By B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V.C. Klema, C.B. Moler
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Extra resources for Matrix Eigensystem Routines — EISPACK Guide
NE. 0 CALL BISECT(N,EPSI,ful,f~2,fv3,RLB,RUB,MM,M,W,iVI,IERR,fv4,fv5) IF (iERR ~NE. NE. O) GO TO 99999 CALL BAKVEC(hrM,N,A,fv2,M,Z,IERR) IF (lEER ~NE. 1-46 The parameter EPSI is used to control the accuracy of the eigenvalue computation. Setting it to zero or calling EISPAC without supplying it causes the use of a default value suitable for most matrices. 3 and in the BISECT and EISPAC documents. Upon completion of the path, M is set to the number of eigenvalues determined to lie in the interval defined by RLB and RUB and, provided M !
O) GO TO 99999 or, using EISPAC: CALL EISPAC(NM,N,MATRIX('COMPLEX',AR,AI,'HERMITIAN'),VALUES(W)) This path returns the eigenvalues in ascending order; it preserves the full upper triangle of AR and the strict upper triangle of AI. Suitable dimensions for the arrays are: fvl(nm), AR(n~n,nm), AI(mm,nm), W(nm), fv2(nm), and fml(2,nm). The array storage required to execute this path is 2N 2 + 5N working precision words. 0 seconds for sample matrices of order I0, 20, 40, and 80 respectively. 9. 6 SOME EIGENVALUES AND CORRESPONDING EIGENVECTORS OF A COMPLEX HERMiTIAN MATRIX To determine the eigenvalues W in an interval extending from RLB to RUB, together with their corresponding eigenvectors (ZR,ZI), of a complex Hermitian matrix (AR,AI) of order N, the recommended EISPACK path is: CALL HTRIDI (NM,N ,AR,AI ~ 7 ,fv2 ,fv 3 ,fml ) EPSI = 0~0 CALL BISECT (N, EPS 1 ,fvi ,fv2 ,fv3 ,RLB ,RUB ,MM,M ,w,ivl, IERR,fv4 ,fvS) IF (IERR ~NE.
This path destroys A. Suitable dimensions for the arrays are: A(r~n,r~n), W R ( ~ ) , WI(~), fvl (~), and iv1(~) ° The array storage required to execute this path is N 2 + 3N working precision words and N integer words. 9 seconds for sample matrices of order I0, 20, 40, and 80 respectively. 2. TRUE. elements in the LOGICAL array SELECT) of a real general matrix A of order N, the recommended EISPACK path is: CALL BALANC(NM,N,A,is2,is2,fvl) CALL ELMHES(NM,N,is2,is2,A,iv2) DO i00 1 = I, N DO 50 J = I, N fml(l,J) 50 = A(I,J) CONTINUE I00 CONTINUE CALL HQR(NM,N,isl,is2,fm2,WR,WI,IERR) IF (IERR ,NE.
Matrix Eigensystem Routines — EISPACK Guide by B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V.C. Klema, C.B. Moler