laed0 - Man Page

subroutine claed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info)
CLAED0 used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
subroutine dlaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)
DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
subroutine slaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)
SLAED0 used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
subroutine zlaed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info)
ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

CLAED0 used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.  

Purpose:

 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.

Parameters

QSIZ

          QSIZ is INTEGER
         The dimension of the unitary matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N

          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.

D

          D is REAL array, dimension (N)
         On entry, the diagonal elements of the tridiagonal matrix.
         On exit, the eigenvalues in ascending order.

E

          E is REAL array, dimension (N-1)
         On entry, the off-diagonal elements of the tridiagonal matrix.
         On exit, E has been destroyed.

Q

          Q is COMPLEX array, dimension (LDQ,N)
         On entry, Q must contain an QSIZ x N matrix whose columns
         unitarily orthonormal. It is a part of the unitary matrix
         that reduces the full dense Hermitian matrix to a
         (reducible) symmetric tridiagonal matrix.

LDQ

          LDQ is INTEGER
         The leading dimension of the array Q.  LDQ >= max(1,N).

IWORK

          IWORK is INTEGER array,
         the dimension of IWORK must be at least
                      6 + 6*N + 5*N*lg N
                      ( lg( N ) = smallest integer k
                                  such that 2^k >= N )

RWORK

          RWORK is REAL array,
                               dimension (1 + 3*N + 2*N*lg N + 3*N**2)
                        ( lg( N ) = smallest integer k
                                    such that 2^k >= N )

QSTORE

          QSTORE is COMPLEX array, dimension (LDQS, N)
         Used to store parts of
         the eigenvector matrix when the updating matrix multiplies
         take place.

LDQS

          LDQS is INTEGER
         The leading dimension of the array QSTORE.
         LDQS >= max(1,N).

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  The algorithm failed to compute an eigenvalue while
                working on the submatrix lying in rows and columns
                INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file claed0.f.

DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.  

Purpose:

 DLAED0 computes all eigenvalues and corresponding eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.

Parameters

ICOMPQ

          ICOMPQ is INTEGER
          = 0:  Compute eigenvalues only.
          = 1:  Compute eigenvectors of original dense symmetric matrix
                also.  On entry, Q contains the orthogonal matrix used
                to reduce the original matrix to tridiagonal form.
          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
                matrix.

QSIZ

          QSIZ is INTEGER
         The dimension of the orthogonal matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N

          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.

D

          D is DOUBLE PRECISION array, dimension (N)
         On entry, the main diagonal of the tridiagonal matrix.
         On exit, its eigenvalues.

E

          E is DOUBLE PRECISION array, dimension (N-1)
         The off-diagonal elements of the tridiagonal matrix.
         On exit, E has been destroyed.

Q

          Q is DOUBLE PRECISION array, dimension (LDQ, N)
         On entry, Q must contain an N-by-N orthogonal matrix.
         If ICOMPQ = 0    Q is not referenced.
         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
                          orthogonal matrix used to reduce the full
                          matrix to tridiagonal form corresponding to
                          the subset of the full matrix which is being
                          decomposed at this time.
         If ICOMPQ = 2    On entry, Q will be the identity matrix.
                          On exit, Q contains the eigenvectors of the
                          tridiagonal matrix.

LDQ

          LDQ is INTEGER
         The leading dimension of the array Q.  If eigenvectors are
         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.

QSTORE

          QSTORE is DOUBLE PRECISION array, dimension (LDQS, N)
         Referenced only when ICOMPQ = 1.  Used to store parts of
         the eigenvector matrix when the updating matrix multiplies
         take place.

LDQS

          LDQS is INTEGER
         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.

WORK

          WORK is DOUBLE PRECISION array,
         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
                     1 + 3*N + 2*N*lg N + 3*N**2
                     ( lg( N ) = smallest integer k
                                 such that 2^k >= N )
         If ICOMPQ = 2, the dimension of WORK must be at least
                     4*N + N**2.

IWORK

          IWORK is INTEGER array,
         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
                        6 + 6*N + 5*N*lg N.
                        ( lg( N ) = smallest integer k
                                    such that 2^k >= N )
         If ICOMPQ = 2, the dimension of IWORK must be at least
                        3 + 5*N.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  The algorithm failed to compute an eigenvalue while
                working on the submatrix lying in rows and columns
                INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 170 of file dlaed0.f.

