LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dgbsvx.f
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1*> \brief <b> DGBSVX computes the solution to system of linear equations A * X = B for GB matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DGBSVX + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbsvx.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbsvx.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbsvx.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
22* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
23* RCOND, FERR, BERR, WORK, IWORK, INFO )
24*
25* .. Scalar Arguments ..
26* CHARACTER EQUED, FACT, TRANS
27* INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
28* DOUBLE PRECISION RCOND
29* ..
30* .. Array Arguments ..
31* INTEGER IPIV( * ), IWORK( * )
32* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
33* $ BERR( * ), C( * ), FERR( * ), R( * ),
34* $ WORK( * ), X( LDX, * )
35* ..
36*
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> DGBSVX uses the LU factorization to compute the solution to a real
44*> system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
45*> where A is a band matrix of order N with KL subdiagonals and KU
46*> superdiagonals, and X and B are N-by-NRHS matrices.
47*>
48*> Error bounds on the solution and a condition estimate are also
49*> provided.
50*> \endverbatim
51*
52*> \par Description:
53* =================
54*>
55*> \verbatim
56*>
57*> The following steps are performed by this subroutine:
58*>
59*> 1. If FACT = 'E', real scaling factors are computed to equilibrate
60*> the system:
61*> TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
62*> TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
63*> TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
64*> Whether or not the system will be equilibrated depends on the
65*> scaling of the matrix A, but if equilibration is used, A is
66*> overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
67*> or diag(C)*B (if TRANS = 'T' or 'C').
68*>
69*> 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
70*> matrix A (after equilibration if FACT = 'E') as
71*> A = L * U,
72*> where L is a product of permutation and unit lower triangular
73*> matrices with KL subdiagonals, and U is upper triangular with
74*> KL+KU superdiagonals.
75*>
76*> 3. If some U(i,i)=0, so that U is exactly singular, then the routine
77*> returns with INFO = i. Otherwise, the factored form of A is used
78*> to estimate the condition number of the matrix A. If the
79*> reciprocal of the condition number is less than machine precision,
80*> INFO = N+1 is returned as a warning, but the routine still goes on
81*> to solve for X and compute error bounds as described below.
82*>
83*> 4. The system of equations is solved for X using the factored form
84*> of A.
85*>
86*> 5. Iterative refinement is applied to improve the computed solution
87*> matrix and calculate error bounds and backward error estimates
88*> for it.
89*>
90*> 6. If equilibration was used, the matrix X is premultiplied by
91*> diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
92*> that it solves the original system before equilibration.
93*> \endverbatim
94*
95* Arguments:
96* ==========
97*
98*> \param[in] FACT
99*> \verbatim
100*> FACT is CHARACTER*1
101*> Specifies whether or not the factored form of the matrix A is
102*> supplied on entry, and if not, whether the matrix A should be
103*> equilibrated before it is factored.
104*> = 'F': On entry, AFB and IPIV contain the factored form of
105*> A. If EQUED is not 'N', the matrix A has been
106*> equilibrated with scaling factors given by R and C.
107*> AB, AFB, and IPIV are not modified.
108*> = 'N': The matrix A will be copied to AFB and factored.
109*> = 'E': The matrix A will be equilibrated if necessary, then
110*> copied to AFB and factored.
111*> \endverbatim
112*>
113*> \param[in] TRANS
114*> \verbatim
115*> TRANS is CHARACTER*1
116*> Specifies the form of the system of equations.
117*> = 'N': A * X = B (No transpose)
118*> = 'T': A**T * X = B (Transpose)
119*> = 'C': A**H * X = B (Transpose)
120*> \endverbatim
121*>
122*> \param[in] N
123*> \verbatim
124*> N is INTEGER
125*> The number of linear equations, i.e., the order of the
126*> matrix A. N >= 0.
