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---
:name: csprfs
:md5sum: 3ec422cb25319a32a48c132c4cf128f4
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ap:
:type: complex
:intent: input
:dims:
- n*(n+1)/2
- afp:
:type: complex
:intent: input
:dims:
- n*(n+1)/2
- 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 CSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CSPRFS improves the computed solution to a system of linear\n\
* equations when the coefficient matrix is symmetric indefinite\n\
* and packed, and provides error bounds and backward error estimates\n\
* for the solution.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\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 matrices B and X. NRHS >= 0.\n\
*\n\
* AP (input) COMPLEX array, dimension (N*(N+1)/2)\n\
* The upper or lower triangle of the symmetric matrix A, packed\n\
* columnwise in a linear array. The j-th column of A is stored\n\
* in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n\
*\n\
* AFP (input) COMPLEX array, dimension (N*(N+1)/2)\n\
* The factored form of the matrix A. AFP contains the block\n\
* diagonal matrix D and the multipliers used to obtain the\n\
* factor U or L from the factorization A = U*D*U**T or\n\
* A = L*D*L**T as computed by CSPTRF, stored as a packed\n\
* triangular matrix.\n\
*\n\
* IPIV (input) INTEGER array, dimension (N)\n\
* Details of the interchanges and the block structure of D\n\
* as determined by CSPTRF.\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 CSPTRS.\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"
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