SRC/ztbrfs.f(3)

okay bestie, welcome to SRC/ztbrfs.f(3) from the Library Functions Manual — this is the LAPACK tea, and it’s lowkey iconic ✨

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✨ NAME ✨

SRC/ztbrfs.f — that’s the name, and that’s literally the whole NAME section. no notes 💅

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🌈 SYNOPSIS 🌈

💖 Functions/Subroutines 💖

   Functions/Subroutines
       subroutine ztbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
           ldx, ferr, berr, work, rwork, info)
           ZTBRFS

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🦋 Function/Subroutine Documentation 🦋

   subroutine ztbrfs (character uplo, character trans, character diag, integer
       n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,
       integer ldab, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( ldx, * ) x, integer ldx, double precision,
       dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,
       dimension( * ) work, double precision, dimension( * ) rwork, integer
       info)
       ZTBRFS

🎀 Purpose 🎀

ZTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix.

🚨 bestie, important: the solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error.

🌸 Parameters 🌸

• UPLO — UPLO is CHARACTER*1. it tells us which triangle we’re dealing with:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — TRANS is CHARACTER*1. specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• DIAG — DIAG is CHARACTER*1:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER. the order of the matrix A. N >= 0.
• KD — KD is INTEGER. the number of superdiagonals or subdiagonals of the triangular band matrix A. 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 COMPLEX*16 array, dimension (LDAB,N). the upper or lower triangular 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).

if DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER. the leading dimension of the array AB. LDAB >= KD+1.
• B — B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS). the solution matrix X.
• LDX — LDX is INTEGER. the leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is DOUBLE PRECISION 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.
• BERR — BERR is DOUBLE PRECISION 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 COMPLEX*16 array, dimension (2*N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• INFO — INFO is INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

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

Definition at line 186 of file ztbrfs.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie — source/version: LAPACK Version 3.12.0, and the page is SRC/ztbrfs.f(3). slay and stay triangular 💅✨