SRC/dstedc.f(3)

🎀 SRC/dstedc.f(3) — Library Functions Manual 🎀

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✨ NAME ✨

SRC/dstedc.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine dstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork,
           info)

DSTEDC

💅 Function/Subroutine Documentation 💅

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
• 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.

Author 🌈 (auto-generated)

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