127*> \endverbatim
128*>
129*> \param[in] KL
130*> \verbatim
131*> KL is INTEGER
132*> The number of subdiagonals within the band of A. KL >= 0.
133*> \endverbatim
134*>
135*> \param[in] KU
136*> \verbatim
137*> KU is INTEGER
138*> The number of superdiagonals within the band of A. KU >= 0.
139*> \endverbatim
140*>
141*> \param[in] NRHS
142*> \verbatim
143*> NRHS is INTEGER
144*> The number of right hand sides, i.e., the number of columns
145*> of the matrices B and X. NRHS >= 0.
146*> \endverbatim
147*>
148*> \param[in,out] AB
149*> \verbatim
150*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
151*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
152*> The j-th column of A is stored in the j-th column of the
153*> array AB as follows:
154*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
155*>
156*> If FACT = 'F' and EQUED is not 'N', then A must have been
157*> equilibrated by the scaling factors in R and/or C. AB is not
158*> modified if FACT = 'F' or 'N', or if FACT = 'E' and
159*> EQUED = 'N' on exit.
160*>
161*> On exit, if EQUED .ne. 'N', A is scaled as follows:
162*> EQUED = 'R': A := diag(R) * A
163*> EQUED = 'C': A := A * diag(C)
164*> EQUED = 'B': A := diag(R) * A * diag(C).
165*> \endverbatim
166*>
167*> \param[in] LDAB
168*> \verbatim
169*> LDAB is INTEGER
170*> The leading dimension of the array AB. LDAB >= KL+KU+1.
171*> \endverbatim
172*>
173*> \param[in,out] AFB
174*> \verbatim
175*> AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
176*> If FACT = 'F', then AFB is an input argument and on entry
177*> contains details of the LU factorization of the band matrix
178*> A, as computed by DGBTRF. U is stored as an upper triangular
179*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
180*> and the multipliers used during the factorization are stored
181*> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is
182*> the factored form of the equilibrated matrix A.
183*>
184*> If FACT = 'N', then AFB is an output argument and on exit
185*> returns details of the LU factorization of A.
186*>
187*> If FACT = 'E', then AFB is an output argument and on exit
188*> returns details of the LU factorization of the equilibrated
189*> matrix A (see the description of AB for the form of the
190*> equilibrated matrix).
191*> \endverbatim
192*>
193*> \param[in] LDAFB
194*> \verbatim
195*> LDAFB is INTEGER
196*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
197*> \endverbatim
198*>
199*> \param[in,out] IPIV
200*> \verbatim
201*> IPIV is INTEGER array, dimension (N)
202*> If FACT = 'F', then IPIV is an input argument and on entry
203*> contains the pivot indices from the factorization A = L*U
204*> as computed by DGBTRF; row i of the matrix was interchanged
205*> with row IPIV(i).
206*>
207*> If FACT = 'N', then IPIV is an output argument and on exit
208*> contains the pivot indices from the factorization A = L*U
209*> of the original matrix A.
210*>
211*> If FACT = 'E', then IPIV is an output argument and on exit
212*> contains the pivot indices from the factorization A = L*U
213*> of the equilibrated matrix A.
214*> \endverbatim
215*>
216*> \param[in,out] EQUED
217*> \verbatim
218*> EQUED is CHARACTER*1
219*> Specifies the form of equilibration that was done.
220*> = 'N': No equilibration (always true if FACT = 'N').
221*> = 'R': Row equilibration, i.e., A has been premultiplied by
222*> diag(R).
223*> = 'C': Column equilibration, i.e., A has been postmultiplied
224*> by diag(C).
225*> = 'B': Both row and column equilibration, i.e., A has been
226*> replaced by diag(R) * A * diag(C).
227*> EQUED is an input argument if FACT = 'F'; otherwise, it is an
228*> output argument.
