--- name: "cstedc.f" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/cstedc.f" --- # cstedc.f(3) ## NAME SRC/cstedc.f ## SYNOPSIS ### Functions/Subroutines subroutine **cstedc** (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)\ **CSTEDC** ## Function/Subroutine 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 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**. ## Author Generated automatically by Doxygen for LAPACK from the source code.