1 SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
2 $ SWORK, ITER, INFO )
3 *
4 * -- LAPACK PROTOTYPE driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * ..
10 * .. Scalar Arguments ..
11 INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
12 * ..
13 * .. Array Arguments ..
14 INTEGER IPIV( * )
15 REAL SWORK( * )
16 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ),
17 $ X( LDX, * )
18 * ..
19 *
20 * Purpose
21 * =======
22 *
23 * DSGESV computes the solution to a real system of linear equations
24 * A * X = B,
25 * where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
26 *
27 * DSGESV first attempts to factorize the matrix in SINGLE PRECISION
28 * and use this factorization within an iterative refinement procedure
29 * to produce a solution with DOUBLE PRECISION normwise backward error
30 * quality (see below). If the approach fails the method switches to a
31 * DOUBLE PRECISION factorization and solve.
32 *
33 * The iterative refinement is not going to be a winning strategy if
34 * the ratio SINGLE PRECISION performance over DOUBLE PRECISION
35 * performance is too small. A reasonable strategy should take the
36 * number of right-hand sides and the size of the matrix into account.
37 * This might be done with a call to ILAENV in the future. Up to now, we
38 * always try iterative refinement.
39 *
40 * The iterative refinement process is stopped if
41 * ITER > ITERMAX
42 * or for all the RHS we have:
43 * RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
44 * where
45 * o ITER is the number of the current iteration in the iterative
46 * refinement process
47 * o RNRM is the infinity-norm of the residual
48 * o XNRM is the infinity-norm of the solution
49 * o ANRM is the infinity-operator-norm of the matrix A
50 * o EPS is the machine epsilon returned by DLAMCH('Epsilon')
51 * The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
52 * respectively.
53 *
54 * Arguments
55 * =========
56 *
57 * N (input) INTEGER
58 * The number of linear equations, i.e., the order of the
59 * matrix A. N >= 0.
60 *
61 * NRHS (input) INTEGER
62 * The number of right hand sides, i.e., the number of columns
63 * of the matrix B. NRHS >= 0.
64 *
65 * A (input/output) DOUBLE PRECISION array,
66 * dimension (LDA,N)
67 * On entry, the N-by-N coefficient matrix A.
68 * On exit, if iterative refinement has been successfully used
69 * (INFO.EQ.0 and ITER.GE.0, see description below), then A is
70 * unchanged, if double precision factorization has been used
71 * (INFO.EQ.0 and ITER.LT.0, see description below), then the
72 * array A contains the factors L and U from the factorization
73 * A = P*L*U; the unit diagonal elements of L are not stored.
74 *
75 * LDA (input) INTEGER
76 * The leading dimension of the array A. LDA >= max(1,N).
77 *
78 * IPIV (output) INTEGER array, dimension (N)
79 * The pivot indices that define the permutation matrix P;
80 * row i of the matrix was interchanged with row IPIV(i).
81 * Corresponds either to the single precision factorization
82 * (if INFO.EQ.0 and ITER.GE.0) or the double precision
83 * factorization (if INFO.EQ.0 and ITER.LT.0).
84 *
85 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
86 * The N-by-NRHS right hand side matrix B.
87 *
88 * LDB (input) INTEGER
89 * The leading dimension of the array B. LDB >= max(1,N).
90 *
91 * X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
92 * If INFO = 0, the N-by-NRHS solution matrix X.
93 *
94 * LDX (input) INTEGER
95 * The leading dimension of the array X. LDX >= max(1,N).
96 *
97 * WORK (workspace) DOUBLE PRECISION array, dimension (N,NRHS)
98 * This array is used to hold the residual vectors.
99 *
100 * SWORK (workspace) REAL array, dimension (N*(N+NRHS))
101 * This array is used to use the single precision matrix and the
102 * right-hand sides or solutions in single precision.
103 *
104 * ITER (output) INTEGER
105 * < 0: iterative refinement has failed, double precision
106 * factorization has been performed
107 * -1 : the routine fell back to full precision for
108 * implementation- or machine-specific reasons
109 * -2 : narrowing the precision induced an overflow,
110 * the routine fell back to full precision
111 * -3 : failure of SGETRF
112 * -31: stop the iterative refinement after the 30th
113 * iterations
114 * > 0: iterative refinement has been sucessfully used.
