slasq2 (3)  Linux Manuals
NAME
slasq2.f 
SYNOPSIS
Functions/Subroutines
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.
Function/Subroutine Documentation
subroutine slasq2 (integerN, real, dimension( * )Z, integerINFO)
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 ieee754 floatingpoint standard in their handling of infinities and NaNs, and false otherwise. This variable is passed to SLASQ3.
Parameters:

N
N is INTEGER The number of rows and columns in the matrix. N >= 0.
ZZ 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.
INFOINFO is INTEGER = 0: successful exit < 0: if the ith argument is a scalar and had an illegal value, then INFO = i, if the ith argument is an array and the jentry 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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Further Details:

Local Variables: I0:N0 defines a current unreduced segment of Z. The shifts are accumulated in SIGMA. Iteration count is in ITER. Pingpong is controlled by PP (alternates between 0 and 1).
Definition at line 113 of file slasq2.f.
Author
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