SRC/dsbgvd.f(3)

🌸 NAME 🌸

Bestie, you're looking at the manual page for SRC/dsbgvd.f — the header vibes are SRC/dsbgvd.f(3), and it's giving LAPACK routine energy. I'm obsessed.

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✨ SYNOPSIS ✨

🌀 Functions/Subroutines 🌀

   Functions/Subroutines
       subroutine dsbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
           work, lwork, iwork, liwork, info)
           DSBGVD

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🧚 Function/Subroutine Documentation 🧚

Here's the full signature, exactly as the source serves it, no cap:

   subroutine dsbgvd (character jobz, character uplo, integer n, integer ka,
       integer kb, double precision, dimension( ldab, * ) ab, integer ldab,
       double precision, dimension( ldbb, * ) bb, integer ldbb, double
       precision, dimension( * ) w, double precision, dimension( ldz, * ) z,
       integer ldz, double precision, dimension( * ) work, integer lwork,
       integer, dimension( * ) iwork, integer liwork, integer info)
       DSBGVD

🎯 Purpose 🎯

Okay so DSBGVD computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.

💖 Parameters 💖

• JOBZ — JOBZ is CHARACTER*1, bestie.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — UPLO is CHARACTER*1.
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — N is INTEGER. The order of the matrices A and B. N >= 0.
• KA — KA is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.
• KB — KB is INTEGER. The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
  • if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
  • Heads up: On exit, the contents of AB are destroyed. Yes, literally gone, bestie — protect your data accordingly. 💀
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KA+1.
• BB — BB is DOUBLE PRECISION array, dimension (LDBB, N).
  • On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows:
  • if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
  • if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
  • On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by DPBSTF.
• LDBB — LDBB is INTEGER. The leading dimension of the array BB. LDBB >= KB+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 matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so Z**T*B*Z = 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 (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 N <= 1, LWORK >= 1.
  • If JOBZ = 'N' and N > 1, LWORK >= 2*N.
  • If JOBZ = 'V' and N > 1, LWORK >= 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 LIWORK > 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — LIWORK is INTEGER. The dimension of the array IWORK.
  • If JOBZ = 'N' or N <= 1, LIWORK >= 1.
  • If JOBZ = 'V' and N > 1, LIWORK >= 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, and i is:
    • <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
    • > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

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🌟 Author 🌟

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

🫶 Contributors 🫶

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 219 of file dsbgvd.f.

🖋️ Author (the generated one) 🖋️

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off, because the footer line is doing the most: this page is LAPACK, Version 3.12.0, source SRC/dsbgvd.f(3). No date in the footer, so I'm not inventing one, periodt. 💖✨