LAPACK  3.7.0 LAPACK: Linear Algebra PACKage
zgbtrs.f
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1 *> \brief \b ZGBTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER TRANS
26 * INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
27 * ..
28 * .. Array Arguments ..
29 * INTEGER IPIV( * )
30 * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZGBTRS solves a system of linear equations
40 *> A * X = B, A**T * X = B, or A**H * X = B
41 *> with a general band matrix A using the LU factorization computed
42 *> by ZGBTRF.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] TRANS
49 *> \verbatim
50 *> TRANS is CHARACTER*1
51 *> Specifies the form of the system of equations.
52 *> = 'N': A * X = B (No transpose)
53 *> = 'T': A**T * X = B (Transpose)
54 *> = 'C': A**H * X = B (Conjugate transpose)
55 *> \endverbatim
56 *>
57 *> \param[in] N
58 *> \verbatim
59 *> N is INTEGER
60 *> The order of the matrix A. N >= 0.
61 *> \endverbatim
62 *>
63 *> \param[in] KL
64 *> \verbatim
65 *> KL is INTEGER
66 *> The number of subdiagonals within the band of A. KL >= 0.
67 *> \endverbatim
68 *>
69 *> \param[in] KU
70 *> \verbatim
71 *> KU is INTEGER
72 *> The number of superdiagonals within the band of A. KU >= 0.
73 *> \endverbatim
74 *>
75 *> \param[in] NRHS
76 *> \verbatim
77 *> NRHS is INTEGER
78 *> The number of right hand sides, i.e., the number of columns
79 *> of the matrix B. NRHS >= 0.
80 *> \endverbatim
81 *>
82 *> \param[in] AB
83 *> \verbatim
84 *> AB is COMPLEX*16 array, dimension (LDAB,N)
85 *> Details of the LU factorization of the band matrix A, as
86 *> computed by ZGBTRF. U is stored as an upper triangular band
87 *> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
88 *> the multipliers used during the factorization are stored in
89 *> rows KL+KU+2 to 2*KL+KU+1.
90 *> \endverbatim
91 *>
92 *> \param[in] LDAB
93 *> \verbatim
94 *> LDAB is INTEGER
95 *> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
96 *> \endverbatim
97 *>
98 *> \param[in] IPIV
99 *> \verbatim
100 *> IPIV is INTEGER array, dimension (N)
101 *> The pivot indices; for 1 <= i <= N, row i of the matrix was
102 *> interchanged with row IPIV(i).
103 *> \endverbatim
104 *>
105 *> \param[in,out] B
106 *> \verbatim
107 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
108 *> On entry, the right hand side matrix B.
109 *> On exit, the solution matrix X.
110 *> \endverbatim
111 *>
112 *> \param[in] LDB
113 *> \verbatim
114 *> LDB is INTEGER
115 *> The leading dimension of the array B. LDB >= max(1,N).
116 *> \endverbatim
117 *>
118 *> \param[out] INFO
119 *> \verbatim
120 *> INFO is INTEGER
121 *> = 0: successful exit
122 *> < 0: if INFO = -i, the i-th argument had an illegal value
123 *> \endverbatim
124 *
125 * Authors:
126 * ========
127 *
128 *> \author Univ. of Tennessee
129 *> \author Univ. of California Berkeley
130 *> \author Univ. of Colorado Denver
131 *> \author NAG Ltd.
132 *
133 *> \date December 2016
134 *
135 *> \ingroup complex16GBcomputational
136 *
137 * =====================================================================
138  SUBROUTINE zgbtrs( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
139  \$ info )
140 *
141 * -- LAPACK computational routine (version 3.7.0) --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 * December 2016
145 *
146 * .. Scalar Arguments ..
147  CHARACTER TRANS
148  INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
149 * ..
150 * .. Array Arguments ..
151  INTEGER IPIV( * )
152  COMPLEX*16 AB( ldab, * ), B( ldb, * )
153 * ..
154 *
155 * =====================================================================
156 *
157 * .. Parameters ..
158  COMPLEX*16 ONE
159  parameter ( one = ( 1.0d+0, 0.0d+0 ) )
160 * ..
161 * .. Local Scalars ..
162  LOGICAL LNOTI, NOTRAN
163  INTEGER I, J, KD, L, LM
164 * ..
165 * .. External Functions ..
166  LOGICAL LSAME
167  EXTERNAL lsame
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL xerbla, zgemv, zgeru, zlacgv, zswap, ztbsv
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC max, min
174 * ..
175 * .. Executable Statements ..
176 *
177 * Test the input parameters.
