1: *> \brief <b> ZGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver)
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGBSV + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbsv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbsv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZGBSV computes the solution to a complex system of linear equations
38: *> A * X = B, where A is a band matrix of order N with KL subdiagonals
39: *> and KU superdiagonals, and X and B are N-by-NRHS matrices.
40: *>
41: *> The LU decomposition with partial pivoting and row interchanges is
42: *> used to factor A as A = L * U, where L is a product of permutation
43: *> and unit lower triangular matrices with KL subdiagonals, and U is
44: *> upper triangular with KL+KU superdiagonals. The factored form of A
45: *> is then used to solve the system of equations A * X = B.
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] N
52: *> \verbatim
53: *> N is INTEGER
54: *> The number of linear equations, i.e., the order of the
55: *> matrix A. N >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in] KL
59: *> \verbatim
60: *> KL is INTEGER
61: *> The number of subdiagonals within the band of A. KL >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] KU
65: *> \verbatim
66: *> KU is INTEGER
67: *> The number of superdiagonals within the band of A. KU >= 0.
68: *> \endverbatim
69: *>
70: *> \param[in] NRHS
71: *> \verbatim
72: *> NRHS is INTEGER
73: *> The number of right hand sides, i.e., the number of columns
74: *> of the matrix B. NRHS >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in,out] AB
78: *> \verbatim
79: *> AB is COMPLEX*16 array, dimension (LDAB,N)
80: *> On entry, the matrix A in band storage, in rows KL+1 to
81: *> 2*KL+KU+1; rows 1 to KL of the array need not be set.
82: *> The j-th column of A is stored in the j-th column of the
83: *> array AB as follows:
84: *> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
85: *> On exit, details of the factorization: U is stored as an
86: *> upper triangular band matrix with KL+KU superdiagonals in
87: *> rows 1 to KL+KU+1, and the multipliers used during the
88: *> factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
89: *> See below for further details.
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[out] IPIV
99: *> \verbatim
100: *> IPIV is INTEGER array, dimension (N)
101: *> The pivot indices that define the permutation matrix P;
102: *> row i of the matrix was 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 N-by-NRHS right hand side matrix B.
109: *> On exit, if INFO = 0, the N-by-NRHS 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: *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization
124: *> has been completed, but the factor U is exactly
125: *> singular, and the solution has not been computed.
126: *> \endverbatim
127: *
128: * Authors:
129: * ========
130: *
131: *> \author Univ. of Tennessee
132: *> \author Univ. of California Berkeley
133: *> \author Univ. of Colorado Denver
134: *> \author NAG Ltd.
135: *
136: *> \date December 2016
137: *
138: *> \ingroup complex16GBsolve
139: *
140: *> \par Further Details:
141: * =====================
142: *>
143: *> \verbatim
144: *>
145: *> The band storage scheme is illustrated by the following example, when
146: *> M = N = 6, KL = 2, KU = 1:
147: *>
148: *> On entry: On exit:
149: *>
150: *> * * * + + + * * * u14 u25 u36
151: *> * * + + + + * * u13 u24 u35 u46
152: *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
153: *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
154: *> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
155: *> a31 a42 a53 a64 * * m31 m42 m53 m64 * *
156: *>
157: *> Array elements marked * are not used by the routine; elements marked
158: *> + need not be set on entry, but are required by the routine to store
159: *> elements of U because of fill-in resulting from the row interchanges.
160: *> \endverbatim
161: *>
162: * =====================================================================
163: SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
164: *
165: * -- LAPACK driver routine (version 3.7.0) --
166: * -- LAPACK is a software package provided by Univ. of Tennessee, --
167: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168: * December 2016
169: *
170: * .. Scalar Arguments ..
171: INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
172: * ..
173: * .. Array Arguments ..
174: INTEGER IPIV( * )
175: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
176: * ..
177: *
178: * =====================================================================
179: *
180: * .. External Subroutines ..
181: EXTERNAL XERBLA, ZGBTRF, ZGBTRS
182: * ..
183: * .. Intrinsic Functions ..
184: INTRINSIC MAX
185: * ..
186: * .. Executable Statements ..
187: *
188: * Test the input parameters.
189: *
190: INFO = 0
191: IF( N.LT.0 ) THEN
192: INFO = -1
193: ELSE IF( KL.LT.0 ) THEN
194: INFO = -2
195: ELSE IF( KU.LT.0 ) THEN
196: INFO = -3
197: ELSE IF( NRHS.LT.0 ) THEN
198: INFO = -4
199: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
200: INFO = -6
201: ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
202: INFO = -9
203: END IF
204: IF( INFO.NE.0 ) THEN
205: CALL XERBLA( 'ZGBSV ', -INFO )
206: RETURN
207: END IF
208: *
209: * Compute the LU factorization of the band matrix A.
210: *
211: CALL ZGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
212: IF( INFO.EQ.0 ) THEN
213: *
214: * Solve the system A*X = B, overwriting B with X.
215: *
216: CALL ZGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
217: $ B, LDB, INFO )
218: END IF
219: RETURN
220: *
221: * End of ZGBSV
222: *
223: END
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