115 * Returns the number of iterations
116 *
117 * INFO (output) INTEGER
118 * = 0: successful exit
119 * < 0: if INFO = -i, the i-th argument had an illegal value
120 * > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is
121 * exactly zero. The factorization has been completed,
122 * but the factor U is exactly singular, so the solution
123 * could not be computed.
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128 LOGICAL DOITREF
129 PARAMETER ( DOITREF = .TRUE. )
130 *
131 INTEGER ITERMAX
132 PARAMETER ( ITERMAX = 30 )
133 *
134 DOUBLE PRECISION BWDMAX
135 PARAMETER ( BWDMAX = 1.0E+00 )
136 *
137 DOUBLE PRECISION NEGONE, ONE
138 PARAMETER ( NEGONE = -1.0D+0, ONE = 1.0D+0 )
139 *
140 * .. Local Scalars ..
141 INTEGER I, IITER, PTSA, PTSX
142 DOUBLE PRECISION ANRM, CTE, EPS, RNRM, XNRM
143 *
144 * .. External Subroutines ..
145 EXTERNAL DAXPY, DGEMM, DLACPY, DLAG2S, SLAG2D, SGETRF,
146 $ SGETRS, XERBLA
147 * ..
148 * .. External Functions ..
149 INTEGER IDAMAX
150 DOUBLE PRECISION DLAMCH, DLANGE
151 EXTERNAL IDAMAX, DLAMCH, DLANGE
152 * ..
153 * .. Intrinsic Functions ..
154 INTRINSIC ABS, DBLE, MAX, SQRT
155 * ..
156 * .. Executable Statements ..
157 *
158 INFO = 0
159 ITER = 0
160 *
161 * Test the input parameters.
162 *
163 IF( N.LT.0 ) THEN
164 INFO = -1
165 ELSE IF( NRHS.LT.0 ) THEN
166 INFO = -2
167 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
168 INFO = -4
169 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
170 INFO = -7
171 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
172 INFO = -9
173 END IF
174 IF( INFO.NE.0 ) THEN
175 CALL XERBLA( 'DSGESV', -INFO )
176 RETURN
177 END IF
178 *
179 * Quick return if (N.EQ.0).
180 *
181 IF( N.EQ.0 )
182 $ RETURN
183 *
184 * Skip single precision iterative refinement if a priori slower
185 * than double precision factorization.
186 *
187 IF( .NOT.DOITREF ) THEN
188 ITER = -1
189 GO TO 40
190 END IF
191 *
192 * Compute some constants.
193 *
194 ANRM = DLANGE( 'I', N, N, A, LDA, WORK )
195 EPS = DLAMCH( 'Epsilon' )
196 CTE = ANRM*EPS*SQRT( DBLE( N ) )*BWDMAX
197 *
198 * Set the indices PTSA, PTSX for referencing SA and SX in SWORK.
199 *
200 PTSA = 1
201 PTSX = PTSA + N*N
202 *
203 * Convert B from double precision to single precision and store the
204 * result in SX.
205 *
206 CALL DLAG2S( N, NRHS, B, LDB, SWORK( PTSX ), N, INFO )
207 *
208 IF( INFO.NE.0 ) THEN
209 ITER = -2
210 GO TO 40
211 END IF
212 *
213 * Convert A from double precision to single precision and store the
214 * result in SA.
215 *
216 CALL DLAG2S( N, N, A, LDA, SWORK( PTSA ), N, INFO )
217 *
218 IF( INFO.NE.0 ) THEN
219 ITER = -2
220 GO TO 40
221 END IF
222 *
223 * Compute the LU factorization of SA.
224 *
225 CALL SGETRF( N, N, SWORK( PTSA ), N, IPIV, INFO )
226 *
227 IF( INFO.NE.0 ) THEN
228 ITER = -3
229 GO TO 40
230 END IF
231 *
232 * Solve the system SA*SX = SB.
