lasq2#

Functions

void slasq2(
    const INT           n,
          f32* restrict Z,
          INT*          info
);
void slasq2(const INT n, f32 *restrict Z, INT *info)#

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[1,3,5,..] and let U be an upper bidiagonal matrix with 1’s above and diagonal Z[0,2,4,..]. 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.

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).

Parameters

in
n

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

inout
Z

Single precision array, dimension (4*n). On entry Z holds the qd array. On exit, entries 0 to n-1 hold the eigenvalues in decreasing order, Z[2*n] holds the trace, and Z[2*n+1] holds the sum of the eigenvalues. If n>2, then Z[2*n+2] holds the iteration count, Z[2*n+3] holds NDIVS/NIN^2, and Z[2*n+4] holds the percentage of shifts that failed.

out
info

  • info=0: successful exit

  • info<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)

  • info>0: the algorithm failed

  • info=1, a split was marked by a positive value in E

  • info=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.

  • info=3, termination criterion of outer while loop not met (program created more than n unreduced blocks)

Functions

void dlasq2(
    const INT           n,
          f64* restrict Z,
          INT*          info
);
void dlasq2(const INT n, f64 *restrict Z, INT *info)#

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[1,3,5,..] and let U be an upper bidiagonal matrix with 1’s above and diagonal Z[0,2,4,..]. 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.

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).

Parameters

in
n

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

inout
Z

Double precision array, dimension (4*n). On entry Z holds the qd array. On exit, entries 0 to n-1 hold the eigenvalues in decreasing order, Z[2*n] holds the trace, and Z[2*n+1] holds the sum of the eigenvalues. If n>2, then Z[2*n+2] holds the iteration count, Z[2*n+3] holds NDIVS/NIN^2, and Z[2*n+4] holds the percentage of shifts that failed.

out
info

  • info=0: successful exit

  • info<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)

  • info>0: the algorithm failed

  • info=1, a split was marked by a positive value in E

  • info=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.

  • info=3, termination criterion of outer while loop not met (program created more than n unreduced blocks)