LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
zpbsv.f
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1 *> \brief <b> ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZPBSV( 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 * COMPLEX*16 AB( LDAB, * ), B( LDB, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZPBSV computes the solution to a complex system of linear equations
38 *> A * X = B,
39 *> where A is an N-by-N Hermitian 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**H * U, if UPLO = 'U', or
44 *> A = L * L**H, 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 COMPLEX*16 array, dimension (LDAB,N)
85 *> On entry, the upper or lower triangle of the Hermitian 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**H *U or A = L*L**H 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 COMPLEX*16 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 *> \date December 2016
136 *
137 *> \ingroup complex16OTHERsolve
138 *
139 *> \par Further Details:
140 * =====================
141 *>
142 *> \verbatim
143 *>
144 *> The band storage scheme is illustrated by the following example, when
145 *> N = 6, KD = 2, and UPLO = 'U':
146 *>
147 *> On entry: On exit:
148 *>
149 *> * * a13 a24 a35 a46 * * u13 u24 u35 u46
150 *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
151 *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
152 *>
153 *> Similarly, if UPLO = 'L' the format of A is as follows:
154 *>
155 *> On entry: On exit:
156 *>
157 *> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
158 *> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
159 *> a31 a42 a53 a64 * * l31 l42 l53 l64 * *
160 *>
161 *> Array elements marked * are not used by the routine.
162 *> \endverbatim
163 *>
164 * =====================================================================
165  SUBROUTINE zpbsv( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
166 *
167 * -- LAPACK driver routine (version 3.7.0) --
168 * -- LAPACK is a software package provided by Univ. of Tennessee, --
169 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
170 * December 2016
171 *
172 * .. Scalar Arguments ..
173  CHARACTER UPLO
174  INTEGER INFO, KD, LDAB, LDB, N, NRHS
175 * ..
176 * .. Array Arguments ..
177  COMPLEX*16 AB( LDAB, * ), B( LDB, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. External Functions ..
183  LOGICAL LSAME
184  EXTERNAL lsame
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL xerbla, zpbtrf, zpbtrs
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC max
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
198  info = -1
199  ELSE IF( n.LT.0 ) THEN
200  info = -2
201  ELSE IF( kd.LT.0 ) THEN
202  info = -3
203  ELSE IF( nrhs.LT.0 ) THEN
204  info = -4
205  ELSE IF( ldab.LT.kd+1 ) THEN
206  info = -6
207  ELSE IF( ldb.LT.max( 1, n ) ) THEN
208  info = -8
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'ZPBSV ', -info )
212  RETURN
213  END IF
214 *
215 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
216 *
217  CALL zpbtrf( uplo, n, kd, ab, ldab, info )
218  IF( info.EQ.0 ) THEN
219 *
220 * Solve the system A*X = B, overwriting B with X.
221 *
222  CALL zpbtrs( uplo, n, kd, nrhs, ab, ldab, b, ldb, info )
223 *
224  END IF
225  RETURN
226 *
227 * End of ZPBSV
228 *
229  END
zpbtrs
subroutine zpbtrs(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
ZPBTRS
Definition: zpbtrs.f:123
zpbtrf
subroutine zpbtrf(UPLO, N, KD, AB, LDAB, INFO)
ZPBTRF
Definition: zpbtrf.f:144
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zpbsv
subroutine zpbsv(UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
ZPBSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: zpbsv.f:166