SRC/spbrfs.f(3)

🌸 NAME 🌸

okay bestie, welcome to SRC/spbrfs.f — this is the page from the Library Functions Manual for SRC/spbrfs.f(3), and it is lowkey iconic. It's giving LAPACK precision-accuracy energy, and we're gonna read it together. 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine spbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x,
    ldx, ferr, berr, work, iwork, info)
    SPBRFS

💖 Function/Subroutine Documentation 💖

subroutine spbrfs (character uplo, integer n, integer kd, integer nrhs,
    real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * )
    afb, integer ldafb, real, dimension( ldb, * ) b, integer ldb, real,
    dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,
    dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )
    iwork, integer info)
    SPBRFS

🎀 Purpose 🎀

So SPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution. That's the whole mission, bestie. ✨

🧚 Parameters 🧚

• 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 matrix A. N >= 0.
• KD — 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 — NRHS is INTEGER
  • The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AB — AB is REAL array, dimension (LDAB,N)
  • The upper or lower triangle of the symmetric band matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

• LDAB — LDAB is INTEGER
  • The leading dimension of the array AB. LDAB >= KD+1.
• AFB — AFB is REAL array, dimension (LDAFB,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 as computed by SPBTRF, in the same storage format as A (see AB).
• LDAFB — LDAFB is INTEGER
  • The leading dimension of the array AFB. LDAFB >= KD+1.
• B — B is REAL array, dimension (LDB,NRHS)
  • The right hand side matrix B.
• LDB — LDB is INTEGER
  • The leading dimension of the array B. LDB >= max(1,N).
• X — X is REAL array, dimension (LDX,NRHS)
  • On entry, the solution matrix X, as computed by SPBTRS.
  • On exit, the improved solution matrix X.
• LDX — LDX is INTEGER
  • The leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS)
  • The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error. ngl, that's a whole paragraph, but it ate. 💅
• BERR — BERR is REAL array, dimension (NRHS)
  • The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
• WORK — WORK is REAL array, dimension (3*N)
• IWORK — IWORK is INTEGER array, dimension (N)
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🧚 Internal Parameters 🧚

• ITMAX is the maximum number of steps of iterative refinement. periodt.

📜 Author 📜

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

📍 Definition at line 187 of file spbrfs.f. 📍

yup, that's the exact line, bestie — Definition at line 187 of file spbrfs.f.

📜 Author 📜

This page was generated automatically by Doxygen for LAPACK from the source code. slay. 🌈

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💖 That's the whole page, bestie — brought to you by LAPACK Version 3.12.0 and SRC/spbrfs.f(3), mwah 💖