SRC/ssbevd.f(3)

Hey bestie 💖 welcome to the SRC/ssbevd.f(3) page from the Library Functions Manual — it’s the LAPACK glow-up for ssbevd, and it’s literally giving main-character energy for real symmetric band matrices. ✨

🎀 NAME 🎀

SRC/ssbevd.f — that’s the page name, bestie, no cap. 🫶

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

• subroutine ssbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, iwork, liwork, info) — SSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💅

🦋 Function/Subroutine Documentation 🦋

✨ ssbevd ✨

subroutine ssbevd (character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🔥

Purpose

Okay so here’s the vibe: SSBEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. Periodt. 👑

Parameters

• JOBZ — JOBZ is CHARACTER*1. = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors. 💅
• UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. 🌸
• N — N is INTEGER. The order of the matrix A. N >= 0. 🎀
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. 🦋
• AB — AB is REAL array, dimension (LDAB, N). On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 🌈

On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB. 💖

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1. ✨
• W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🍓
• Z — Z is REAL array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced. 🦋
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). 🌸
• WORK — WORK is REAL array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 💜
• LWORK — LWORK is INTEGER. The dimension of the array WORK. IF N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. If JOBZ = 'V' and N > 2, LWORK must be at least ( 1 + 5*N + 2*N**2 ). 🫶

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 JOBZ = 'N' or N <= 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N. 🌟

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. 😭

Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 185 of file ssbevd.f. 📌

Author

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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Later, bestie! 💜 This iconic page is from LAPACK, Version 3.12.0, and the page file is SRC/ssbevd.f(3). Slay. 🌈👑