178 *
179  info = 0
180  notran = lsame( trans, 'N' )
181  IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) .AND. .NOT.
182  \$ lsame( trans, 'C' ) ) THEN
183  info = -1
184  ELSE IF( n.LT.0 ) THEN
185  info = -2
186  ELSE IF( kl.LT.0 ) THEN
187  info = -3
188  ELSE IF( ku.LT.0 ) THEN
189  info = -4
190  ELSE IF( nrhs.LT.0 ) THEN
191  info = -5
192  ELSE IF( ldab.LT.( 2*kl+ku+1 ) ) THEN
193  info = -7
194  ELSE IF( ldb.LT.max( 1, n ) ) THEN
195  info = -10
196  END IF
197  IF( info.NE.0 ) THEN
198  CALL xerbla( 'ZGBTRS', -info )
199  RETURN
200  END IF
201 *
202 * Quick return if possible
203 *
204  IF( n.EQ.0 .OR. nrhs.EQ.0 )
205  \$ RETURN
206 *
207  kd = ku + kl + 1
208  lnoti = kl.GT.0
209 *
210  IF( notran ) THEN
211 *
212 * Solve A*X = B.
213 *
214 * Solve L*X = B, overwriting B with X.
215 *
216 * L is represented as a product of permutations and unit lower
217 * triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
218 * where each transformation L(i) is a rank-one modification of
219 * the identity matrix.
220 *
221  IF( lnoti ) THEN
222  DO 10 j = 1, n - 1
223  lm = min( kl, n-j )
224  l = ipiv( j )
225  IF( l.NE.j )
226  \$ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
227  CALL zgeru( lm, nrhs, -one, ab( kd+1, j ), 1, b( j, 1 ),
228  \$ ldb, b( j+1, 1 ), ldb )
229  10 CONTINUE
230  END IF
231 *
232  DO 20 i = 1, nrhs
233 *
234 * Solve U*X = B, overwriting B with X.
235 *
236  CALL ztbsv( 'Upper', 'No transpose', 'Non-unit', n, kl+ku,
237  \$ ab, ldab, b( 1, i ), 1 )
238  20 CONTINUE
239 *
240  ELSE IF( lsame( trans, 'T' ) ) THEN
241 *
242 * Solve A**T * X = B.
243 *
244  DO 30 i = 1, nrhs
245 *
246 * Solve U**T * X = B, overwriting B with X.
247 *
248  CALL ztbsv( 'Upper', 'Transpose', 'Non-unit', n, kl+ku, ab,
249  \$ ldab, b( 1, i ), 1 )
250  30 CONTINUE
251 *
252 * Solve L**T * X = B, overwriting B with X.
253 *
254  IF( lnoti ) THEN
255  DO 40 j = n - 1, 1, -1
256  lm = min( kl, n-j )
257  CALL zgemv( 'Transpose', lm, nrhs, -one, b( j+1, 1 ),
258  \$ ldb, ab( kd+1, j ), 1, one, b( j, 1 ), ldb )
259  l = ipiv( j )
260  IF( l.NE.j )
261  \$ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
262  40 CONTINUE
263  END IF
264 *
265  ELSE
266 *
267 * Solve A**H * X = B.
268 *
269  DO 50 i = 1, nrhs
270 *
271 * Solve U**H * X = B, overwriting B with X.
272 *
273  CALL ztbsv( 'Upper', 'Conjugate transpose', 'Non-unit', n,
274  \$ kl+ku, ab, ldab, b( 1, i ), 1 )
275  50 CONTINUE
276 *
277 * Solve L**H * X = B, overwriting B with X.
278 *
279  IF( lnoti ) THEN
280  DO 60 j = n - 1, 1, -1
281  lm = min( kl, n-j )
282  CALL zlacgv( nrhs, b( j, 1 ), ldb )
283  CALL zgemv( 'Conjugate transpose', lm, nrhs, -one,
284  \$ b( j+1, 1 ), ldb, ab( kd+1, j ), 1, one,
285  \$ b( j, 1 ), ldb )
286  CALL zlacgv( nrhs, b( j, 1 ), ldb )
287  l = ipiv( j )
288  IF( l.NE.j )
289  \$ CALL zswap( nrhs, b( l, 1 ), ldb, b( j, 1 ), ldb )
290  60 CONTINUE
291  END IF
292  END IF
293  RETURN
294 *
295 * End of ZGBTRS
296 *
297  END
subroutine zgbtrs(TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
ZGBTRS
Definition: zgbtrs.f:140
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:52
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ztbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBSV
Definition: ztbsv.f:191
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:132