SRC/ssbgvd.f(3)

💅 SRC/ssbgvd.f(3) 💅

okay bestie, this is a page from the Library Functions Manual, and it's literally all about SSBGVD — banded generalized symmetric-definite eigenproblems, no cap 💖

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🌸 NAME 🌸

SRC/ssbgvd.f

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ssbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info) — SSBGVD

subroutine ssbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
    work, lwork, iwork, liwork, info)

SSBGVD

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🧚 Function/Subroutine Documentation 🧚

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

SSBGVD

🎯 Purpose 🎯

okay so SSBGVD 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
  • = '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 REAL 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).
  • On exit, the contents of AB are destroyed 💀
• LDAB — LDAB is INTEGER
  • The leading dimension of the array AB. LDAB >= KA+1.
• BB — BB is REAL 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 SPBSTF.
• LDBB — LDBB is INTEGER
  • The leading dimension of the array BB. LDBB >= KB+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 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 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 N <= 1, LWORK >= 1.
  • If JOBZ = 'N' and N > 1, LWORK >= 3*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 SPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

👑 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 ssbgvd.f. 📌

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie that's the whole page — LAPACK Version 3.12.0, source page SRC/ssbgvd.f(3), no date on this footer, just vibes and eigenvalues 💅✨ byeee, go slay those banded matrices 🫶🔥