SSL II USER'S GUIDE - Lahey Computer Systems

storage mode. (For details, see Section 2.8)
Obtaining all eigenvalues
All eigenvalues of a Hermitian matrix A can be obtained
in steps 1) and 2) below.
:
CALL TRIDH(A,K,N,D,SD,V,ICON) 1)
IF(ICON .EQ. 30000)GO TO 1000
CALL TRQL(D,SD,N,E,M,ICON) 2)
:
1) A Hermitian matrix A is reduced to a real symmetric
tridiagonal matrix using the Householder method.
2) All eigenvalues of the real symmetric tridiagonal
matrix are obtained using the QL method.
Obtaining selected eigenvalues
By using steps 1) and 2) below, the largest (or smallest)
m eigenvalues of a matrix A can be obtained.
:
CALL TRIDH(A,K,N,D,SD,V,ICON) 1)
IF(ICON .EQ. 30000)GO TO 1000
CALL BSCT1(D,SD,N,M,EPST,E,VW,ICON) 2)
:
1) A Hermitian metrics A is reduced to a real symmetric
tridiagonal matrix by the Householder method.
2) The largest (or smallest) m eigenvalues of the real
symmetric tridiagonal matrix are obtained using the
bisection method.
When obtaining more than n/4 eigenvalues of A of order
n, it is generally faster to use subroutines TRIDH and
TRQL as described in “Obtaining all eigenvalues”.
Obtaining all eigenvalues and corresponding
eigenvectors
All eigenvalues and corresponding eigenvectors can be
obtained either by using steps 1) through 3)or by using
step 4), (see below).
:
CALL TRIDH(A,K,N,D,SD,V,ICON) 1)
IF(ICON .EQ. 30000)GO TO 1000
CALL TEIG1(D,SD,N,E,EV,K,M,ICON) 2)
IF(ICON .GE. 20000)GO TO 2000
CALL TRBKH(EV,EVI,K,N,M,P,V,ICON) 3)
IF(ICON .EQ. 30000)GO TO 3000
:
or standard routine
:
CALL HEIG2(A,K,N,N,E,EVR,EVI,VW,
*ICON) 4)
IF(ICON .GE. 20000)GO TO 1000
:
EIGENVALUES AND EIGENVECTORS
1) A Hermitian matrix A is reduced to a real symmetric
tridiagonal matrix
2) Eigenvalues of the real symmetric tridiagonal matrix
(i.e., eigenvalues of A) and corresponding
eigenvectors are obtained using the QL method.
3) The Eigenvectors obtained in 2) are transformed to
the eigenvectors of A.
4) The standard routine HEIG2 can perform all the
above steps 1) through 3). In this case, the fourth
parameter N of HEIG2 indicates to obtain the largest
n eigenvalues.
Obtaining selected eigenvalues and corresponding
eigenvectors
A selected number of eigenvalues (m) and corresponding
eigenvectors of a Hermitian matrix can be obtained either
by using steps 1) through 3)or by using step 4), (see
below).
:
CALL TRIDH(A,K,N,D,SD,V,ICON) 1)
IF(ICON .EQ. 30000)GO TO 1000
CALL TEIG2(D,SD,N,M,E,EV,K,VW,ICON) 2)
IF(ICON .GE. 20000)GO TO 2000
CALL TRBKH(EV,EVI,K,N,M,P,V,ICON) 3)
IF(ICON .EQ. 30000)GO TO 3000
:
or standard routine
:
CALL HEIG2(A,K,N,M,E,EVR,EVI,VW,ICON) 4)
IF(ICON .GE. 20000)GO TO 1000
:
1) A Hermitian matrix A is reduced to a real symmetric
tridiagonal matrix.
2) The largest (or smallest) m eigenvalues and
corresponding eigenvectors of the real symmetric
tridiagonal matrix are obtained using the bisection
method and the inverse iteration method.
3) Back transformation of the eigenvectors obtained in
2) are performed.
4) The standard routine HEIG2 can perform all the
above steps 1) through 3).
4.6 EIGENVALUES AND
EIGENVECTORS OF A REAL
SYMMETRIC BAND MATRIX
Subroutines BSEG, BTRID, BSVEC and BSEGJ are
provided for obtaining eigenvalues and eigenvectors of a
real symmetric band matrix.
These subroutines are suitable for large matrices, for
example, matrices of the order n > 100 and h/n < 1/6,
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