1SSPRFS(1) LAPACK routine (version 3.2) SSPRFS(1)
2
6 SSPRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is symmetric indefinite and packed, and
8 provides error bounds and backward error estimates for the solution
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11 SUBROUTINE SSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR,
12 BERR, WORK, IWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 INTEGER IPIV( * ), IWORK( * )
19 REAL AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( *
21 ), WORK( * ), X( LDX, * )
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24 SSPRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is symmetric indefinite and packed, and
26 provides error bounds and backward error estimates for the solution.
27
29 UPLO (input) CHARACTER*1
30 = 'U': Upper triangle of A is stored;
31 = 'L': Lower triangle of A is stored.
32 N (input) INTEGER
34 The order of the matrix A. N >= 0.
35 NRHS (input) INTEGER
37 The number of right hand sides, i.e., the number of columns of
38 the matrices B and X. NRHS >= 0.
39 AP (input) REAL array, dimension (N*(N+1)/2)
41 The upper or lower triangle of the symmetric matrix A, packed
42 columnwise in a linear array. The j-th column of A is stored
43 in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
44 A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
45 A(i,j) for j<=i<=n.
46 AFP (input) REAL array, dimension (N*(N+1)/2)
48 The factored form of the matrix A. AFP contains the block
49 diagonal matrix D and the multipliers used to obtain the factor
50 U or L from the factorization A = U*D*U**T or A = L*D*L**T as
51 computed by SSPTRF, stored as a packed triangular matrix.
52 IPIV (input) INTEGER array, dimension (N)
54 Details of the interchanges and the block structure of D as
55 determined by SSPTRF.
56 B (input) REAL array, dimension (LDB,NRHS)
58 The right hand side matrix B.
59 LDB (input) INTEGER
61 The leading dimension of the array B. LDB >= max(1,N).
62 X (input/output) REAL array, dimension (LDX,NRHS)
64 On entry, the solution matrix X, as computed by SSPTRS. On
65 exit, the improved solution matrix X.
66 LDX (input) INTEGER
68 The leading dimension of the array X. LDX >= max(1,N).
69 FERR (output) REAL array, dimension (NRHS)
71 The estimated forward error bound for each solution vector X(j)
72 (the j-th column of the solution matrix X). If XTRUE is the
73 true solution corresponding to X(j), FERR(j) is an estimated
74 upper bound for the magnitude of the largest element in (X(j) -
75 XTRUE) divided by the magnitude of the largest element in X(j).
76 The estimate is as reliable as the estimate for RCOND, and is
77 almost always a slight overestimate of the true error.
78 BERR (output) REAL array, dimension (NRHS)
80 The componentwise relative backward error of each solution vec‐
81 tor X(j) (i.e., the smallest relative change in any element of
82 A or B that makes X(j) an exact solution).
83 WORK (workspace) REAL array, dimension (3*N)
85 IWORK (workspace) INTEGER array, dimension (N)
87 INFO (output) INTEGER
89 = 0: successful exit
90 < 0: if INFO = -i, the i-th argument had an illegal value
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93 ITMAX is the maximum number of steps of iterative refinement.
94 LAPACK routine (version 3.2) November 2008 SSPRFS(1)