229*> \endverbatim
230*>
231*> \param[in,out] R
232*> \verbatim
233*> R is DOUBLE PRECISION array, dimension (N)
234*> The row scale factors for A. If EQUED = 'R' or 'B', A is
235*> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
236*> is not accessed. R is an input argument if FACT = 'F';
237*> otherwise, R is an output argument. If FACT = 'F' and
238*> EQUED = 'R' or 'B', each element of R must be positive.
239*> \endverbatim
240*>
241*> \param[in,out] C
242*> \verbatim
243*> C is DOUBLE PRECISION array, dimension (N)
244*> The column scale factors for A. If EQUED = 'C' or 'B', A is
245*> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
246*> is not accessed. C is an input argument if FACT = 'F';
247*> otherwise, C is an output argument. If FACT = 'F' and
248*> EQUED = 'C' or 'B', each element of C must be positive.
249*> \endverbatim
250*>
251*> \param[in,out] B
252*> \verbatim
253*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
254*> On entry, the right hand side matrix B.
255*> On exit,
256*> if EQUED = 'N', B is not modified;
257*> if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by
258*> diag(R)*B;
259*> if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is
260*> overwritten by diag(C)*B.
261*> \endverbatim
262*>
263*> \param[in] LDB
264*> \verbatim
265*> LDB is INTEGER
266*> The leading dimension of the array B. LDB >= max(1,N).
267*> \endverbatim
268*>
269*> \param[out] X
270*> \verbatim
271*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
272*> If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X
273*> to the original system of equations. Note that A and B are
274*> modified on exit if EQUED .ne. 'N', and the solution to the
275*> equilibrated system is inv(diag(C))*X if TRANS = 'N' and
276*> EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'
277*> and EQUED = 'R' or 'B'.
278*> \endverbatim
279*>
280*> \param[in] LDX
281*> \verbatim
282*> LDX is INTEGER
283*> The leading dimension of the array X. LDX >= max(1,N).
284*> \endverbatim
285*>
286*> \param[out] RCOND
287*> \verbatim
288*> RCOND is DOUBLE PRECISION
289*> The estimate of the reciprocal condition number of the matrix
290*> A after equilibration (if done). If RCOND is less than the
291*> machine precision (in particular, if RCOND = 0), the matrix
292*> is singular to working precision. This condition is
293*> indicated by a return code of INFO > 0.
294*> \endverbatim
295*>
296*> \param[out] FERR
297*> \verbatim
298*> FERR is DOUBLE PRECISION array, dimension (NRHS)
299*> The estimated forward error bound for each solution vector
300*> X(j) (the j-th column of the solution matrix X).
301*> If XTRUE is the true solution corresponding to X(j), FERR(j)
302*> is an estimated upper bound for the magnitude of the largest
303*> element in (X(j) - XTRUE) divided by the magnitude of the
304*> largest element in X(j). The estimate is as reliable as
305*> the estimate for RCOND, and is almost always a slight
306*> overestimate of the true error.
307*> \endverbatim
308*>
309*> \param[out] BERR
310*> \verbatim
311*> BERR is DOUBLE PRECISION array, dimension (NRHS)
312*> The componentwise relative backward error of each solution
313*> vector X(j) (i.e., the smallest relative change in
314*> any element of A or B that makes X(j) an exact solution).
315*> \endverbatim
316*>
317*> \param[out] WORK
318*> \verbatim
319*> WORK is DOUBLE PRECISION array, dimension (3*N)
320*> On exit, WORK(1) contains the reciprocal pivot growth
321*> factor norm(A)/norm(U). The "max absolute element" norm is
322*> used. If WORK(1) is much less than 1, then the stability
323*> of the LU factorization of the (equilibrated) matrix A
324*> could be poor. This also means that the solution X, condition
325*> estimator RCOND, and forward error bound FERR could be
326*> unreliable. If factorization fails with 0<INFO<=N, then
327*> WORK(1) contains the reciprocal pivot growth factor for the
328*> leading INFO columns of A.
