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---
:name: sptrfs
:md5sum: 4ecbb01d7ec0c479ca08bee758afed59
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- n
- e:
:type: real
:intent: input
:dims:
- n-1
- df:
:type: real
:intent: input
:dims:
- n
- ef:
:type: real
:intent: input
:dims:
- n-1
- b:
:type: real
:intent: input
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: real
: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: real
:intent: workspace
:dims:
- 2*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SPTRFS improves the computed solution to a system of linear\n\
* equations when the coefficient matrix is symmetric positive definite\n\
* and tridiagonal, and provides error bounds and backward error\n\
* estimates for the solution.\n\
*\n\n\
* Arguments\n\
* =========\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\
* D (input) REAL array, dimension (N)\n\
* The n diagonal elements of the tridiagonal matrix A.\n\
*\n\
* E (input) REAL array, dimension (N-1)\n\
* The (n-1) subdiagonal elements of the tridiagonal matrix A.\n\
*\n\
* DF (input) REAL array, dimension (N)\n\
* The n diagonal elements of the diagonal matrix D from the\n\
* factorization computed by SPTTRF.\n\
*\n\
* EF (input) REAL array, dimension (N-1)\n\
* The (n-1) subdiagonal elements of the unit bidiagonal factor\n\
* L from the factorization computed by SPTTRF.\n\
*\n\
* B (input) REAL 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) REAL array, dimension (LDX,NRHS)\n\
* On entry, the solution matrix X, as computed by SPTTRS.\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 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).\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) REAL array, dimension (2*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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