233 *
234 CALL SGETRS( 'No transpose', N, NRHS, SWORK( PTSA ), N, IPIV,
235 $ SWORK( PTSX ), N, INFO )
236 *
237 * Convert SX back to double precision
238 *
239 CALL SLAG2D( N, NRHS, SWORK( PTSX ), N, X, LDX, INFO )
240 *
241 * Compute R = B - AX (R is WORK).
242 *
243 CALL DLACPY( 'All', N, NRHS, B, LDB, WORK, N )
244 *
245 CALL DGEMM( 'No Transpose', 'No Transpose', N, NRHS, N, NEGONE, A,
246 $ LDA, X, LDX, ONE, WORK, N )
247 *
248 * Check whether the NRHS normwise backward errors satisfy the
249 * stopping criterion. If yes, set ITER=0 and return.
250 *
251 DO I = 1, NRHS
252 XNRM = ABS( X( IDAMAX( N, X( 1, I ), 1 ), I ) )
253 RNRM = ABS( WORK( IDAMAX( N, WORK( 1, I ), 1 ), I ) )
254 IF( RNRM.GT.XNRM*CTE )
255 $ GO TO 10
256 END DO
257 *
258 * If we are here, the NRHS normwise backward errors satisfy the
259 * stopping criterion. We are good to exit.
260 *
261 ITER = 0
262 RETURN
263 *
264 10 CONTINUE
265 *
266 DO 30 IITER = 1, ITERMAX
267 *
268 * Convert R (in WORK) from double precision to single precision
269 * and store the result in SX.
270 *
271 CALL DLAG2S( N, NRHS, WORK, N, SWORK( PTSX ), N, INFO )
272 *
273 IF( INFO.NE.0 ) THEN
274 ITER = -2
275 GO TO 40
276 END IF
277 *
278 * Solve the system SA*SX = SR.
279 *
280 CALL SGETRS( 'No transpose', N, NRHS, SWORK( PTSA ), N, IPIV,
281 $ SWORK( PTSX ), N, INFO )
282 *
283 * Convert SX back to double precision and update the current
284 * iterate.
285 *
286 CALL SLAG2D( N, NRHS, SWORK( PTSX ), N, WORK, N, INFO )
287 *
288 DO I = 1, NRHS
289 CALL DAXPY( N, ONE, WORK( 1, I ), 1, X( 1, I ), 1 )
290 END DO
291 *
292 * Compute R = B - AX (R is WORK).
293 *
294 CALL DLACPY( 'All', N, NRHS, B, LDB, WORK, N )
295 *
296 CALL DGEMM( 'No Transpose', 'No Transpose', N, NRHS, N, NEGONE,
297 $ A, LDA, X, LDX, ONE, WORK, N )
298 *
299 * Check whether the NRHS normwise backward errors satisfy the
300 * stopping criterion. If yes, set ITER=IITER>0 and return.
301 *
302 DO I = 1, NRHS
303 XNRM = ABS( X( IDAMAX( N, X( 1, I ), 1 ), I ) )
304 RNRM = ABS( WORK( IDAMAX( N, WORK( 1, I ), 1 ), I ) )
305 IF( RNRM.GT.XNRM*CTE )
306 $ GO TO 20
307 END DO
308 *
309 * If we are here, the NRHS normwise backward errors satisfy the
310 * stopping criterion, we are good to exit.
311 *
312 ITER = IITER
313 *
314 RETURN
315 *
316 20 CONTINUE
317 *
318 30 CONTINUE
319 *
320 * If we are at this place of the code, this is because we have
321 * performed ITER=ITERMAX iterations and never satisified the
322 * stopping criterion, set up the ITER flag accordingly and follow up
323 * on double precision routine.
324 *
325 ITER = -ITERMAX - 1
326 *
327 40 CONTINUE
328 *
329 * Single-precision iterative refinement failed to converge to a
330 * satisfactory solution, so we resort to double precision.
331 *
332 CALL DGETRF( N, N, A, LDA, IPIV, INFO )
333 *
334 IF( INFO.NE.0 )
335 $ RETURN
336 *
337 CALL DLACPY( 'All', N, NRHS, B, LDB, X, LDX )
338 CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, X, LDX,
339 $ INFO )
340 *
341 RETURN
342 *
343 * End of DSGESV.
