stedc(3) Library Functions Manual stedc(3)

stedc - stedc: eig, divide and conquer


subroutine cstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CSTEDC subroutine dstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
DSTEDC subroutine sstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
SSTEDC subroutine zstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZSTEDC

CSTEDC

Purpose:

 CSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer 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.

Parameters

COMPZ 
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original Hermitian matrix
                  also.  On entry, Z contains the unitary matrix used
                  to reduce the original matrix to tridiagonal form.

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, if INFO = 0, the eigenvalues in ascending order.

E

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

Z

          Z is COMPLEX array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the unitary
          matrix used in the reduction to tridiagonal form.
          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
          orthonormal eigenvectors of the original Hermitian matrix,
          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
          of the symmetric tridiagonal matrix.
          If  COMPZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If eigenvectors are desired, then LDZ >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
          Note that for COMPZ = 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LWORK need
          only be 1.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK, RWORK and
          IWORK arrays, returns these values as the first entries of
          the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

          RWORK is REAL array, dimension (MAX(1,LRWORK))
          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

          LRWORK is INTEGER
          The dimension of the array RWORK.
          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LRWORK must be at least
                         1 + 3*N + 2*N*lg N + 4*N**2 ,
                         where lg( N ) = smallest integer k such
                         that 2**k >= N.
          If COMPZ = 'I' and N > 1, LRWORK must be at least
                         1 + 4*N + 2*N**2 .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LRWORK
          need only be max(1,2*(N-1)).
          If LRWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          LIWORK is INTEGER
          The dimension of the array IWORK.
          If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
          If COMPZ = 'V' or N > 1,  LIWORK must be at least
                                    6 + 6*N + 5*N*lg N.
          If COMPZ = 'I' or N > 1,  LIWORK must be at least
                                    3 + 5*N .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LIWORK
          need only be 1.
          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

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 204 of file cstedc.f.

DSTEDC

Purpose:

 DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.
 The eigenvectors of a full or band real symmetric matrix can also be
 found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
 matrix to tridiagonal form.

Parameters

COMPZ 
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original dense symmetric
                  matrix also.  On entry, Z contains the orthogonal
                  matrix used to reduce the original matrix to
                  tridiagonal form.

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, if INFO = 0, the eigenvalues in ascending order.

E

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

Z

          Z is DOUBLE PRECISION array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the orthogonal
          matrix used in the reduction to tridiagonal form.
          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
          orthonormal eigenvectors of the original symmetric matrix,
          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
          of the symmetric tridiagonal matrix.
          If  COMPZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If eigenvectors are desired, then LDZ >= max(1,N).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
          If COMPZ = 'V' and N > 1 then LWORK must be at least
                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
                         where lg( N ) = smallest integer k such
                         that 2**k >= N.
          If COMPZ = 'I' and N > 1 then LWORK must be at least
                         ( 1 + 4*N + N**2 ).
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LWORK need
          only be max(1,2*(N-1)).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          LIWORK is INTEGER
          The dimension of the array IWORK.
          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
          If COMPZ = 'V' and N > 1 then LIWORK must be at least
                         ( 6 + 6*N + 5*N*lg N ).
          If COMPZ = 'I' and N > 1 then LIWORK must be at least
                         ( 3 + 5*N ).
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LIWORK
          need only be 1.
          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of the IWORK array,
          returns this value as the first entry of the IWORK array, and
          no error message related to LIWORK is issued by XERBLA.

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
Modified by Francoise Tisseur, University of Tennessee

Definition at line 180 of file dstedc.f.

SSTEDC

Purpose:

 SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer method.
 The eigenvectors of a full or band real symmetric matrix can also be
 found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
 matrix to tridiagonal form.

Parameters

COMPZ 
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original dense symmetric
                  matrix also.  On entry, Z contains the orthogonal
                  matrix used to reduce the original matrix to
                  tridiagonal form.

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, if INFO = 0, the eigenvalues in ascending order.

E

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

Z

          Z is REAL array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the orthogonal
          matrix used in the reduction to tridiagonal form.
          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
          orthonormal eigenvectors of the original symmetric matrix,
          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
          of the symmetric tridiagonal matrix.
          If  COMPZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If eigenvectors are desired, then LDZ >= max(1,N).

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
          If COMPZ = 'V' and N > 1 then LWORK must be at least
                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
                         where lg( N ) = smallest integer k such
                         that 2**k >= N.
          If COMPZ = 'I' and N > 1 then LWORK must be at least
                         ( 1 + 4*N + N**2 ).
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LWORK need
          only be max(1,2*(N-1)).
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          LIWORK is INTEGER
          The dimension of the array IWORK.
          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
          If COMPZ = 'V' and N > 1 then LIWORK must be at least
                         ( 6 + 6*N + 5*N*lg N ).
          If COMPZ = 'I' and N > 1 then LIWORK must be at least
                         ( 3 + 5*N ).
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LIWORK
          need only be 1.
          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of the IWORK array,
          returns this value as the first entry of the IWORK array, and
          no error message related to LIWORK is issued by XERBLA.

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
Modified by Francoise Tisseur, University of Tennessee

Definition at line 180 of file sstedc.f.

ZSTEDC

Purpose:

 ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
 symmetric tridiagonal matrix using the divide and conquer 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.

Parameters

COMPZ 
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original Hermitian matrix
                  also.  On entry, Z contains the unitary matrix used
                  to reduce the original matrix to tridiagonal form.

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, if INFO = 0, the eigenvalues in ascending order.

E

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

Z

          Z is COMPLEX*16 array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the unitary
          matrix used in the reduction to tridiagonal form.
          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
          orthonormal eigenvectors of the original Hermitian matrix,
          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
          of the symmetric tridiagonal matrix.
          If  COMPZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1.
          If eigenvectors are desired, then LDZ >= max(1,N).

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.
          Note that for COMPZ = 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LWORK need
          only be 1.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal sizes of the WORK, RWORK and
          IWORK arrays, returns these values as the first entries of
          the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

          LRWORK is INTEGER
          The dimension of the array RWORK.
          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.
          If COMPZ = 'V' and N > 1, LRWORK must be at least
                         1 + 3*N + 2*N*lg N + 4*N**2 ,
                         where lg( N ) = smallest integer k such
                         that 2**k >= N.
          If COMPZ = 'I' and N > 1, LRWORK must be at least
                         1 + 4*N + 2*N**2 .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LRWORK
          need only be max(1,2*(N-1)).
          If LRWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          LIWORK is INTEGER
          The dimension of the array IWORK.
          If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.
          If COMPZ = 'V' or N > 1,  LIWORK must be at least
                                    6 + 6*N + 5*N*lg N.
          If COMPZ = 'I' or N > 1,  LIWORK must be at least
                                    3 + 5*N .
          Note that for COMPZ = 'I' or 'V', then if N is less than or
          equal to the minimum divide size, usually 25, then LIWORK
          need only be 1.
          If LIWORK = -1, then a workspace query is assumed; the
          routine only calculates the optimal sizes of the WORK, RWORK
          and IWORK arrays, returns these values as the first entries
          of the WORK, RWORK and IWORK arrays, and no error message
          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

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 204 of file zstedc.f.

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