LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlasq2.f File Reference

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## Functions/Subroutines

subroutine dlasq2 (N, Z, INFO)
DLASQ2 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 dlasq2 ( integer N, double precision, dimension( * ) Z, integer INFO )

DLASQ2 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:
``` 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.```
Parameters:
 [in] N ``` N is INTEGER The number of rows and columns in the matrix. N >= 0.``` [in,out] Z ``` Z is 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.``` [out] 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)```
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.
Ping-pong is controlled by PP (alternates between 0 and 1).```

Definition at line 113 of file dlasq2.f.

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