DSBGST(3)

💅 DSBGST(3) 💅

Manual name: Library Functions Manual. Okay so bestie, this is the DSBGST page, and it is a lot of matrix math, but we are gonna get through it together. 🫶

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🦋 NAME 🦋

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsbgst.f

Yes, that’s the whole name section. It’s giving “the file path is the main character.” 💀

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🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

subroutine DSBGST (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx,
    work, info)

DSBGST

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🌈 Function/Subroutine Documentation 🌈

subroutine DSBGST (character vect, 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( ldx, * ) x, integer ldx, double precision,
    dimension( * ) work, integer info)

DSBGST

🎀 Purpose 🎀

Okay so here’s the vibe: DSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, and it does it so that C has the same bandwidth as A. Slay. ✨

B must have been previously factorized as S**T*S by DPBSTF, using a split Cholesky factorization. That part is non-negotiable, bestie. 🫶

A is overwritten by C = X**T*A*X, where X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the bandwidth of A. The way that matrix gets transformed? Obsessed. 💅

🎀 Parameters 🎀

• VECT — CHARACTER*1, the “are we forming X or not” switch:
  • = 'N': do not form the transformation matrix X;
  • = 'V': form X.
• UPLO — CHARACTER*1, which triangle of A is stored:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The order of the matrices A and B. N >= 0.
• KA — INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.
• KB — INTEGER. The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0.
• AB — DOUBLE PRECISION array, dimension (LDAB,N). On entry, this is 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 transformed matrix X**T*A*X, stored in the same format as A. 💖

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KA+1.
• BB — DOUBLE PRECISION array, dimension (LDBB,N). The banded factor S from the split Cholesky factorization of B, as returned by DPBSTF, stored in the first KB+1 rows of the array.
• LDBB — INTEGER. The leading dimension of the array BB. LDBB >= KB+1.
• X — DOUBLE PRECISION array, dimension (LDX,N). If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
• WORK — DOUBLE PRECISION array, dimension (2*N).
• INFO — INTEGER, the little status icon:
  • = 0: successful exit;
  • < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

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

📌 Definition at line 📌

Definition at line 157 of file dsbgst.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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Mwah 💋 — LAPACK Version 3.12.0, source /home/abui...RC/dsbgst.f(3).