LAED1: computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles the case in which eigenvalues only or eigenvalues and eigenvectors of a full symmetric matrix (which was reduced to tridiagonal form) are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**T*u, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurrence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine DLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine DLAED4 (as called by DLAED3). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.
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| pure subroutine | dlaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info) |
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| | la_dlaed1 |
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| | la_qlaed1 |
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| pure subroutine | slaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info) |
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| | la_slaed1 |
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LAED1: computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles the case in which eigenvalues only or eigenvalues and eigenvectors of a full symmetric matrix (which was reduced to tridiagonal form) are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**T*u, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurrence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine DLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine DLAED4 (as called by DLAED3). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.
◆ dlaed1()
| pure subroutine la_lapack::laed1::dlaed1 |
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integer(ilp), intent(in) |
n, |
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real(dp), dimension(*), intent(inout) |
d, |
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real(dp), dimension(ldq,*), intent(inout) |
q, |
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integer(ilp), intent(in) |
ldq, |
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integer(ilp), dimension(*), intent(inout) |
indxq, |
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real(dp), intent(inout) |
rho, |
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integer(ilp), intent(in) |
cutpnt, |
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real(dp), dimension(*), intent(out) |
work, |
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integer(ilp), dimension(*), intent(out) |
iwork, |
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integer(ilp), intent(out) |
info |
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◆ la_dlaed1()
| la_lapack::laed1::la_dlaed1 |
◆ la_qlaed1()
| la_lapack::laed1::la_qlaed1 |
◆ la_slaed1()
| la_lapack::laed1::la_slaed1 |
◆ slaed1()
| pure subroutine la_lapack::laed1::slaed1 |
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integer(ilp), intent(in) |
n, |
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real(sp), dimension(*), intent(inout) |
d, |
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real(sp), dimension(ldq,*), intent(inout) |
q, |
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integer(ilp), intent(in) |
ldq, |
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integer(ilp), dimension(*), intent(inout) |
indxq, |
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real(sp), intent(inout) |
rho, |
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integer(ilp), intent(in) |
cutpnt, |
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real(sp), dimension(*), intent(out) |
work, |
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integer(ilp), dimension(*), intent(out) |
iwork, |
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integer(ilp), intent(out) |
info |
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) |
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The documentation for this interface was generated from the following file:
1.9.8