LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dpbtrs.f
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1*> \brief \b DPBTRS
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DPBTRS + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrs.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpbtrs.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpbtrs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DPBTRS( 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*> DPBTRS solves a system of linear equations A*X = B with a symmetric
38*> positive definite band matrix A using the Cholesky factorization
39*> A = U**T*U or A = L*L**T computed by DPBTRF.
40*> \endverbatim
41*
42* Arguments:
43* ==========
44*
45*> \param[in] UPLO
46*> \verbatim
47*> UPLO is CHARACTER*1
48*> = 'U': Upper triangular factor stored in AB;
49*> = 'L': Lower triangular factor stored in AB.
50*> \endverbatim
51*>
52*> \param[in] N
53*> \verbatim
54*> N is INTEGER
55*> The order of the matrix A. N >= 0.
56*> \endverbatim
57*>
58*> \param[in] KD
59*> \verbatim
60*> KD is INTEGER
61*> The number of superdiagonals of the matrix A if UPLO = 'U',
62*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
63*> \endverbatim
64*>
65*> \param[in] NRHS
66*> \verbatim
67*> NRHS is INTEGER
68*> The number of right hand sides, i.e., the number of columns
69*> of the matrix B. NRHS >= 0.
70*> \endverbatim
71*>
72*> \param[in] AB
73*> \verbatim
74*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
75*> The triangular factor U or L from the Cholesky factorization
76*> A = U**T*U or A = L*L**T of the band matrix A, stored in the
77*> first KD+1 rows of the array. The j-th column of U or L is
78*> stored in the j-th column of the array AB as follows:
79*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
80*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
81*> \endverbatim
82*>
83*> \param[in] LDAB
84*> \verbatim
85*> LDAB is INTEGER
86*> The leading dimension of the array AB. LDAB >= KD+1.
87*> \endverbatim
88*>
89*> \param[in,out] B
90*> \verbatim
91*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
92*> On entry, the right hand side matrix B.
93*> On exit, the solution matrix X.
94*> \endverbatim
95*>
96*> \param[in] LDB
97*> \verbatim
98*> LDB is INTEGER
99*> The leading dimension of the array B. LDB >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] INFO
103*> \verbatim
104*> INFO is INTEGER
105*> = 0: successful exit
106*> < 0: if INFO = -i, the i-th argument had an illegal value
107*> \endverbatim
108*
109* Authors:
110* ========
111*
112*> \author Univ. of Tennessee
113*> \author Univ. of California Berkeley
114*> \author Univ. of Colorado Denver
115*> \author NAG Ltd.
116*
117*> \ingroup doubleOTHERcomputational
118*
119* =====================================================================
120 SUBROUTINE dpbtrs( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
121*
122* -- LAPACK computational routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 CHARACTER UPLO
128 INTEGER INFO, KD, LDAB, LDB, N, NRHS
129* ..
130* .. Array Arguments ..
131 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
132* ..
133*
134* =====================================================================
135*
136* .. Local Scalars ..
137 LOGICAL UPPER
138 INTEGER J
139* ..
140* .. External Functions ..
141 LOGICAL LSAME
142 EXTERNAL lsame
143* ..
144* .. External Subroutines ..
145 EXTERNAL dtbsv, xerbla
146* ..
147* .. Intrinsic Functions ..
148 INTRINSIC max
149* ..
150* .. Executable Statements ..
151*
152* Test the input parameters.
153*
154 info = 0
155 upper = lsame( uplo, 'U' )
156 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157 info = -1
158 ELSE IF( n.LT.0 ) THEN
159 info = -2
160 ELSE IF( kd.LT.0 ) THEN
161 info = -3
162 ELSE IF( nrhs.LT.0 ) THEN
163 info = -4
164 ELSE IF( ldab.LT.kd+1 ) THEN
165 info = -6
166 ELSE IF( ldb.LT.max( 1, n ) ) THEN
167 info = -8
168 END IF
169 IF( info.NE.0 ) THEN
170 CALL xerbla( 'DPBTRS', -info )
171 RETURN
172 END IF
173*
174* Quick return if possible
175*
176 IF( n.EQ.0 .OR. nrhs.EQ.0 )
177 $ RETURN
178*
179 IF( upper ) THEN
180*
181* Solve A*X = B where A = U**T *U.
182*
183 DO 10 j = 1, nrhs
184*
185* Solve U**T *X = B, overwriting B with X.
186*
187 CALL dtbsv( 'Upper', 'Transpose', 'Non-unit', n, kd, ab,
188 $ ldab, b( 1, j ), 1 )
189*
190* Solve U*X = B, overwriting B with X.
191*
192 CALL dtbsv( 'Upper', 'No transpose', 'Non-unit', n, kd, ab,
193 $ ldab, b( 1, j ), 1 )
194 10 CONTINUE
195 ELSE
196*
197* Solve A*X = B where A = L*L**T.
198*
199 DO 20 j = 1, nrhs
200*
201* Solve L*X = B, overwriting B with X.
202*
203 CALL dtbsv( 'Lower', 'No transpose', 'Non-unit', n, kd, ab,
204 $ ldab, b( 1, j ), 1 )
205*
206* Solve L**T *X = B, overwriting B with X.
207*
208 CALL dtbsv( 'Lower', 'Transpose', 'Non-unit', n, kd, ab,
209 $ ldab, b( 1, j ), 1 )
210 20 CONTINUE
211 END IF
212*
213 RETURN
214*
215* End of DPBTRS
216*
217 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtbsv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBSV
Definition: dtbsv.f:189
subroutine dpbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
DPBTRS
Definition: dpbtrs.f:121