344 *
345 END
2 $ SWORK, ITER, INFO )
3 *
4 * -- LAPACK PROTOTYPE driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * ..
10 * .. Scalar Arguments ..
11 INTEGER INFO, ITER, LDA, LDB, LDX, N, NRHS
12 * ..
13 * .. Array Arguments ..
14 INTEGER IPIV( * )
15 REAL SWORK( * )
16 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( N, * ),
17 $ X( LDX, * )
18 * ..
19 *
20 * Purpose
21 * =======
22 *
23 * DSGESV computes the solution to a real system of linear equations
24 * A * X = B,
25 * where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
26 *
27 * DSGESV first attempts to factorize the matrix in SINGLE PRECISION
28 * and use this factorization within an iterative refinement procedure
29 * to produce a solution with DOUBLE PRECISION normwise backward error
30 * quality (see below). If the approach fails the method switches to a
31 * DOUBLE PRECISION factorization and solve.
32 *
33 * The iterative refinement is not going to be a winning strategy if
34 * the ratio SINGLE PRECISION performance over DOUBLE PRECISION
35 * performance is too small. A reasonable strategy should take the
36 * number of right-hand sides and the size of the matrix into account.
37 * This might be done with a call to ILAENV in the future. Up to now, we
38 * always try iterative refinement.
39 *
40 * The iterative refinement process is stopped if
41 * ITER > ITERMAX
42 * or for all the RHS we have:
43 * RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
44 * where
45 * o ITER is the number of the current iteration in the iterative
46 * refinement process
47 * o RNRM is the infinity-norm of the residual
48 * o XNRM is the infinity-norm of the solution
49 * o ANRM is the infinity-operator-norm of the matrix A
50 * o EPS is the machine epsilon returned by DLAMCH('Epsilon')
51 * The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
52 * respectively.
53 *
54 * Arguments
55 * =========
56 *
57 * N (input) INTEGER
58 * The number of linear equations, i.e., the order of the
59 * matrix A. N >= 0.
60 *
61 * NRHS (input) INTEGER
62 * The number of right hand sides, i.e., the number of columns
63 * of the matrix B. NRHS >= 0.
64 *
65 * A (input/output) DOUBLE PRECISION array,
66 * dimension (LDA,N)
67 * On entry, the N-by-N coefficient matrix A.
68 * On exit, if iterative refinement has been successfully used
69 * (INFO.EQ.0 and ITER.GE.0, see description below), then A is
70 * unchanged, if double precision factorization has been used
71 * (INFO.EQ.0 and ITER.LT.0, see description below), then the
72 * array A contains the factors L and U from the factorization
73 * A = P*L*U; the unit diagonal elements of L are not stored.
74 *
75 * LDA (input) INTEGER
76 * The leading dimension of the array A. LDA >= max(1,N).
77 *
78 * IPIV (output) INTEGER array, dimension (N)
79 * The pivot indices that define the permutation matrix P;
80 * row i of the matrix was interchanged with row IPIV(i).
81 * Corresponds either to the single precision factorization
82 * (if INFO.EQ.0 and ITER.GE.0) or the double precision
83 * factorization (if INFO.EQ.0 and ITER.LT.0).
84 *
85 * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
86 * The N-by-NRHS right hand side matrix B.
87 *
88 * LDB (input) INTEGER
89 * The leading dimension of the array B. LDB >= max(1,N).
90 *
91 * X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)
92 * If INFO = 0, the N-by-NRHS solution matrix X.
93 *
94 * LDX (input) INTEGER
95 * The leading dimension of the array X. LDX >= max(1,N).
96 *
97 * WORK (workspace) DOUBLE PRECISION array, dimension (N,NRHS)
98 * This array is used to hold the residual vectors.
99 *
100 * SWORK (workspace) REAL array, dimension (N*(N+NRHS))
101 * This array is used to use the single precision matrix and the
102 * right-hand sides or solutions in single precision.
103 *
104 * ITER (output) INTEGER
105 * < 0: iterative refinement has failed, double precision
106 * factorization has been performed
107 * -1 : the routine fell back to full precision for
108 * implementation- or machine-specific reasons
109 * -2 : narrowing the precision induced an overflow,
110 * the routine fell back to full precision
111 * -3 : failure of SGETRF
112 * -31: stop the iterative refinement after the 30th
113 * iterations
114 * > 0: iterative refinement has been sucessfully used.
