--- /dev/null
+*DECK TRED2
+ SUBROUTINE TRED2 (NM, N, A, D, E, Z)
+C***BEGIN PROLOGUE TRED2
+C***PURPOSE Reduce a real symmetric matrix to a symmetric tridiagonal
+C matrix using and accumulating orthogonal transformations.
+C***LIBRARY SLATEC (EISPACK)
+C***CATEGORY D4C1B1
+C***TYPE SINGLE PRECISION (TRED2-S)
+C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
+C***AUTHOR Smith, B. T., et al.
+C***DESCRIPTION
+C
+C This subroutine is a translation of the ALGOL procedure TRED2,
+C NUM. MATH. 11, 181-195(1968) by Martin, Reinsch, and Wilkinson.
+C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971).
+C
+C This subroutine reduces a REAL SYMMETRIC matrix to a
+C symmetric tridiagonal matrix using and accumulating
+C orthogonal similarity transformations.
+C
+C On Input
+C
+C NM must be set to the row dimension of the two-dimensional
+C array parameters, A and Z, as declared in the calling
+C program dimension statement. NM is an INTEGER variable.
+C
+C N is the order of the matrix A. N is an INTEGER variable.
+C N must be less than or equal to NM.
+C
+C A contains the real symmetric input matrix. Only the lower
+C triangle of the matrix need be supplied. A is a two-
+C dimensional REAL array, dimensioned A(NM,N).
+C
+C On Output
+C
+C D contains the diagonal elements of the symmetric tridiagonal
+C matrix. D is a one-dimensional REAL array, dimensioned D(N).
+C
+C E contains the subdiagonal elements of the symmetric
+C tridiagonal matrix in its last N-1 positions. E(1) is set
+C to zero. E is a one-dimensional REAL array, dimensioned
+C E(N).
+C
+C Z contains the orthogonal transformation matrix produced in
+C the reduction. Z is a two-dimensional REAL array,
+C dimensioned Z(NM,N).
+C
+C A and Z may coincide. If distinct, A is unaltered.
+C
+C Questions and comments should be directed to B. S. Garbow,
+C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
+C ------------------------------------------------------------------
+C
+C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
+C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
+C system Routines - EISPACK Guide, Springer-Verlag,
+C 1976.
+C***ROUTINES CALLED (NONE)
+C***REVISION HISTORY (YYMMDD)
+C 760101 DATE WRITTEN
+C 890831 Modified array declarations. (WRB)
+C 890831 REVISION DATE from Version 3.2
+C 891214 Prologue converted to Version 4.0 format. (BAB)
+C 920501 Reformatted the REFERENCES section. (WRB)
+C***END PROLOGUE TRED2
+C
+ INTEGER I,J,K,L,N,II,NM,JP1
+ REAL A(NM,*),D(*),E(*),Z(NM,*)
+ REAL F,G,H,HH,SCALE
+C
+C***FIRST EXECUTABLE STATEMENT TRED2
+ DO 100 I = 1, N
+C
+ DO 100 J = 1, I
+ Z(I,J) = A(I,J)
+ 100 CONTINUE
+C
+ IF (N .EQ. 1) GO TO 320
+C .......... FOR I=N STEP -1 UNTIL 2 DO -- ..........
+ DO 300 II = 2, N
+ I = N + 2 - II
+ L = I - 1
+ H = 0.0E0
+ SCALE = 0.0E0
+ IF (L .LT. 2) GO TO 130
+C .......... SCALE ROW (ALGOL TOL THEN NOT NEEDED) ..........
+ DO 120 K = 1, L
+ 120 SCALE = SCALE + ABS(Z(I,K))
+C
+ IF (SCALE .NE. 0.0E0) GO TO 140
+ 130 E(I) = Z(I,L)
+ GO TO 290
+C
+ 140 DO 150 K = 1, L
+ Z(I,K) = Z(I,K) / SCALE
+ H = H + Z(I,K) * Z(I,K)
+ 150 CONTINUE
+C
+ F = Z(I,L)
+ G = -SIGN(SQRT(H),F)
+ E(I) = SCALE * G
+ H = H - F * G
+ Z(I,L) = F - G
+ F = 0.0E0
+C
+ DO 240 J = 1, L
+ Z(J,I) = Z(I,J) / H
+ G = 0.0E0
+C .......... FORM ELEMENT OF A*U ..........
+ DO 180 K = 1, J
+ 180 G = G + Z(J,K) * Z(I,K)
+C
+ JP1 = J + 1
+ IF (L .LT. JP1) GO TO 220
+C
+ DO 200 K = JP1, L
+ 200 G = G + Z(K,J) * Z(I,K)
+C .......... FORM ELEMENT OF P ..........
+ 220 E(J) = G / H
+ F = F + E(J) * Z(I,J)
+ 240 CONTINUE
+C
+ HH = F / (H + H)
+C .......... FORM REDUCED A ..........
+ DO 260 J = 1, L
+ F = Z(I,J)
+ G = E(J) - HH * F
+ E(J) = G
+C
+ DO 260 K = 1, J
+ Z(J,K) = Z(J,K) - F * E(K) - G * Z(I,K)
+ 260 CONTINUE
+C
+ 290 D(I) = H
+ 300 CONTINUE
+C
+ 320 D(1) = 0.0E0
+ E(1) = 0.0E0
+C .......... ACCUMULATION OF TRANSFORMATION MATRICES ..........
+ DO 500 I = 1, N
+ L = I - 1
+ IF (D(I) .EQ. 0.0E0) GO TO 380
+C
+ DO 360 J = 1, L
+ G = 0.0E0
+C
+ DO 340 K = 1, L
+ 340 G = G + Z(I,K) * Z(K,J)
+C
+ DO 360 K = 1, L
+ Z(K,J) = Z(K,J) - G * Z(K,I)
+ 360 CONTINUE
+C
+ 380 D(I) = Z(I,I)
+ Z(I,I) = 1.0E0
+ IF (L .LT. 1) GO TO 500
+C
+ DO 400 J = 1, L
+ Z(I,J) = 0.0E0
+ Z(J,I) = 0.0E0
+ 400 CONTINUE
+C
+ 500 CONTINUE
+C
+ RETURN
+ END
git://source.jalview.org / jabaws.git / blobdiff