329*> \endverbatim
330*>
331*> \param[out] IWORK
332*> \verbatim
333*> IWORK is INTEGER array, dimension (N)
334*> \endverbatim
335*>
336*> \param[out] INFO
337*> \verbatim
338*> INFO is INTEGER
339*> = 0: successful exit
340*> < 0: if INFO = -i, the i-th argument had an illegal value
341*> > 0: if INFO = i, and i is
342*> <= N: U(i,i) is exactly zero. The factorization
343*> has been completed, but the factor U is exactly
344*> singular, so the solution and error bounds
345*> could not be computed. RCOND = 0 is returned.
346*> = N+1: U is nonsingular, but RCOND is less than machine
347*> precision, meaning that the matrix is singular
348*> to working precision. Nevertheless, the
349*> solution and error bounds are computed because
350*> there are a number of situations where the
351*> computed solution can be more accurate than the
352*> value of RCOND would suggest.
353*> \endverbatim
354*
355* Authors:
356* ========
357*
358*> \author Univ. of Tennessee
359*> \author Univ. of California Berkeley
360*> \author Univ. of Colorado Denver
361*> \author NAG Ltd.
362*
363*> \ingroup doubleGBsolve
364*
365* =====================================================================
366 SUBROUTINE dgbsvx( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB,
367 $ LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX,
368 $ RCOND, FERR, BERR, WORK, IWORK, INFO )
369*
370* -- LAPACK driver routine --
371* -- LAPACK is a software package provided by Univ. of Tennessee, --
372* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
373*
374* .. Scalar Arguments ..
375 CHARACTER EQUED, FACT, TRANS
376 INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
377 DOUBLE PRECISION RCOND
378* ..
379* .. Array Arguments ..
380 INTEGER IPIV( * ), IWORK( * )
381 DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
382 $ berr( * ), c( * ), ferr( * ), r( * ),
383 $ work( * ), x( ldx, * )
384* ..
385*
386* =====================================================================
387*
388* .. Parameters ..
389 DOUBLE PRECISION ZERO, ONE
390 PARAMETER ( ZERO = 0.0d+0, one = 1.0d+0 )
391* ..
392* .. Local Scalars ..
393 LOGICAL COLEQU, EQUIL, NOFACT, NOTRAN, ROWEQU
394 CHARACTER NORM
395 INTEGER I, INFEQU, J, J1, J2
396 DOUBLE PRECISION AMAX, ANORM, BIGNUM, COLCND, RCMAX, RCMIN,
397 $ rowcnd, rpvgrw, smlnum
398* ..
399* .. External Functions ..
400 LOGICAL LSAME
401 DOUBLE PRECISION DLAMCH, DLANGB, DLANTB
402 EXTERNAL lsame, dlamch, dlangb, dlantb
403* ..
404* .. External Subroutines ..
405 EXTERNAL dcopy, dgbcon, dgbequ, dgbrfs, dgbtrf, dgbtrs,
407* ..
408* .. Intrinsic Functions ..
409 INTRINSIC abs, max, min
410* ..
411* .. Executable Statements ..
412*
413 info = 0
414 nofact = lsame( fact, 'N' )
415 equil = lsame( fact, 'E' )
416 notran = lsame( trans, 'N' )
417 IF( nofact .OR. equil ) THEN
418 equed = 'N'
419 rowequ = .false.
420 colequ = .false.
421 ELSE
422 rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
423 colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
424 smlnum = dlamch( 'Safe minimum' )
425 bignum = one / smlnum
426 END IF
427*
428* Test the input parameters.
