\brief \b ESMF_DLASQ2 \htmlonly Download ESMF_DLASQ2 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:
\verbatim
ESMF_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 : ESMF_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 ESMF_DLASQ3. \endverbatim \param[in] N \verbatim N is INTEGER The number of rows and columns in the matrix. N >= 0. \endverbatim
\param[in,out] Z \verbatim Z is DOUBLE PRECISION array, dimension ( 4N ) On entry Z holds the qd array. On exit, entries 1 to N hold the eigenvalues in decreasing order, Z( 2N+1 ) holds the trace, and Z( 2N+2 ) holds the sum of the eigenvalues. If N > 2, then Z( 2N+3 ) holds the iteration count, Z( 2N+4 ) holds NDIVS/NIN^2, and Z( 2N+5 ) holds the percentage of shifts that failed. \endverbatim
\param[out] INFO \verbatim 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 = -(i100+j) > 0: the algorithm failed = 1, a split was marked by a positive value in E = 2, current block of Z not diagonalized after 100N 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) \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup auxOTHERcomputational \par Further Details:
\verbatim
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). \endverbatim
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer | :: | N | ||||
| double precision | :: | Z(*) | ||||
| integer | :: | INFO |