# slasq2.f - Man Page

## 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 (integer N, real, dimension( * ) Z, integer 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.

**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 ieee-754 floating-point 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.

*Z*Z 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.

*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)

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**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 114 of file slasq2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slasq2(3) is an alias of slasq2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK