LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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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. 
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.
Download DLASQ2 + dependencies [TGZ] [ZIP] [TXT]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 ieee754 floatingpoint standard in their handling of infinities and NaNs, and false otherwise. This variable is passed to DLASQ3.
[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 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 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) 
Local Variables: I0:N0 defines a current unreduced segment of Z. The shifts are accumulated in SIGMA. Iteration count is in ITER. Pingpong is controlled by PP (alternates between 0 and 1).
Definition at line 113 of file dlasq2.f.