1DSPOSV(1) LAPACK PROTOTYPE driver routine (version 3.1.2) DSPOSV(1)
2
6 DSPOSV - computes the solution to a real system of linear equations A
7 * X = B,
8
10 SUBROUTINE DSPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK,
11 + SWORK, ITER, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
17 REAL SWORK( * )
19 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ),
21 + X( LDX, * )
23
25 DSPOSV computes the solution to a real system of linear equations
26 A * X = B, where A is an N-by-N symmetric positive definite matrix
27 and X and B are N-by-NRHS matrices.
28 DSPOSV first attempts to factorize the matrix in SINGLE PRECISION and
29 use this factorization within an iterative refinement procedure to pro‐
30 duce a solution with DOUBLE PRECISION normwise backward error quality
31 (see below). If the approach fails the method switches to a DOUBLE PRE‐
32 CISION factorization and solve.
33 The iterative refinement is not going to be a winning strategy if the
34 ratio SINGLE PRECISION performance over DOUBLE PRECISION performance is
35 too small. A reasonable strategy should take the number of right-hand
36 sides and the size of the matrix into account. This might be done with
37 a call to ILAENV in the future. Up to now, we always try iterative
38 refinement.
39 The iterative refinement process is stopped if
40 ITER > ITERMAX
41 or for all the RHS we have:
42 RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
43 where
44 o ITER is the number of the current iteration in the iterative
45 refinement process
46 o RNRM is the infinity-norm of the residual
47 o XNRM is the infinity-norm of the solution
48 o ANRM is the infinity-operator-norm of the matrix A
49 o EPS is the machine epsilon returned by DLAMCH('Epsilon') The
50 value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
51 respectively.
52
54 UPLO (input) CHARACTER
55 = 'U': Upper triangle of A is stored;
56 = 'L': Lower triangle of A is stored.
57 N (input) INTEGER
59 The number of linear equations, i.e., the order of the matrix
60 A. N >= 0.
61 NRHS (input) INTEGER
63 The number of right hand sides, i.e., the number of columns of
64 the matrix B. NRHS >= 0.
65 A (input or input/ouptut) DOUBLE PRECISION array,
67 dimension (LDA,N) On entry, the symmetric matrix A. If UPLO =
68 'U', the leading N-by-N upper triangular part of A contains the
69 upper triangular part of the matrix A, and the strictly lower
70 triangular part of A is not referenced. If UPLO = 'L', the
71 leading N-by-N lower triangular part of A contains the lower
72 triangular part of the matrix A, and the strictly upper trian‐
73 gular part of A is not referenced. On exit, if iterative
74 refinement has been successfully used (INFO.EQ.0 and ITER.GE.0,
75 see description below), then A is unchanged, if double preci‐
76 sion factorization has been used (INFO.EQ.0 and ITER.LT.0, see
77 description below), then the array A contains the factor U or L
78 from the Cholesky factorization A = U**T*U or A = L*L**T.
79 LDA (input) INTEGER
81 The leading dimension of the array A. LDA >= max(1,N).
82 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
84 The N-by-NRHS right hand side matrix B.
85 LDB (input) INTEGER
87 The leading dimension of the array B. LDB >= max(1,N).
88 X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
90 If INFO = 0, the N-by-NRHS solution matrix X.
91 LDX (input) INTEGER
93 The leading dimension of the array X. LDX >= max(1,N).
94 WORK (workspace) DOUBLE PRECISION array, dimension (N*NRHS)
96 This array is used to hold the residual vectors.
97 SWORK (workspace) REAL array, dimension (N*(N+NRHS))
99 This array is used to use the single precision matrix and the
100 right-hand sides or solutions in single precision.
101 ITER (output) INTEGER
103 < 0: iterative refinement has failed, double precision factor‐
104 ization has been performed -1 : the routine fell back to full
105 precision for implementation- or machine-specific reasons -2 :
106 narrowing the precision induced an overflow, the routine fell
107 back to full precision -3 : failure of SPOTRF
108 -31: stop the iterative refinement after the 30th iterations >
109 0: iterative refinement has been sucessfully used. Returns the
110 number of iterations
111 INFO (output) INTEGER
113 = 0: successful exit
114 < 0: if INFO = -i, the i-th argument had an illegal value
115 > 0: if INFO = i, the leading minor of order i of (DOUBLE PRE‐
116 CISION) A is not positive definite, so the factorization could
117 not be completed, and the solution has not been computed.
118 =========
119 LAPACK PROTOTYPE driver routine (Nvoevresmiboenr 32.010.82) DSPOSV(1)