SPPRFS(3F) SPPRFS(3F)
SPPRFS  improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solution
SUBROUTINE SPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR,
WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( * ),
WORK( * ), X( LDX, * )
SPPRFS improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solution.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
AP (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The jth column of A is stored in
the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/2) =
A(i,j) for j<=i<=n.
AFP (input) REAL array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed
columnwise in a linear array in the same format as A (see AP).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
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SPPRFS(3F) SPPRFS(3F)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPPTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth column of the solution matrix X). If XTRUE is the true
solution corresponding to X(j), FERR(j) is an estimated upper
bound for the magnitude of the largest element in (X(j)  XTRUE)
divided by the magnitude of the largest element in X(j). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
SPPRFS(3F) SPPRFS(3F)
SPPRFS  improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solution
SUBROUTINE SPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR,
WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( * ),
WORK( * ), X( LDX, * )
SPPRFS improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite and packed,
and provides error bounds and backward error estimates for the solution.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
AP (input) REAL array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The jth column of A is stored in
the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/2) =
A(i,j) for j<=i<=n.
AFP (input) REAL array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed
columnwise in a linear array in the same format as A (see AP).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
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SPPRFS(3F) SPPRFS(3F)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPPTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth column of the solution matrix X). If XTRUE is the true
solution corresponding to X(j), FERR(j) is an estimated upper
bound for the magnitude of the largest element in (X(j)  XTRUE)
divided by the magnitude of the largest element in X(j). The
estimate is as reliable as the estimate for RCOND, and is almost
always a slight overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vector
X(j) (i.e., the smallest relative change in any element of A or B
that makes X(j) an exact solution).
WORK (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
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