SRC/sstedc.f(3)

🎀 SRC/sstedc.f 🎀

from the Library Functions Manual, bestie — this is the SSTEDC page, and she is giving divide-and-conquer main character energy. 💅

✨ NAME ✨

SRC/sstedc.f

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

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

SSTEDC

💖 Function/Subroutine Documentation 💖

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 🌸

okay so 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
• 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 📌

Definition at line 180 of file sstedc.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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sign-off bestie: source/version vibes are SRC/sstedc.f(3) · LAPACK · Version 3.12.0 — and the footer didn’t actually hand us a date, so that’s the whole cute little ending we got 😭🎀