SUBROUTINE HTRID3 (NM, N, A, D, E, E2, TAU) C***BEGIN PROLOGUE HTRID3 C***PURPOSE Reduce a complex Hermitian (packed) matrix to a real C symmetric tridiagonal matrix by unitary similarity C transformations. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4C1B1 C***TYPE SINGLE PRECISION (HTRID3-S) C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION C C This subroutine is a translation of a complex analogue of C the ALGOL procedure TRED3, NUM. MATH. 11, 181-195(1968) C by Martin, Reinsch, and Wilkinson. C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). C C This subroutine reduces a COMPLEX HERMITIAN matrix, stored as C a single square array, to a real symmetric tridiagonal matrix C using unitary 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. N is an INTEGER variable. C N must be less than or equal to NM. C C A contains the lower triangle of the complex Hermitian input C matrix. The real parts of the matrix elements are stored C in the full lower triangle of A, and the imaginary parts C are stored in the transposed positions of the strict upper C triangle of A. No storage is required for the zero C imaginary parts of the diagonal elements. A is a two- C dimensional REAL array, dimensioned A(NM,N). C C On OUTPUT C C A contains some information about the unitary transformations C used in the reduction. C C D contains the diagonal elements of the real symmetric C tridiagonal matrix. D is a one-dimensional REAL array, C dimensioned D(N). C C E contains the subdiagonal elements of the real tridiagonal C matrix in its last N-1 positions. E(1) is set to zero. C E is a one-dimensional REAL array, dimensioned E(N). C C E2 contains the squares of the corresponding elements of E. C E2(1) is set to zero. E2 may coincide with E if the squares C are not needed. E2 is a one-dimensional REAL array, C dimensioned E2(N). C C TAU contains further information about the transformations. C TAU is a one-dimensional REAL array, dimensioned TAU(2,N). C C Calls PYTHAG(A,B) for sqrt(A**2 + B**2). 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 PYTHAG 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 HTRID3