SRC/dsbgst.f(3)

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version 3.12.1 · 4 versions
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💖 SRC/dsbgst.f 💖

okay so bestie, this is SRC/dsbgst.f from the LAPACK Library Functions Manual — the page for the DSBGST subroutine, and it is lowkey giving linear algebra main character energy. ✨

🎀 NAME 🎀

SRC/dsbgst.f — that’s the name, no cap. 🫶

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

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

🦋 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 🌸

DSBGST 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 DPBSTF, 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.

🎀 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 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).

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 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

LDBB is INTEGER

The leading dimension of the array BB. LDBB >= KB+1.

💜 X

X is 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

LDX is INTEGER

The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.

💜 WORK

WORK is DOUBLE PRECISION 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 dsbgst.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

kisses and bye bestie 💖 LAPACK Version 3.12.0, source SRC/dsbgst.f(3) ✨🎀

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