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---
:name: cgbrfs
:md5sum: b26da869b9502286688e2b2960b3e223
:category: :subroutine
:arguments:
- trans:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kl:
:type: integer
:intent: input
- ku:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ab:
:type: complex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- afb:
:type: complex
:intent: input
:dims:
- ldafb
- n
- ldafb:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: input
:dims:
- n
- b:
:type: complex
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: complex
:intent: input/output
: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 CGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGBRFS improves the computed solution to a system of linear\n\
* equations when the coefficient matrix is banded, and provides\n\
* error bounds and backward error estimates for the solution.\n\
*\n\n\
* Arguments\n\
* =========\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\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KL (input) INTEGER\n\
* The number of subdiagonals within the band of A. KL >= 0.\n\
*\n\
* KU (input) INTEGER\n\
* The number of superdiagonals within the band of A. KU >= 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 original band matrix A, stored in rows 1 to KL+KU+1.\n\
* The j-th column of A is stored in the j-th column of the\n\
* array AB as follows:\n\
* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KL+KU+1.\n\
*\n\
* AFB (input) COMPLEX array, dimension (LDAFB,N)\n\
* Details of the LU factorization of the band matrix A, as\n\
* computed by CGBTRF. U is stored as an upper triangular band\n\
* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and\n\
* the multipliers used during the factorization are stored in\n\
* rows KL+KU+2 to 2*KL+KU+1.\n\
*\n\
* LDAFB (input) INTEGER\n\
* The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N)\n\
* The pivot indices from CGBTRF; for 1<=i<=N, row i of the\n\
* matrix was interchanged with row IPIV(i).\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/output) COMPLEX array, dimension (LDX,NRHS)\n\
* On entry, the solution matrix X, as computed by CGBTRS.\n\
* On exit, the improved 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\
* Internal Parameters\n\
* ===================\n\
*\n\
* ITMAX is the maximum number of steps of iterative refinement.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
