRAC 370
C NONE TRAC 380
C TRAC 390
C METHOD TRAC 400
C EACH EIGENVALUE GREATER THAN OR EQUAL TO CON IS DIVIDED BY MTRAC 410
C AND THE RESULT IS ADDED TO THE PREVIOUS TOTAL TO OBTAIN TRAC 420
C THE CUMULATIVE PERCENTAGE FOR EACH EIGENVALUE. TRAC 430
C TRAC 440
C ..................................................................TRAC 450
C TRAC 460
SUBROUTINE TRACE (M,R,CON,K,D) TRAC 470
DIMENSION R(1),D(1) TRAC 480
C TRAC 490
C ...............................................................TRAC 500
C TRAC 510
C IF A DOUBLE PRECISION VERSION OF THIS ROUTINE IS DESIRED, THE TRAC 520
C C IN COLUMN 1 SHOULD BE REMOVED FROM THE DOUBLE PRECISION TRAC 530
C STATEMENT WHICH FOLLOWS. TRAC 540
C TRAC 550
C DOUBLE PRECISION R,D TRAC 560
C TRAC 570
C THE C MUST ALSO BE REMOVED FROM DOUBLE PRECISION STATEMENTS TRAC 580
C APPEARING IN OTHER ROUTINES USED IN CONJUNCTION WITH THIS TRAC 590
C ROUTINE. TRAC 600
C TRAC 610
C ...............................................................TRAC 620
C TRAC 630
FM=M TRAC 640
L=0 TRAC 650
DO 100 I=1,M TRAC 660
L=L+I TRAC 670
100 D(I)=R(L) TRAC 680
K=0 TRAC 690
C TRAC 700
C TEST WHETHER I-TH EIGENVALUE IS GREATER TRAC 710
C THAN OR EQUAL TO THE CONSTANT TRAC 720
C TRAC 730
DO 110 I=1,M TRAC 740
IF(D(I)-CON) 120, 105, 105 TRAC 750
105 K=K+1 TRAC 760
110 D(I)=D(I)/FM TRAC 770
C TRAC 780
C COMPUTE CUMULATIVE PERCENTAGE OF EIGENVALUES TRAC 790
C TRAC 800
120 DO 130 I=2,K TRAC 810
130 D(I)=D(I)+D(I-1) TRAC 820
RETURN TRAC 830
END TRAC 840