man dlasq2 (Fonctions bibliothèques) - compute 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
NAME
DLASQ2 - compute 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
SYNOPSIS
- SUBROUTINE DLASQ2(
- N, Z, INFO )
- INTEGER INFO, N
- DOUBLE PRECISION Z( * )
PURPOSE
DLASQ2 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 : DLASQ2 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 DLASQ3.
ARGUMENTS
- N (input) INTEGER
- The number of rows and columns in the matrix. N >= 0.
- Z (workspace) DOUBLE PRECISION 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 (output) 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 30*N iterations (in inner while loop) = 3, termination criterion of outer while loop not met (program created more than N unreduced blocks)
FURTHER DETAILS
The shifts are accumulated in SIGMA. Iteration count is in ITER. Ping-pong is controlled by PP (alternates between 0 and 1).