115 * Returns the number of iterations
116 *
117 * INFO (output) INTEGER
118 * = 0: successful exit
119 * < 0: if INFO = -i, the i-th argument had an illegal value
120 * > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is
121 * exactly zero. The factorization has been completed,
122 * but the factor U is exactly singular, so the solution
123 * could not be computed.
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128 LOGICAL DOITREF
129 PARAMETER ( DOITREF = .TRUE. )
130 *
131 INTEGER ITERMAX
132 PARAMETER ( ITERMAX = 30 )
133 *
134 DOUBLE PRECISION BWDMAX
135 PARAMETER ( BWDMAX = 1.0E+00 )
136 *
137 DOUBLE PRECISION NEGONE, ONE
138 PARAMETER ( NEGONE = -1.0D+0, ONE = 1.0D+0 )
139 *
140 * .. Local Scalars ..
141 INTEGER I, IITER, PTSA, PTSX
142 DOUBLE PRECISION ANRM, CTE, EPS, RNRM, XNRM
143 *
144 * .. External Subroutines ..
145 EXTERNAL DAXPY, DGEMM, DLACPY, DLAG2S, SLAG2D, SGETRF,
146 $ SGETRS, XERBLA
147 * ..
148 * .. External Functions ..
149 INTEGER IDAMAX
150 DOUBLE PRECISION DLAMCH, DLANGE
151 EXTERNAL IDAMAX, DLAMCH, DLANGE
152 * ..
153 * .. Intrinsic Functions ..
154 INTRINSIC ABS, DBLE, MAX, SQRT
155 * ..
156 * .. Executable Statements ..
157 *
158 INFO = 0
159 ITER = 0
160 *
161 * Test the input parameters.
162 *
163 IF( N.LT.0 ) THEN
164 INFO = -1
165 ELSE IF( NRHS.LT.0 ) THEN
166 INFO = -2
167 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
168 INFO = -4
169 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
170 INFO = -7
171 ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
172 INFO = -9
173 END IF
174 IF( INFO.NE.0 ) THEN
175 CALL XERBLA( 'DSGESV', -INFO )
176 RETURN
177 END IF
178 *
179 * Quick return if (N.EQ.0).
180 *
181 IF( N.EQ.0 )
182 $ RETURN
183 *
184 * Skip single precision iterative refinement if a priori slower
185 * than double precision factorization.
186 *
187 IF( .NOT.DOITREF ) THEN
188 ITER = -1
189 GO TO 40
190 END IF
191 *
192 * Compute some constants.
193 *
194 ANRM = DLANGE( 'I', N, N, A, LDA, WORK )
195 EPS = DLAMCH( 'Epsilon' )
196 CTE = ANRM*EPS*SQRT( DBLE( N ) )*BWDMAX
197 *
198 * Set the indices PTSA, PTSX for referencing SA and SX in SWORK.
199 *
200 PTSA = 1
201 PTSX = PTSA + N*N
202 *
203 * Convert B from double precision to single precision and store the
204 * result in SX.
205 *
206 CALL DLAG2S( N, NRHS, B, LDB, SWORK( PTSX ), N, INFO )
207 *
208 IF( INFO.NE.0 ) THEN
209 ITER = -2
210 GO TO 40
211 END IF
212 *
213 * Convert A from double precision to single precision and store the
214 * result in SA.
215 *
216 CALL DLAG2S( N, N, A, LDA, SWORK( PTSA ), N, INFO )
217 *
218 IF( INFO.NE.0 ) THEN
219 ITER = -2
220 GO TO 40
221 END IF
222 *
223 * Compute the LU factorization of SA.
224 *
225 CALL SGETRF( N, N, SWORK( PTSA ), N, IPIV, INFO )
226 *
227 IF( INFO.NE.0 ) THEN
228 ITER = -3
229 GO TO 40
230 END IF
231 *
232 * Solve the system SA*SX = SB.
