1DSGESV(1) LAPACK PROTOTYPE driver routine (version 3.2) DSGESV(1)
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6 DSGESV - computes the solution to a real system of linear equations A
7 * X = B,
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10 SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
11 + SWORK, ITER, INFO )
13 INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
15 INTEGER IPIV( * )
17 REAL SWORK( * )
19 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ),
21 + X( LDX, * )
23
25 DSGESV computes the solution to a real system of linear equations
26 A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS
27 matrices. DSGESV first attempts to factorize the matrix in SINGLE PRE‐
28 CISION and use this factorization within an iterative refinement proce‐
29 dure to produce a solution with DOUBLE PRECISION normwise backward
30 error quality (see below). If the approach fails the method switches to
31 a DOUBLE PRECISION factorization and solve.
32 The iterative refinement is not going to be a winning strategy if the
33 ratio SINGLE PRECISION performance over DOUBLE PRECISION performance is
34 too small. A reasonable strategy should take the number of right-hand
35 sides and the size of the matrix into account. This might be done with
36 a call to ILAENV in the future. Up to now, we always try iterative
37 refinement.
38 The iterative refinement process is stopped if
39 ITER > ITERMAX
40 or for all the RHS we have:
41 RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
42 where
43 o ITER is the number of the current iteration in the iterative
44 refinement process
45 o RNRM is the infinity-norm of the residual
46 o XNRM is the infinity-norm of the solution
47 o ANRM is the infinity-operator-norm of the matrix A
48 o EPS is the machine epsilon returned by DLAMCH('Epsilon') The
49 value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
50 respectively.
51
53 N (input) INTEGER
54 The number of linear equations, i.e., the order of the matrix
55 A. N >= 0.
56 NRHS (input) INTEGER
58 The number of right hand sides, i.e., the number of columns of
59 the matrix B. NRHS >= 0.
60 A (input or input/ouptut) DOUBLE PRECISION array,
62 dimension (LDA,N) On entry, the N-by-N coefficient matrix A.
63 On exit, if iterative refinement has been successfully used
64 (INFO.EQ.0 and ITER.GE.0, see description below), then A is
65 unchanged, if double precision factorization has been used
66 (INFO.EQ.0 and ITER.LT.0, see description below), then the
67 array A contains the factors L and U from the factorization A =
68 P*L*U; the unit diagonal elements of L are not stored.
69 LDA (input) INTEGER
71 The leading dimension of the array A. LDA >= max(1,N).
72 IPIV (output) INTEGER array, dimension (N)
74 The pivot indices that define the permutation matrix P; row i
75 of the matrix was interchanged with row IPIV(i). Corresponds
76 either to the single precision factorization (if INFO.EQ.0 and
77 ITER.GE.0) or the double precision factorization (if INFO.EQ.0
78 and ITER.LT.0).
79 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
81 The N-by-NRHS right hand side matrix B.
82 LDB (input) INTEGER
84 The leading dimension of the array B. LDB >= max(1,N).
85 X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
87 If INFO = 0, the N-by-NRHS solution matrix X.
88 LDX (input) INTEGER
90 The leading dimension of the array X. LDX >= max(1,N).
91 WORK (workspace) DOUBLE PRECISION array, dimension (N*NRHS)
93 This array is used to hold the residual vectors.
94 SWORK (workspace) REAL array, dimension (N*(N+NRHS))
96 This array is used to use the single precision matrix and the
97 right-hand sides or solutions in single precision.
98 ITER (output) INTEGER
100 < 0: iterative refinement has failed, double precision factor‐
101 ization has been performed -1 : the routine fell back to full
102 precision for implementation- or machine-specific reasons -2 :
103 narrowing the precision induced an overflow, the routine fell
104 back to full precision -3 : failure of SGETRF
105 -31: stop the iterative refinement after the 30th iterations >
106 0: iterative refinement has been sucessfully used. Returns the
107 number of iterations
108 INFO (output) INTEGER
110 = 0: successful exit
111 < 0: if INFO = -i, the i-th argument had an illegal value
112 > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is
113 exactly zero. The factorization has been completed, but the
114 factor U is exactly singular, so the solution could not be com‐
115 puted. =========
116 LAPACK PROTOTYPE driver routine (Nvoevresmiboenr 32.020)8 DSGESV(1)