1 2 SUBROUTINE HTRIDI(NM,N,AR,AI,D,E,E2,TAU) 3C***BEGIN PROLOGUE HTRIDI 4C***DATE WRITTEN 760101 (YYMMDD) 5C***REVISION DATE 830518 (YYMMDD) 6C***CATEGORY NO. D4C1B1 7C***KEYWORDS EIGENVALUES,EIGENVECTORS,EISPACK 8C***AUTHOR SMITH, B. T., ET AL. 9C***PURPOSE Reduces complex Hermitian matrix to real symmetric 10C tridiagonal matrix using unitary similarity 11C transformations. 12C***DESCRIPTION 13C 14C This subroutine is a translation of a complex analogue of 15C the ALGOL procedure TRED1, NUM. MATH. 11, 181-195(1968) 16C by Martin, Reinsch, and Wilkinson. 17C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 212-226(1971). 18C 19C This subroutine reduces a COMPLEX HERMITIAN matrix 20C to a real symmetric tridiagonal matrix using 21C unitary similarity transformations. 22C 23C On INPUT 24C 25C NM must be set to the row dimension of two-dimensional 26C array parameters as declared in the calling program 27C dimension statement. 28C 29C N is the order of the matrix. 30C 31C AR and AI contain the real and imaginary parts, 32C respectively, of the complex hermitian input matrix. 33C Only the lower triangle of the matrix need be supplied. 34C 35C On OUTPUT 36C 37C AR and AI contain information about the unitary trans- 38C formations used in the reduction in their full lower 39C triangles. Their strict upper triangles and the 40C diagonal of AR are unaltered. 41C 42C D contains the diagonal elements of the tridiagonal matrix. 43C 44C E contains the subdiagonal elements of the tridiagonal 45C matrix in its last N-1 positions. E(1) is set to zero. 46C 47C E2 contains the squares of the corresponding elements of E. 48C E2 may coincide with E if the squares are not needed. 49C 50C TAU contains further information about the transformations. 51C 52C Calls PYTHAG(A,B) for sqrt(A**2 + B**2). 53C 54C Questions and comments should be directed to B. S. Garbow, 55C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY 56C ------------------------------------------------------------------ 57C***REFERENCES B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW, 58C Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN- 59C SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG, 60C 1976. 61C***ROUTINES CALLED PYTHAG 62C***END PROLOGUE HTRIDI 63 64 65