LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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spbsv.f
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1*> \brief <b> SPBSV 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*
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spbsv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SPBSV( 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* REAL AB( LDAB, * ), B( LDB, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SPBSV 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 REAL 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 REAL 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 principal minor of order i
123*> of A is not positive, so the factorization could not
124*> be 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 pbsv
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 spbsv( 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 REAL AB( LDAB, * ), B( LDB, * )
175* ..
176*
177* =====================================================================
178*
179* .. External Functions ..
180 LOGICAL LSAME
181 EXTERNAL lsame
182* ..
183* .. External Subroutines ..
184 EXTERNAL spbtrf, spbtrs, 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( 'SPBSV ', -info )
209 RETURN
210 END IF
211*
212* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
213*
214 CALL spbtrf( 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 spbtrs( uplo, n, kd, nrhs, ab, ldab, b, ldb, info )
220*
221 END IF
222 RETURN
223*
224* End of SPBSV
225*
226 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine spbsv(uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition spbsv.f:164
subroutine spbtrf(uplo, n, kd, ab, ldab, info)
SPBTRF
Definition spbtrf.f:142
subroutine spbtrs(uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
SPBTRS
Definition spbtrs.f:121