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template<typename T>
void stedc(char *compz, integer *n, T *d, T *e, T *z, integer *ldz, T *work, integer *lwork, integer *iwork, integer *liwork, integer *info)# Tridiagonal divide-and-conquer algorithm.
Purpose:
Computation of 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. 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. See SLAED3 for details.
- Parameters:
compz – [in]
compz is char*
= ‘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 – [in]
n is integer*
The dimension of the symmetric tridiagonal matrix. n >= 0.
d – [inout]
d is float/double array, dimension (n)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, if info = 0, the eigenvalues in ascending order.e – [inout]
e is float/double array, dimension (n-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.z – [inout]
z is float/double 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 – [in]
ldz is integer*
The leading dimension of the array Z. ldz >= 1.
If eigenvectors are desired, then ldz >= fla_max(1,n).WORK – [out]
WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK – [in]
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 – [out]
RWORK is REAL array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK – [in]
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 fla_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 – [out]
IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK – [in]
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 – [out]
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).