dlasq2 (l)  Linux Man Pages
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
NAME
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 overflowSYNOPSIS
 SUBROUTINE DLASQ2(
 N, Z, INFO )
 INTEGER INFO, N
 DOUBLE PRECISION Z( * )
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 1aqs 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 ieee754 floatingpoint standard in their handling of infinities and NaNs, and false otherwise. This variable is passed to DLASQ3.
ARGUMENTS
 N (input) INTEGER
 The number of rows and columns in the matrix. N >= 0.
 Z (input/output) 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.
 INFO (output) 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 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. Pingpong is controlled by PP (alternates between 0 and 1).