SSBGST(3)

💖 SSBGST(3) 💖

okay bestie, welcome to the Library Functions Manual corner of the group chat — this one is all about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssbgst.f and the subroutine SSBGST. The header path is /home/abui...RC/ssbgst.f(3) (yes, the truncated one, slay). No cap, this is real LAPACK business, and we are gonna walk through every single parameter like it's a fit check. 💅

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssbgst.f — that's the file, bestie. This page is literally named after it, and SSBGST is the subroutine inside doing the main character work. ✨

🧩 SYNOPSIS 🧩

Functions/Subroutines

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

📚 Function/Subroutine Documentation 📚

subroutine SSBGST (character vect, character uplo, integer n, integer ka,
    integer kb, real, dimension( ldab, * ) ab, integer ldab, real,
    dimension( ldbb, * ) bb, integer ldbb, real, dimension( ldx, * ) x,
    integer ldx, real, dimension( * ) work, integer info)
    SSBGST

SSBGST — yes, the name again, because it's iconic.

🎯 Purpose 🎯

SSBGST reduces a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A.

B must have been previously factorized as S**T*S by SPBSTF, using a split Cholesky factorization. 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.

lowkey this is giving "don't come for me unless B was already split-Cholesky-factorized by SPBSTF" energy. Respect the prep work. 🫶

🎀 Parameters 🎀

• VECT — VECT is CHARACTER*1
  • = 'N': do not form the transformation matrix X;
  • = 'V': form X.
• 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 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'. KA >= 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 transformed matrix X**T*A*X, stored in the same format as A.
• LDAB — LDAB is INTEGER
  • The leading dimension of the array AB. LDAB >= KA+1.
• BB — BB is REAL array, dimension (LDBB,N)
  • The banded factor S from the split Cholesky factorization of B, as returned by SPBSTF, stored in the first KB+1 rows of the array.
• LDBB — LDBB is INTEGER
  • The leading dimension of the array BB. LDBB >= KB+1.
• X — X is REAL array, dimension (LDX,N)
  • If VECT = 'V', the n-by-n matrix X.
  • If VECT = 'N', the array X is not referenced.
• LDX — LDX is INTEGER
  • The leading dimension of the array X.
  • LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
• WORK — WORK is REAL array, dimension (2*N)
• INFO — INFO is INTEGER
  • = 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 157 of file ssbgst.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💜 okay that's the whole page, bestie — final sign-off vibes: LAPACK, Version 3.12.0, footer path /home/abui...RC/ssbgst.f(3) — mwah, you ate this manual page, periodt. 💜