SRC/ssbgv.f(3)

💅 SRC/ssbgv.f(3)

Library Functions Manual energy, bestie — this page is SRC/ssbgv.f(3), and it is giving LAPACK subroutine realness. ✨

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🌸 NAME

SRC/ssbgv.f

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✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine ssbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
           work, info)
           SSBGV

This is the main-character subroutine, no cap: SSBGV 💖

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🦋 Function/Subroutine Documentation

💫 subroutine ssbgv

subroutine ssbgv (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
    info)

SSBGV

🎯 Purpose

okay so bestie, SSBGV 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. That's the whole vibe. 💅

🫶 Lowkey important: this is the banded symmetric-definite generalized eigenproblem, not your average messy matrix situation.

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🎀 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. Not me warning you, the manpage is warning you. 💀

🧚 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(kb+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 that 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 >= N.

✨ WORK

WORK is REAL array, dimension (3*N)

🔥 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.

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👑 Author

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

Definition at line 175 of file ssbgv.f.

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💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Footer vibe check: LAPACK Version 3.12.0 on SRC/ssbgv.f(3). Stay banded, stay positive definite — B only, obvi — and slay those eigenvalues. 💅✨🎀