SLAED0 used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.  

Purpose:

 SLAED0 computes all eigenvalues and corresponding eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.

Parameters

ICOMPQ

          ICOMPQ is INTEGER
          = 0:  Compute eigenvalues only.
          = 1:  Compute eigenvectors of original dense symmetric matrix
                also.  On entry, Q contains the orthogonal matrix used
                to reduce the original matrix to tridiagonal form.
          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
                matrix.

QSIZ

          QSIZ is INTEGER
         The dimension of the orthogonal matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N

          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.

D

          D is REAL array, dimension (N)
         On entry, the main diagonal of the tridiagonal matrix.
         On exit, its eigenvalues.

E

          E is REAL array, dimension (N-1)
         The off-diagonal elements of the tridiagonal matrix.
         On exit, E has been destroyed.

Q

          Q is REAL array, dimension (LDQ, N)
         On entry, Q must contain an N-by-N orthogonal matrix.
         If ICOMPQ = 0    Q is not referenced.
         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
                          orthogonal matrix used to reduce the full
                          matrix to tridiagonal form corresponding to
                          the subset of the full matrix which is being
                          decomposed at this time.
         If ICOMPQ = 2    On entry, Q will be the identity matrix.
                          On exit, Q contains the eigenvectors of the
                          tridiagonal matrix.

LDQ

          LDQ is INTEGER
         The leading dimension of the array Q.  If eigenvectors are
         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.

QSTORE

          QSTORE is REAL array, dimension (LDQS, N)
         Referenced only when ICOMPQ = 1.  Used to store parts of
         the eigenvector matrix when the updating matrix multiplies
         take place.

LDQS

          LDQS is INTEGER
         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.

WORK

          WORK is REAL array,
         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
                     1 + 3*N + 2*N*lg N + 3*N**2
                     ( lg( N ) = smallest integer k
                                 such that 2^k >= N )
         If ICOMPQ = 2, the dimension of WORK must be at least
                     4*N + N**2.

IWORK

          IWORK is INTEGER array,
         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
                        6 + 6*N + 5*N*lg N.
                        ( lg( N ) = smallest integer k
                                    such that 2^k >= N )
         If ICOMPQ = 2, the dimension of IWORK must be at least
                        3 + 5*N.

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  The algorithm failed to compute an eigenvalue while
                working on the submatrix lying in rows and columns
                INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 170 of file slaed0.f.

ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.  

Purpose:

 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.

Parameters

QSIZ

          QSIZ is INTEGER
         The dimension of the unitary matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N

          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.

D

          D is DOUBLE PRECISION array, dimension (N)
         On entry, the diagonal elements of the tridiagonal matrix.
         On exit, the eigenvalues in ascending order.

E

          E is DOUBLE PRECISION array, dimension (N-1)
         On entry, the off-diagonal elements of the tridiagonal matrix.
         On exit, E has been destroyed.

Q

          Q is COMPLEX*16 array, dimension (LDQ,N)
         On entry, Q must contain an QSIZ x N matrix whose columns
         unitarily orthonormal. It is a part of the unitary matrix
         that reduces the full dense Hermitian matrix to a
         (reducible) symmetric tridiagonal matrix.

LDQ

          LDQ is INTEGER
         The leading dimension of the array Q.  LDQ >= max(1,N).

IWORK

          IWORK is INTEGER array,
         the dimension of IWORK must be at least
                      6 + 6*N + 5*N*lg N
                      ( lg( N ) = smallest integer k
                                  such that 2^k >= N )

RWORK

          RWORK is DOUBLE PRECISION array,
                               dimension (1 + 3*N + 2*N*lg N + 3*N**2)
                        ( lg( N ) = smallest integer k
                                    such that 2^k >= N )

QSTORE

          QSTORE is COMPLEX*16 array, dimension (LDQS, N)
         Used to store parts of
         the eigenvector matrix when the updating matrix multiplies
         take place.

LDQS

          LDQS is INTEGER
         The leading dimension of the array QSTORE.
         LDQS >= max(1,N).

INFO

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  The algorithm failed to compute an eigenvalue while
                working on the submatrix lying in rows and columns
                INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file zlaed0.f.