EOF.rar_EOF matlab_EOF.M_EOF分析_eof_matlab求距平

function [D,E,Z,IERR]=TQL2(NM,N,D,E,Z) % % INTEGER I,J,K,L,M,N,II,L1,NM,MML,IERR % REAL D(N),E(N),Z(NM,N) % REAL B,C,F,G,H,P,R,S,MACHEP % REAL SQRT,ABS,SIGN % % THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TQL2, % NUM. MATH. 11, 293-306(1968) BY BOWDLER, MARTIN, REINSCH, AND % WILKINSON. % HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971). % % THIS SUBROUTINE FINDS THE EIGENVALUES AND EIGENVECTORS % OF A SYMMETRIC TRIDIAGONAL MATRIX BY THE QL METHOD. % THE EIGENVECTORS OF A FULL SYMMETRIC MATRIX CAN ALSO % BE FOUND IF TRED2 HAS BEEN USED TO REDUCE THIS % FULL MATRIX TO TRIDIAGONAL FORM. % % ON INPUT- % % NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL % ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM % DIMENSION STATEMENT, % % N IS THE ORDER OF THE MATRIX, % % D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX, % % E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX % IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY, % % Z CONTAINS THE TRANSFORMATION MATRIX PRODUCED IN THE % REDUCTION BY TRED2, IF PERFORMED. IF THE EIGENVECTORS % OF THE TRIDIAGONAL MATRIX ARE DESIRED, Z MUST CONTAIN % THE IDENTITY MATRIX. % % ON OUTPUT- % % D CONTAINS THE EIGENVALUES IN ASCENDING ORDER. IF AN % ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT BUT % UNORDERED FOR INDICES 1,2,...,IERR-1, % % E HAS BEEN DESTROYED, % % Z CONTAINS ORTHONORMAL EIGENVECTORS OF THE SYMMETRI% % TRIDIAGONAL (OR FULL) MATRIX. IF AN ERROR EXIT IS MADE, % Z CONTAINS THE EIGENVECTORS ASSOCIATED WITH THE STORED % EIGENVALUES, % % IERR IS SET TO % ZERO FOR NORMAL RETURN, % J IF THE J-TH EIGENVALUE HAS NOT BEEN % DETERMINED AFTER 30 ITERATIONS. % % QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO B. S. GARBOW, % APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY % ------------------------------------------------------------------ TQL2 % % ********** MACHEP IS A MACHINE DEPENDENT PARAMETER SPECIFYING % THE RELATIVE PRECISION OF FLOATING POINT ARITHMETIC. % % ********** MACHEP = 2.^(-32); IERR = 0; %IF (N .EQ. 1) GO TO 1001 if N==1 return; end for I = 2: N E(I-1) = E(I); end F = 0.0; B = 0.0; E(N) = 0.0; % DO 240 L = 1, N for L = 1: N J = 0; H = MACHEP * (abs(D(L)) + abs(E(L))); if B < H B = H; end % ********** LOOK FOR SMALL SUB-DIAGONAL ELEMENT ********** for M = L: N %IF (ABS(E(M)) .LE. B) GO TO 120 if abs(E(M))<=B break; end % ********** E(N) IS ALWAYS ZERO, SO THERE IS NO EXIT % THROUGH THE BOTTOM OF THE LOOP ********** end %120 IF (M .EQ. L) GO TO 220 if M==L D(L) = D(L) + F; continue; end %130 IF (J .EQ. 30) GO TO 1000 while(1) if J==30 IERR = L; return; end J = J + 1; % ********** FORM SHIFT ********** L1 = L + 1; G = D(L); P = (D(L1) - G) / (2.0 * E(L)); R = sqrt(P*P+1.0); D(L) = E(L) / (P + abs(R)*sign(P)); H = G - D(L); for I = L1: N D(I) = D(I) - H; end F = F + H; % ********** QL TRANSFORMATION ********** P = D(M); C = 1.0; S = 0.0; MML = M - L; % ********** FOR I=M-1 STEP -1 UNTIL L DO -- ********** for II = 1: MML I = M - II; G = C * E(I); H = C * P; %IF (ABS(P) .LT. ABS(E(I))) GO TO 150 if abs(P)>=abs(E(I)) C = E(I) / P; R = sqrt(C*C+1.0); E(I+1) = S * P * R; S = C / R; C = 1.0 / R; else C = P / E(I); R = sqrt(C*C+1.0); E(I+1) = S * E(I) * R; S = 1.0 / R; C = C * S; end P = C * D(I) - S * G; D(I+1) = H + S * (C * G + S * D(I)); % ********** FORM VECTOR ********** for K = 1: N H = Z(K,I+1); Z(K,I+1) = S * Z(K,I) + C * H; Z(K,I) = C * Z(K,I) - S * H; end end E(L) = S * P; D(L) = C * P; %IF (ABS(E(L)) .GT. B) GO TO 130 if abs(E(L))<=B break; end end D(L) = D(L) + F; end % ********** ORDER EIGENVALUES AND EIGENVECTORS ********** for II = 2: N I = II - 1; K = I; P = D(I); for J = II: N %IF (D(J) .GE. P) GO TO 260 if D(J)<=P continue; end K = J; P = D(J); end %IF (K .EQ. I) GO TO 300 if K==I continue; end D(K) = D(I); D(I) = P; for J = 1: N P = Z(J,I); Z(J,I) = Z(J,K); Z(J,K) = P; end end