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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed5 (i, d, z, delta, rho, dlam) |
| | This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z) . The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed5 (i, d, z, delta, rho, dlam) |
| | This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z) . The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed5 (i, d, z, delta, rho, dlam) |
| | This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z) . The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed6 (kniter, orgati, rho, d, z, finit, tau, info) |
| | SLAED6: computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + ------— + -------— + ------— d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) This routine will be called by SLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed6 (kniter, orgati, rho, d, z, finit, tau, info) |
| | DLAED6: computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + ------— + -------— + ------— d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) This routine will be called by DLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed6 (kniter, orgati, rho, d, z, finit, tau, info) |
| | QLAED6: computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + ------— + -------— + ------— d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) This routine will be called by QLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_ssteqr (compz, n, d, e, z, ldz, work, info) |
| | SSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dsteqr (compz, n, d, e, z, ldz, work, info) |
| | DSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qsteqr (compz, n, d, e, z, ldz, work, info) |
| | QSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if QSYTRD or QSPTRD or QSBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed4 (n, i, d, z, delta, rho, dlam, info) |
| | This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed4 (n, i, d, z, delta, rho, dlam, info) |
| | This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed4 (n, i, d, z, delta, rho, dlam, info) |
| | This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlamda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info) |
| | SLAED8: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlamda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info) |
| | DLAED8: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlamda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info) |
| | QLAED8: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info) |
| | SLAED9: finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP. It makes the appropriate calls to SLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info) |
| | DLAED9: finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP. It makes the appropriate calls to DLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info) |
| | QLAED9: finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP. It makes the appropriate calls to QLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed3 (k, n, n1, d, q, ldq, rho, dlamda, q2, indx, ctot, w, s, info) |
| | SLAED3: finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to SLAED4 and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the K-by-K system which is solved here. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed3 (k, n, n1, d, q, ldq, rho, dlamda, q2, indx, ctot, w, s, info) |
| | DLAED3: finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to DLAED4 and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the K-by-K system which is solved here. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed3 (k, n, n1, d, q, ldq, rho, dlamda, q2, indx, ctot, w, s, info) |
| | QLAED3: finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to QLAED4 and then updates the eigenvectors by multiplying the matrix of eigenvectors of the pair of eigensystems being combined by the matrix of eigenvectors of the K-by-K system which is solved here. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info) |
| | SLAED7: 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 optionally eigenvectors of a dense symmetric matrix that has been reduced to tridiagonal form. SLAED1 handles the case in which all eigenvalues and eigenvectors of a symmetric tridiagonal matrix are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**Tu, 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 SLAED8. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED9). 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, public | la_lapack_eigv_tridiag::la_dlaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info) |
| | DLAED7: 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 optionally eigenvectors of a dense symmetric matrix that has been reduced to tridiagonal form. DLAED1 handles the case in which all eigenvalues and eigenvectors of a symmetric tridiagonal matrix are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**Tu, 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 DLAED8. 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 DLAED9). 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, public | la_lapack_eigv_tridiag::la_qlaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info) |
| | QLAED7: 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 optionally eigenvectors of a dense symmetric matrix that has been reduced to tridiagonal form. QLAED1 handles the case in which all eigenvalues and eigenvectors of a symmetric tridiagonal matrix are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**Tu, 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 QLAED8. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine QLAED4 (as called by QLAED9). 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, public | la_lapack_eigv_tridiag::la_slaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlamda, w, q2, indx, indxc, indxp, coltyp, info) |
| | SLAED2: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlamda, w, q2, indx, indxc, indxp, coltyp, info) |
| | DLAED2: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlamda, w, q2, indx, indxc, indxp, coltyp, info) |
| | QLAED2: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_slaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info) |
| | SLAED1: 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. SLAED7 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 SLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED3). 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, public | la_lapack_eigv_tridiag::la_dlaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info) |
| | DLAED1: 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, public | la_lapack_eigv_tridiag::la_qlaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info) |
| | QLAED1: 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. QLAED7 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 QLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine QLAED4 (as called by QLAED3). 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, public | la_lapack_eigv_tridiag::la_slaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info) |
| | SLAED0: computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_dlaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info) |
| | DLAED0: computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_qlaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info) |
| | QLAED0: computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_claed8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlamda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info) |
| | CLAED8: merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_zlaed8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlamda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info) |
| | ZLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_wlaed8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlamda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info) |
| | WLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_csteqr (compz, n, d, e, z, ldz, work, info) |
| | CSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_zsteqr (compz, n, d, e, z, ldz, work, info) |
| | ZSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_wsteqr (compz, n, d, e, z, ldz, work, info) |
| | WSTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if WHETRD or WHPTRD or WHBTRD has been used to reduce this matrix to tridiagonal form.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_claed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info) |
| | CLAED7: 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 optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) where Z = Q**Hu, 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 SLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED3). 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, public | la_lapack_eigv_tridiag::la_zlaed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info) |
| | ZLAED7: 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 optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) where Z = Q**Hu, 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 SLAED3). 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, public | la_lapack_eigv_tridiag::la_wlaed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info) |
| | WLAED7: 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 optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) where Z = Q**Hu, 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 QLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine QLAED4 (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, public | la_lapack_eigv_tridiag::la_claed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info) |
| | Using the divide and conquer method, CLAED0: computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_zlaed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info) |
| | Using the divide and conquer method, ZLAED0: computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.
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| pure subroutine, public | la_lapack_eigv_tridiag::la_wlaed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info) |
| | Using the divide and conquer method, WLAED0: computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix.
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1.13.2