subroutine slasq2 (N, Z, INFO)
SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
Purpose:
SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. To see the relation of Z to the tridiagonal matrix, let L be a unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and let U be an upper bidiagonal matrix with 1's above and diagonal Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the symmetric tridiagonal to which it is similar. Note : SLASQ2 defines a logical variable, IEEE, which is true on machines which follow ieee-754 floating-point standard in their handling of infinities and NaNs, and false otherwise. This variable is passed to SLASQ3.
Parameters:
N is INTEGER
The number of rows and columns in the matrix. N >= 0.
Z
Z is REAL array, dimension ( 4*N )
On entry Z holds the qd array. On exit, entries 1 to N hold
the eigenvalues in decreasing order, Z( 2*N+1 ) holds the
trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If
N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 )
holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of
shifts that failed.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if the i-th argument is a scalar and had an illegal
value, then INFO = -i, if the i-th argument is an
array and the j-entry had an illegal value, then
INFO = -(i*100+j)
> 0: the algorithm failed
= 1, a split was marked by a positive value in E
= 2, current block of Z not diagonalized after 100*N
iterations (in inner while loop). On exit Z holds
a qd array with the same eigenvalues as the given Z.
= 3, termination criterion of outer while loop not met
(program created more than N unreduced blocks)
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Further Details:
Local Variables: I0:N0 defines a current unreduced segment of Z. The shifts are accumulated in SIGMA. Iteration count is in ITER. Ping-pong is controlled by PP (alternates between 0 and 1).
Definition at line 114 of file slasq2.f.
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