# stedc - Man Page

stedc: eig, divide and conquer

## Synopsis

### Functions

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

## Function Documentation

### subroutine cstedc (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

NAG Ltd.

Contributors:

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

Definition at line 204 of file cstedc.f.

### subroutine dstedc (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

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.

### subroutine sstedc (character compz, integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

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.

### subroutine zstedc (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

NAG Ltd.

Contributors:

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

Definition at line 204 of file zstedc.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK