slasq2(3)

NAME

SLASQ2 - compute all the eigenvalues of the symmetric pos

itive 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 SLASQ2( N, Z, INFO )
    INTEGER        INFO, N
    REAL           Z( * )

PURPOSE

SLASQ2 computes all the eigenvalues of the symmetric posi

tive 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 sym

metric 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.

ARGUMENTS

N (input) INTEGER

The number of rows and columns in the matrix. N >=

0.

Z (workspace) 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 NDI

VS/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 il

legal 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).

LAPACK version 3.0 15 June 2000

SLASQ2(3)