Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - 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

**SYNOPSIS**

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

**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.

**ARGUMENTS**

N (input) INTEGER The number of rows and columns in the matrix. N >= 0. Z (input/output) 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 (output) 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 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 routine (version 3.2) April 2011 SLASQ2(3lapack)