BADNELL & BURGESS D.A.M.T.P. CAMBRIDGE C DIAGONALIZATION OF REAL SYMMETRIC N-BY-N MATRIX Z. C METHOD: HOUSEHOLDER REDUCTION TO TRI-DIAGONAL FORM AND SHIFTED C QL ALGORITHM TO DETERMINE THE E-VALUES AND E-VECTORS. C BASED ON MARTIN, REINSCH & WILKINSON: NUM. MATH. 11, 181-95 (1968). C C INPUT REQUIRED. N, IUP AND Z. ONLY LOWER TRIANGLE OF Z NEED BE SUPPLIED. C MATRIX Z OVERWRITTEN BY EIGENVECTORS OF Z. C IUP=1/-1 ASC/DESCENDING SORT, 0 NO SORT. C MXMAT, IS THE ROW DIMENSION OF Z IN THE CALLING ROUTINE. C C OUTPUT. Z AND D, WHERE Z CONSISTS OF COLUMN EIGENVECTORS C AND D CONSISTS OF CORRESPONDING EIGENVALUES. C C NOTE: E IS A WORKING ARRAY. C

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