429*
430 IF( .NOT.nofact .AND. .NOT.equil .AND. .NOT.lsame( fact, 'F' ) )
431 $ THEN
432 info = -1
433 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
434 $ lsame( trans, 'C' ) ) THEN
435 info = -2
436 ELSE IF( n.LT.0 ) THEN
437 info = -3
438 ELSE IF( kl.LT.0 ) THEN
439 info = -4
440 ELSE IF( ku.LT.0 ) THEN
441 info = -5
442 ELSE IF( nrhs.LT.0 ) THEN
443 info = -6
444 ELSE IF( ldab.LT.kl+ku+1 ) THEN
445 info = -8
446 ELSE IF( ldafb.LT.2*kl+ku+1 ) THEN
447 info = -10
448 ELSE IF( lsame( fact, 'F' ) .AND. .NOT.
449 $ ( rowequ .OR. colequ .OR. lsame( equed, 'N' ) ) ) THEN
450 info = -12
451 ELSE
452 IF( rowequ ) THEN
453 rcmin = bignum
454 rcmax = zero
455 DO 10 j = 1, n
456 rcmin = min( rcmin, r( j ) )
457 rcmax = max( rcmax, r( j ) )
458 10 CONTINUE
459 IF( rcmin.LE.zero ) THEN
460 info = -13
461 ELSE IF( n.GT.0 ) THEN
462 rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
463 ELSE
464 rowcnd = one
465 END IF
466 END IF
467 IF( colequ .AND. info.EQ.0 ) THEN
468 rcmin = bignum
469 rcmax = zero
470 DO 20 j = 1, n
471 rcmin = min( rcmin, c( j ) )
472 rcmax = max( rcmax, c( j ) )
473 20 CONTINUE
474 IF( rcmin.LE.zero ) THEN
475 info = -14
476 ELSE IF( n.GT.0 ) THEN
477 colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
478 ELSE
479 colcnd = one
480 END IF
481 END IF
482 IF( info.EQ.0 ) THEN
483 IF( ldb.LT.max( 1, n ) ) THEN
484 info = -16
485 ELSE IF( ldx.LT.max( 1, n ) ) THEN
486 info = -18
487 END IF
488 END IF
489 END IF
490*
491 IF( info.NE.0 ) THEN
492 CALL xerbla( 'DGBSVX', -info )
493 RETURN
494 END IF
495*
496 IF( equil ) THEN
497*
498* Compute row and column scalings to equilibrate the matrix A.
499*
500 CALL dgbequ( n, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd,
501 $ amax, infequ )
502 IF( infequ.EQ.0 ) THEN
503*
504* Equilibrate the matrix.
505*
506 CALL dlaqgb( n, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd,
507 $ amax, equed )
508 rowequ = lsame( equed, 'R' ) .OR. lsame( equed, 'B' )
509 colequ = lsame( equed, 'C' ) .OR. lsame( equed, 'B' )
510 END IF
511 END IF
512*
513* Scale the right hand side.
514*
515 IF( notran ) THEN
516 IF( rowequ ) THEN
517 DO 40 j = 1, nrhs
518 DO 30 i = 1, n
519 b( i, j ) = r( i )*b( i, j )
520 30 CONTINUE
521 40 CONTINUE
522 END IF
523 ELSE IF( colequ ) THEN
524 DO 60 j = 1, nrhs
525 DO 50 i = 1, n
526 b( i, j ) = c( i )*b( i, j )
527 50 CONTINUE
528 60 CONTINUE
529 END IF
530*
531 IF( nofact .OR. equil ) THEN
532*
533* Compute the LU factorization of the band matrix A.
534*
535 DO 70 j = 1, n
536 j1 = max( j-ku, 1 )
537 j2 = min( j+kl, n )
538 CALL dcopy( j2-j1+1, ab( ku+1-j+j1, j ), 1,
539 $ afb( kl+ku+1-j+j1, j ), 1 )
540 70 CONTINUE
541*
542 CALL dgbtrf( n, n, kl, ku, afb, ldafb, ipiv, info )
543*
544* Return if INFO is non-zero.
545*
546 IF( info.GT.0 ) THEN
547*
548* Compute the reciprocal pivot growth factor of the
549* leading rank-deficient INFO columns of A.
