lasq2

slasq2

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(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.

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 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

• = 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)

dlasq2

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(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.

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 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

• = 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)