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---
:name: ctbrfs
:md5sum: 7c86c62620f2a6d4354d70f9e0b25b2c
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- trans:
:type: char
:intent: input
- diag:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ab:
:type: complex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- b:
:type: complex
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: complex
:intent: input
:dims:
- ldx
- nrhs
- ldx:
:type: integer
:intent: input
- ferr:
:type: real
:intent: output
:dims:
- nrhs
- berr:
:type: real
:intent: output
:dims:
- nrhs
- work:
:type: complex
:intent: workspace
:dims:
- 2*n
- rwork:
:type: real
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CTBRFS provides error bounds and backward error estimates for the\n\
* solution to a system of linear equations with a triangular band\n\
* coefficient matrix.\n\
*\n\
* The solution matrix X must be computed by CTBTRS or some other\n\
* means before entering this routine. CTBRFS does not do iterative\n\
* refinement because doing so cannot improve the backward error.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': A is upper triangular;\n\
* = 'L': A is lower triangular.\n\
*\n\
* TRANS (input) CHARACTER*1\n\
* Specifies the form of the system of equations:\n\
* = 'N': A * X = B (No transpose)\n\
* = 'T': A**T * X = B (Transpose)\n\
* = 'C': A**H * X = B (Conjugate transpose)\n\
*\n\
* DIAG (input) CHARACTER*1\n\
* = 'N': A is non-unit triangular;\n\
* = 'U': A is unit triangular.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals or subdiagonals of the\n\
* triangular band matrix A. KD >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrices B and X. NRHS >= 0.\n\
*\n\
* AB (input) COMPLEX array, dimension (LDAB,N)\n\
* The upper or lower triangular band matrix A, stored in the\n\
* first kd+1 rows of the array. The j-th column of A is stored\n\
* in the j-th column of the array AB as follows:\n\
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).\n\
* If DIAG = 'U', the diagonal elements of A are not referenced\n\
* and are assumed to be 1.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* B (input) COMPLEX array, dimension (LDB,NRHS)\n\
* The right hand side matrix B.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* X (input) COMPLEX array, dimension (LDX,NRHS)\n\
* The solution matrix X.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X. LDX >= max(1,N).\n\
*\n\
* FERR (output) REAL array, dimension (NRHS)\n\
* The estimated forward error bound for each solution vector\n\
* X(j) (the j-th column of the solution matrix X).\n\
* If XTRUE is the true solution corresponding to X(j), FERR(j)\n\
* is an estimated upper bound for the magnitude of the largest\n\
* element in (X(j) - XTRUE) divided by the magnitude of the\n\
* largest element in X(j). The estimate is as reliable as\n\
* the estimate for RCOND, and is almost always a slight\n\
* overestimate of the true error.\n\
*\n\
* BERR (output) REAL array, dimension (NRHS)\n\
* The componentwise relative backward error of each solution\n\
* vector X(j) (i.e., the smallest relative change in\n\
* any element of A or B that makes X(j) an exact solution).\n\
*\n\
* WORK (workspace) COMPLEX array, dimension (2*N)\n\
*\n\
* RWORK (workspace) REAL array, dimension (N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n"
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