LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine slarrf | ( | integer | N, |
real, dimension( * ) | D, | ||
real, dimension( * ) | L, | ||
real, dimension( * ) | LD, | ||
integer | CLSTRT, | ||
integer | CLEND, | ||
real, dimension( * ) | W, | ||
real, dimension( * ) | WGAP, | ||
real, dimension( * ) | WERR, | ||
real | SPDIAM, | ||
real | CLGAPL, | ||
real | CLGAPR, | ||
real | PIVMIN, | ||
real | SIGMA, | ||
real, dimension( * ) | DPLUS, | ||
real, dimension( * ) | LPLUS, | ||
real, dimension( * ) | WORK, | ||
integer | INFO | ||
) |
SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.
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Given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... W( CLEND ), SLARRF finds a new relatively robust representation L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the eigenvalues of L(+) D(+) L(+)^T is relatively isolated.
[in] | N | N is INTEGER The order of the matrix (subblock, if the matrix split). |
[in] | D | D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D. |
[in] | L | L is REAL array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L. |
[in] | LD | LD is REAL array, dimension (N-1) The (N-1) elements L(i)*D(i). |
[in] | CLSTRT | CLSTRT is INTEGER The index of the first eigenvalue in the cluster. |
[in] | CLEND | CLEND is INTEGER The index of the last eigenvalue in the cluster. |
[in] | W | W is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The eigenvalue APPROXIMATIONS of L D L^T in ascending order. W( CLSTRT ) through W( CLEND ) form the cluster of relatively close eigenalues. |
[in,out] | WGAP | WGAP is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W. |
[in] | WERR | WERR is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W |
[in] | SPDIAM | SPDIAM is REAL estimate of the spectral diameter obtained from the Gerschgorin intervals |
[in] | CLGAPL | CLGAPL is REAL |
[in] | CLGAPR | CLGAPR is REAL absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster. |
[in] | PIVMIN | PIVMIN is REAL The minimum pivot allowed in the Sturm sequence. |
[out] | SIGMA | SIGMA is REAL The shift used to form L(+) D(+) L(+)^T. |
[out] | DPLUS | DPLUS is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D(+). |
[out] | LPLUS | LPLUS is REAL array, dimension (N-1) The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+). |
[out] | WORK | WORK is REAL array, dimension (2*N) Workspace. |
[out] | INFO | INFO is INTEGER Signals processing OK (=0) or failure (=1) |
Definition at line 195 of file slarrf.f.