lasq2 - Man Page

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 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.

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.  

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 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.

Parameters

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)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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 111 of file dlasq2.f.

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.

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 111 of file slasq2.f.