+++ /dev/null
-*DECK TRED1
- SUBROUTINE TRED1 (NM, N, A, D, E, E2)
-C***BEGIN PROLOGUE TRED1
-C***PURPOSE Reduce a real symmetric matrix to symmetric tridiagonal
-C matrix using orthogonal similarity transformations.
-C***LIBRARY SLATEC (EISPACK)
-C***CATEGORY D4C1B1
-C***TYPE SINGLE PRECISION (TRED1-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 TRED1,
-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
-C to a symmetric tridiagonal matrix using
-C orthogonal similarity transformations.
-C
-C On Input
-C
-C NM must be set to the row dimension of the two-dimensional
-C array parameter, A, as declared in the calling program
-C 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 A contains information about the orthogonal transformations
-C used in the reduction in its strict lower triangle. The
-C full upper triangle of A is unaltered.
-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 E2 contains the squares of the corresponding elements of E.
-C E2 may coincide with E if the squares are not needed.
-C E2 is a one-dimensional REAL array, dimensioned E2(N).
-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 TRED1
-C
- INTEGER I,J,K,L,N,II,NM,JP1
- REAL A(NM,*),D(*),E(*),E2(*)
- REAL F,G,H,SCALE
-C
-C***FIRST EXECUTABLE STATEMENT TRED1
- DO 100 I = 1, N
- 100 D(I) = A(I,I)
-C .......... FOR I=N STEP -1 UNTIL 1 DO -- ..........
- DO 300 II = 1, N
- I = N + 1 - II
- L = I - 1
- H = 0.0E0
- SCALE = 0.0E0
- IF (L .LT. 1) GO TO 130
-C .......... SCALE ROW (ALGOL TOL THEN NOT NEEDED) ..........
- DO 120 K = 1, L
- 120 SCALE = SCALE + ABS(A(I,K))
-C
- IF (SCALE .NE. 0.0E0) GO TO 140
- 130 E(I) = 0.0E0
- E2(I) = 0.0E0
- GO TO 290
-C
- 140 DO 150 K = 1, L
- A(I,K) = A(I,K) / SCALE
- H = H + A(I,K) * A(I,K)
- 150 CONTINUE
-C
- E2(I) = SCALE * SCALE * H
- F = A(I,L)
- G = -SIGN(SQRT(H),F)
- E(I) = SCALE * G
- H = H - F * G
- A(I,L) = F - G
- IF (L .EQ. 1) GO TO 270
- F = 0.0E0
-C
- DO 240 J = 1, L
- G = 0.0E0
-C .......... FORM ELEMENT OF A*U ..........
- DO 180 K = 1, J
- 180 G = G + A(J,K) * A(I,K)
-C
- JP1 = J + 1
- IF (L .LT. JP1) GO TO 220
-C
- DO 200 K = JP1, L
- 200 G = G + A(K,J) * A(I,K)
-C .......... FORM ELEMENT OF P ..........
- 220 E(J) = G / H
- F = F + E(J) * A(I,J)
- 240 CONTINUE
-C
- H = F / (H + H)
-C .......... FORM REDUCED A ..........
- DO 260 J = 1, L
- F = A(I,J)
- G = E(J) - H * F
- E(J) = G
-C
- DO 260 K = 1, J
- A(J,K) = A(J,K) - F * E(K) - G * A(I,K)
- 260 CONTINUE
-C
- 270 DO 280 K = 1, L
- 280 A(I,K) = SCALE * A(I,K)
-C
- 290 H = D(I)
- D(I) = A(I,I)
- A(I,I) = H
- 300 CONTINUE
-C
- RETURN
- END
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