233 *
234 CALL SGETRS( 'No transpose', N, NRHS, SWORK( PTSA ), N, IPIV,
235 $ SWORK( PTSX ), N, INFO )
236 *
237 * Convert SX back to double precision
238 *
239 CALL SLAG2D( N, NRHS, SWORK( PTSX ), N, X, LDX, INFO )
240 *
241 * Compute R = B - AX (R is WORK).
242 *
243 CALL DLACPY( 'All', N, NRHS, B, LDB, WORK, N )
244 *
245 CALL DGEMM( 'No Transpose', 'No Transpose', N, NRHS, N, NEGONE, A,
246 $ LDA, X, LDX, ONE, WORK, N )
247 *
248 * Check whether the NRHS normwise backward errors satisfy the
249 * stopping criterion. If yes, set ITER=0 and return.
250 *
251 DO I = 1, NRHS
252 XNRM = ABS( X( IDAMAX( N, X( 1, I ), 1 ), I ) )
253 RNRM = ABS( WORK( IDAMAX( N, WORK( 1, I ), 1 ), I ) )
254 IF( RNRM.GT.XNRM*CTE )
255 $ GO TO 10
256 END DO
257 *
258 * If we are here, the NRHS normwise backward errors satisfy the
259 * stopping criterion. We are good to exit.
260 *
261 ITER = 0
262 RETURN
263 *
264 10 CONTINUE
265 *
266 DO 30 IITER = 1, ITERMAX
267 *
268 * Convert R (in WORK) from double precision to single precision
269 * and store the result in SX.
270 *
271 CALL DLAG2S( N, NRHS, WORK, N, SWORK( PTSX ), N, INFO )
272 *
273 IF( INFO.NE.0 ) THEN
274 ITER = -2
275 GO TO 40
276 END IF
277 *
278 * Solve the system SA*SX = SR.
279 *
280 CALL SGETRS( 'No transpose', N, NRHS, SWORK( PTSA ), N, IPIV,
281 $ SWORK( PTSX ), N, INFO )
282 *
283 * Convert SX back to double precision and update the current
284 * iterate.
285 *
286 CALL SLAG2D( N, NRHS, SWORK( PTSX ), N, WORK, N, INFO )
287 *
288 DO I = 1, NRHS
289 CALL DAXPY( N, ONE, WORK( 1, I ), 1, X( 1, I ), 1 )
290 END DO
291 *
292 * Compute R = B - AX (R is WORK).
293 *
294 CALL DLACPY( 'All', N, NRHS, B, LDB, WORK, N )
295 *
296 CALL DGEMM( 'No Transpose', 'No Transpose', N, NRHS, N, NEGONE,
297 $ A, LDA, X, LDX, ONE, WORK, N )
298 *
299 * Check whether the NRHS normwise backward errors satisfy the
300 * stopping criterion. If yes, set ITER=IITER>0 and return.
301 *
302 DO I = 1, NRHS
303 XNRM = ABS( X( IDAMAX( N, X( 1, I ), 1 ), I ) )
304 RNRM = ABS( WORK( IDAMAX( N, WORK( 1, I ), 1 ), I ) )
305 IF( RNRM.GT.XNRM*CTE )
306 $ GO TO 20
307 END DO
308 *
309 * If we are here, the NRHS normwise backward errors satisfy the
310 * stopping criterion, we are good to exit.
311 *
312 ITER = IITER
313 *
314 RETURN
315 *
316 20 CONTINUE
317 *
318 30 CONTINUE
319 *
320 * If we are at this place of the code, this is because we have
321 * performed ITER=ITERMAX iterations and never satisified the
322 * stopping criterion, set up the ITER flag accordingly and follow up
323 * on double precision routine.
324 *
325 ITER = -ITERMAX - 1
326 *
327 40 CONTINUE
328 *
329 * Single-precision iterative refinement failed to converge to a
330 * satisfactory solution, so we resort to double precision.
331 *
332 CALL DGETRF( N, N, A, LDA, IPIV, INFO )
333 *
334 IF( INFO.NE.0 )
335 $ RETURN
336 *
337 CALL DLACPY( 'All', N, NRHS, B, LDB, X, LDX )
338 CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, X, LDX,
339 $ INFO )
340 *
341 RETURN
342 *
343 * End of DSGESV.
344 *
345 END