SRC/dsbevd.f(3)

💖 NAME 💖

Okay so bestie, this page is SRC/dsbevd.f — the manual entry for the dsbevd Fortran routine, and it is literally here to compute eigenvalues and eigenvectors for symmetric band matrices. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dsbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork,
    iwork, liwork, info)

DSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🫶

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🦋 Function/Subroutine Documentation 🦋

🌸 subroutine dsbevd

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

DSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🎀

🎯 Purpose:

DSBEVD 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. obsessed with the efficiency tbh. ✨

🌈 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🌈
• Z — Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dsbevd.f. 💜

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 🎀

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sign-off bestie: the footer says LAPACK Version 3.12.0 SRC/dsbevd.f(3) — source/version/file tag secured, and yes, that's the whole mood. 🫶✨💅