550*
551 anorm = zero
552 DO 90 j = 1, info
553 DO 80 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
554 anorm = max( anorm, abs( ab( i, j ) ) )
555 80 CONTINUE
556 90 CONTINUE
557 rpvgrw = dlantb( 'M', 'U', 'N', info, min( info-1, kl+ku ),
558 $ afb( max( 1, kl+ku+2-info ), 1 ), ldafb,
559 $ work )
560 IF( rpvgrw.EQ.zero ) THEN
561 rpvgrw = one
562 ELSE
563 rpvgrw = anorm / rpvgrw
564 END IF
565 work( 1 ) = rpvgrw
566 rcond = zero
567 RETURN
568 END IF
569 END IF
570*
571* Compute the norm of the matrix A and the
572* reciprocal pivot growth factor RPVGRW.
573*
574 IF( notran ) THEN
575 norm = '1'
576 ELSE
577 norm = 'I'
578 END IF
579 anorm = dlangb( norm, n, kl, ku, ab, ldab, work )
580 rpvgrw = dlantb( 'M', 'U', 'N', n, kl+ku, afb, ldafb, work )
581 IF( rpvgrw.EQ.zero ) THEN
582 rpvgrw = one
583 ELSE
584 rpvgrw = dlangb( 'M', n, kl, ku, ab, ldab, work ) / rpvgrw
585 END IF
586*
587* Compute the reciprocal of the condition number of A.
588*
589 CALL dgbcon( norm, n, kl, ku, afb, ldafb, ipiv, anorm, rcond,
590 $ work, iwork, info )
591*
592* Compute the solution matrix X.
593*
594 CALL dlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
595 CALL dgbtrs( trans, n, kl, ku, nrhs, afb, ldafb, ipiv, x, ldx,
596 $ info )
597*
598* Use iterative refinement to improve the computed solution and
599* compute error bounds and backward error estimates for it.
600*
601 CALL dgbrfs( trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv,
602 $ b, ldb, x, ldx, ferr, berr, work, iwork, info )
603*
604* Transform the solution matrix X to a solution of the original
605* system.
606*
607 IF( notran ) THEN
608 IF( colequ ) THEN
609 DO 110 j = 1, nrhs
610 DO 100 i = 1, n
611 x( i, j ) = c( i )*x( i, j )
612 100 CONTINUE
613 110 CONTINUE
614 DO 120 j = 1, nrhs
615 ferr( j ) = ferr( j ) / colcnd
616 120 CONTINUE
617 END IF
618 ELSE IF( rowequ ) THEN
619 DO 140 j = 1, nrhs
620 DO 130 i = 1, n
621 x( i, j ) = r( i )*x( i, j )
622 130 CONTINUE
623 140 CONTINUE
624 DO 150 j = 1, nrhs
625 ferr( j ) = ferr( j ) / rowcnd
626 150 CONTINUE
627 END IF
628*
629* Set INFO = N+1 if the matrix is singular to working precision.
630*
631 IF( rcond.LT.dlamch( 'Epsilon' ) )
632 $ info = n + 1
633*
634 work( 1 ) = rpvgrw
635 RETURN
636*
637* End of DGBSVX
638*
639 END
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dlaqgb(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED)
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
Definition: dlaqgb.f:159
subroutine dgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
DGBTRS
Definition: dgbtrs.f:138
subroutine dgbtrf(M, N, KL, KU, AB, LDAB, IPIV, INFO)
DGBTRF
Definition: dgbtrf.f:144
subroutine dgbequ(M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
DGBEQU
Definition: dgbequ.f:153
subroutine dgbcon(NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
DGBCON
Definition: dgbcon.f:146
subroutine dgbrfs(TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DGBRFS
Definition: dgbrfs.f:205
subroutine dgbsvx(FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO)
DGBSVX computes the solution to system of linear equations A * X = B for GB matrices
Definition: dgbsvx.f:369