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 ieee-754 floating-point standard in their


 handling of infinities and NaNs, and false otherwise. This variable


 is passed to DLASQ3.

N

          N is INTEGER


        The number of rows and columns in the matrix. N >= 0.

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.

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)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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).

 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.

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)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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).