SRC/cstedc.f(3)

🌸 NAME 🌸

SRC/cstedc.f — the CSTEDC icon itself, bestie 💅

okay so real talk: this is the SRC/cstedc.f(3) page from the Library Functions Manual, and it's literally giving “divide and conquer eigenvalue routine” main character energy ✨

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✨ 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.

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🌸 Parameters 🌸

• COMPZ — CHARACTER*1. The values are:
  • '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 — INTEGER. The dimension of the symmetric tridiagonal matrix. N >= 0.
• D — REAL array, dimension (N). On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.
• E — REAL array, dimension (N-1). On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.
• Z — 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 — INTEGER. The leading dimension of the array Z. LDZ >= 1. If eigenvectors are desired, then LDZ >= max(1,N).
• WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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 — REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
• LRWORK — 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 — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — 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 — INTEGER. The values are:
  • = 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).

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👑 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.

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And that's the tea, bestie ☕💖 this whole page is LAPACK Version 3.12.0, SRC/cstedc.f(3), and it's lowkey iconic. Mwah 💋✨