1: *> \brief <b> DPBSV computes the solution to system of linear equations A * X = B for OTHER 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 DPBSV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbsv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbsv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbsv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, KD, LDAB, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPBSV computes the solution to a real system of linear equations
38: *> A * X = B,
39: *> where A is an N-by-N symmetric positive definite band matrix and X
40: *> and B are N-by-NRHS matrices.
41: *>
42: *> The Cholesky decomposition is used to factor A as
43: *> A = U**T * U, if UPLO = 'U', or
44: *> A = L * L**T, if UPLO = 'L',
45: *> where U is an upper triangular band matrix, and L is a lower
46: *> triangular band matrix, with the same number of superdiagonals or
47: *> subdiagonals as A. The factored form of A is then used to solve the
48: *> system of equations A * X = B.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] UPLO
55: *> \verbatim
56: *> UPLO is CHARACTER*1
57: *> = 'U': Upper triangle of A is stored;
58: *> = 'L': Lower triangle of A is stored.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The number of linear equations, i.e., the order of the
65: *> matrix A. N >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] KD
69: *> \verbatim
70: *> KD is INTEGER
71: *> The number of superdiagonals of the matrix A if UPLO = 'U',
72: *> or the number of subdiagonals if UPLO = 'L'. KD >= 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,out] AB
83: *> \verbatim
84: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
85: *> On entry, the upper or lower triangle of the symmetric band
86: *> matrix A, stored in the first KD+1 rows of the array. The
87: *> j-th column of A is stored in the j-th column of the array AB
88: *> as follows:
89: *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
90: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
91: *> See below for further details.
92: *>
93: *> On exit, if INFO = 0, the triangular factor U or L from the
94: *> Cholesky factorization A = U**T*U or A = L*L**T of the band
95: *> matrix A, in the same storage format as A.
96: *> \endverbatim
97: *>
98: *> \param[in] LDAB
99: *> \verbatim
100: *> LDAB is INTEGER
101: *> The leading dimension of the array AB. LDAB >= KD+1.
102: *> \endverbatim
103: *>
104: *> \param[in,out] B
105: *> \verbatim
106: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
107: *> On entry, the N-by-NRHS right hand side matrix B.
108: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
109: *> \endverbatim
110: *>
111: *> \param[in] LDB
112: *> \verbatim
113: *> LDB is INTEGER
114: *> The leading dimension of the array B. LDB >= max(1,N).
115: *> \endverbatim
116: *>
117: *> \param[out] INFO
118: *> \verbatim
119: *> INFO is INTEGER
120: *> = 0: successful exit
121: *> < 0: if INFO = -i, the i-th argument had an illegal value
122: *> > 0: if INFO = i, the leading minor of order i of A is not
123: *> positive definite, so the factorization could not be
124: *> completed, and the solution has not been computed.
125: *> \endverbatim
126: *
127: * Authors:
128: * ========
129: *
130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
134: *
135: *> \ingroup doubleOTHERsolve
136: *
137: *> \par Further Details:
138: * =====================
139: *>
140: *> \verbatim
141: *>
142: *> The band storage scheme is illustrated by the following example, when
143: *> N = 6, KD = 2, and UPLO = 'U':
144: *>
145: *> On entry: On exit:
146: *>
147: *> * * a13 a24 a35 a46 * * u13 u24 u35 u46
148: *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
149: *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
150: *>
151: *> Similarly, if UPLO = 'L' the format of A is as follows:
152: *>
153: *> On entry: On exit:
154: *>
155: *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
156: *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
157: *> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
158: *>
159: *> Array elements marked * are not used by the routine.
160: *> \endverbatim
161: *>
162: * =====================================================================
163: SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
164: *
165: * -- LAPACK driver routine --
166: * -- LAPACK is a software package provided by Univ. of Tennessee, --
167: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168: *
169: * .. Scalar Arguments ..
170: CHARACTER UPLO
171: INTEGER INFO, KD, LDAB, LDB, N, NRHS
172: * ..
173: * .. Array Arguments ..
174: DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
175: * ..
176: *
177: * =====================================================================
178: *
179: * .. External Functions ..
180: LOGICAL LSAME
181: EXTERNAL LSAME
182: * ..
183: * .. External Subroutines ..
184: EXTERNAL DPBTRF, DPBTRS, XERBLA
185: * ..
186: * .. Intrinsic Functions ..
187: INTRINSIC MAX
188: * ..
189: * .. Executable Statements ..
190: *
191: * Test the input parameters.
192: *
193: INFO = 0
194: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
195: INFO = -1
196: ELSE IF( N.LT.0 ) THEN
197: INFO = -2
198: ELSE IF( KD.LT.0 ) THEN
199: INFO = -3
200: ELSE IF( NRHS.LT.0 ) THEN
201: INFO = -4
202: ELSE IF( LDAB.LT.KD+1 ) THEN
203: INFO = -6
204: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
205: INFO = -8
206: END IF
207: IF( INFO.NE.0 ) THEN
208: CALL XERBLA( 'DPBSV ', -INFO )
209: RETURN
210: END IF
211: *
212: * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
213: *
214: CALL DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
215: IF( INFO.EQ.0 ) THEN
216: *
217: * Solve the system A*X = B, overwriting B with X.
218: *
219: CALL DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
220: *
221: END IF
222: RETURN
223: *
224: * End of DPBSV
225: *
226: END
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