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---
:name: zgtrfs
:md5sum: 8d4d4d8d907eb8ca2c144546d27fcda8
:category: :subroutine
:arguments:
- trans:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- dl:
:type: doublecomplex
:intent: input
:dims:
- n-1
- d:
:type: doublecomplex
:intent: input
:dims:
- n
- du:
:type: doublecomplex
:intent: input
:dims:
- n-1
- dlf:
:type: doublecomplex
:intent: input
:dims:
- n-1
- df:
:type: doublecomplex
:intent: input
:dims:
- n
- duf:
:type: doublecomplex
:intent: input
:dims:
- n-1
- du2:
:type: doublecomplex
:intent: input
:dims:
- n-2
- ipiv:
:type: integer
:intent: input
:dims:
- n
- b:
:type: doublecomplex
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: doublecomplex
:intent: input/output
:dims:
- ldx
- nrhs
- ldx:
:type: integer
:intent: input
- ferr:
:type: doublereal
:intent: output
:dims:
- nrhs
- berr:
:type: doublereal
:intent: output
:dims:
- nrhs
- work:
:type: doublecomplex
:intent: workspace
:dims:
- 2*n
- rwork:
:type: doublereal
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGTRFS improves the computed solution to a system of linear\n\
* equations when the coefficient matrix is tridiagonal, 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\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrix B. NRHS >= 0.\n\
*\n\
* DL (input) COMPLEX*16 array, dimension (N-1)\n\
* The (n-1) subdiagonal elements of A.\n\
*\n\
* D (input) COMPLEX*16 array, dimension (N)\n\
* The diagonal elements of A.\n\
*\n\
* DU (input) COMPLEX*16 array, dimension (N-1)\n\
* The (n-1) superdiagonal elements of A.\n\
*\n\
* DLF (input) COMPLEX*16 array, dimension (N-1)\n\
* The (n-1) multipliers that define the matrix L from the\n\
* LU factorization of A as computed by ZGTTRF.\n\
*\n\
* DF (input) COMPLEX*16 array, dimension (N)\n\
* The n diagonal elements of the upper triangular matrix U from\n\
* the LU factorization of A.\n\
*\n\
* DUF (input) COMPLEX*16 array, dimension (N-1)\n\
* The (n-1) elements of the first superdiagonal of U.\n\
*\n\
* DU2 (input) COMPLEX*16 array, dimension (N-2)\n\
* The (n-2) elements of the second superdiagonal of U.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N)\n\
* The pivot indices; for 1 <= i <= n, row i of the matrix was\n\
* interchanged with row IPIV(i). IPIV(i) will always be either\n\
* i or i+1; IPIV(i) = i indicates a row interchange was not\n\
* required.\n\
*\n\
* B (input) COMPLEX*16 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*16 array, dimension (LDX,NRHS)\n\
* On entry, the solution matrix X, as computed by ZGTTRS.\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) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N)\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION 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"
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