+++ /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