SPBTRS(3)

Bestie, welcome to SPBTRS(3) from the LAPACK Library Functions Manual 💅 This is the group chat where Fortran linear algebra gets explained, and the main character is a subroutine that solves banded symmetric positive definite systems. No cap.

💖 NAME 💖

This manual page is literally the source file path, bestie:

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

✨ SYNOPSIS ✨

Functions/Subroutines 🤝

Here's the call shape, character-for-character:

       subroutine SPBTRS (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
           SPBTRS

🎀 Function/Subroutine Documentation 🎀

subroutine SPBTRS 🦋

   subroutine SPBTRS (character uplo, integer n, integer kd, integer nrhs,
       real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * )
       b, integer ldb, integer info)
       SPBTRS

Purpose ✨

SPBTRS solves a system of linear equations A*X = B with a symmetric positive definite band matrix A, using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF. That's the whole point, and it's iconic.

Parameters 🧚

• UPLO — is CHARACTER*1.
  • = 'U': Upper triangular factor stored in AB;
  • = 'L': Lower triangular factor stored in AB.
• N — is INTEGER. The order of the matrix A. N >= 0.
• KD — is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• AB — is REAL array, dimension (LDAB,N). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:

if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

• LDAB — is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• B — is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X.
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• INFO — is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

💜 Author 💜

These absolute legends wrote it:

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

Definition at line 120 of file spbtrs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Signed with glitter and exact details: LAPACK Version 3.12.0, footer path /home/abui...RC/spbtrs.f(3) — that's the source/version energy from the page footer, bestie. We did it 💖✨🎀