1DSPRFS(1) LAPACK routine (version 3.1) DSPRFS(1)
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6 DSPRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is symmetric indefinite and packed, and provides
8 error bounds and backward error estimates for the solution
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11 SUBROUTINE DSPRFS( 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 DOUBLE PRECISION AFP( * ), AP( * ), B( LDB, * ), BERR( * ),
21 FERR( * ), WORK( * ), X( LDX, * )
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24 DSPRFS 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.
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30 UPLO (input) CHARACTER*1
31 = 'U': Upper triangle of A is stored;
32 = 'L': Lower triangle of A is stored.
33 N (input) INTEGER
35 The order of the matrix A. N >= 0.
36 NRHS (input) INTEGER
38 The number of right hand sides, i.e., the number of columns of
39 the matrices B and X. NRHS >= 0.
40 AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
42 The upper or lower triangle of the symmetric matrix A, packed
43 columnwise in a linear array. The j-th column of A is stored
44 in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
45 A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
46 A(i,j) for j<=i<=n.
47 AFP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
49 The factored form of the matrix A. AFP contains the block
50 diagonal matrix D and the multipliers used to obtain the factor
51 U or L from the factorization A = U*D*U**T or A = L*D*L**T as
52 computed by DSPTRF, stored as a packed triangular matrix.
53 IPIV (input) INTEGER array, dimension (N)
55 Details of the interchanges and the block structure of D as
56 determined by DSPTRF.
57 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
59 The right hand side matrix B.
60 LDB (input) INTEGER
62 The leading dimension of the array B. LDB >= max(1,N).
63 X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
65 On entry, the solution matrix X, as computed by DSPTRS. On
66 exit, the improved solution matrix X.
67 LDX (input) INTEGER
69 The leading dimension of the array X. LDX >= max(1,N).
70 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
72 The estimated forward error bound for each solution vector X(j)
73 (the j-th column of the solution matrix X). If XTRUE is the
74 true solution corresponding to X(j), FERR(j) is an estimated
75 upper bound for the magnitude of the largest element in (X(j) -
76 XTRUE) divided by the magnitude of the largest element in X(j).
77 The estimate is as reliable as the estimate for RCOND, and is
78 almost always a slight overestimate of the true error.
79 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
81 The componentwise relative backward error of each solution vec‐
82 tor X(j) (i.e., the smallest relative change in any element of
83 A or B that makes X(j) an exact solution).
84 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
86 IWORK (workspace) INTEGER array, dimension (N)
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value
92
94 ITMAX is the maximum number of steps of iterative refinement.
95 LAPACK routine (version 3.1) November 2006 DSPRFS(1)