LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cspsv.f
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1 *> \brief <b> CSPSV 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/cspsv.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDB, N, NRHS
26 * ..
27 * .. Array Arguments ..
28 * INTEGER IPIV( * )
29 * COMPLEX AP( * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CSPSV computes the solution to a complex system of linear equations
39 *> A * X = B,
40 *> where A is an N-by-N symmetric matrix stored in packed format and X
41 *> and B are N-by-NRHS matrices.
42 *>
43 *> The diagonal pivoting method is used to factor A as
44 *> A = U * D * U**T, if UPLO = 'U', or
45 *> A = L * D * L**T, if UPLO = 'L',
46 *> where U (or L) is a product of permutation and unit upper (lower)
47 *> triangular matrices, D is symmetric and block diagonal with 1-by-1
48 *> and 2-by-2 diagonal blocks. The factored form of A is then used to
49 *> solve the system of equations A * X = B.
50 *> \endverbatim
51 *
52 * Arguments:
53 * ==========
54 *
55 *> \param[in] UPLO
56 *> \verbatim
57 *> UPLO is CHARACTER*1
58 *> = 'U': Upper triangle of A is stored;
59 *> = 'L': Lower triangle of A is stored.
60 *> \endverbatim
61 *>
62 *> \param[in] N
63 *> \verbatim
64 *> N is INTEGER
65 *> The number of linear equations, i.e., the order of the
66 *> matrix A. N >= 0.
67 *> \endverbatim
68 *>
69 *> \param[in] NRHS
70 *> \verbatim
71 *> NRHS is INTEGER
72 *> The number of right hand sides, i.e., the number of columns
73 *> of the matrix B. NRHS >= 0.
74 *> \endverbatim
75 *>
76 *> \param[in,out] AP
77 *> \verbatim
78 *> AP is COMPLEX array, dimension (N*(N+1)/2)
79 *> On entry, the upper or lower triangle of the symmetric matrix
80 *> A, packed columnwise in a linear array. The j-th column of A
81 *> is stored in the array AP as follows:
82 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
83 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
84 *> See below for further details.
85 *>
86 *> On exit, the block diagonal matrix D and the multipliers used
87 *> to obtain the factor U or L from the factorization
88 *> A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as
89 *> a packed triangular matrix in the same storage format as A.
90 *> \endverbatim
91 *>
92 *> \param[out] IPIV
93 *> \verbatim
94 *> IPIV is INTEGER array, dimension (N)
95 *> Details of the interchanges and the block structure of D, as
96 *> determined by CSPTRF. If IPIV(k) > 0, then rows and columns
97 *> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
98 *> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
99 *> then rows and columns k-1 and -IPIV(k) were interchanged and
100 *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
101 *> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
102 *> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
103 *> diagonal block.
104 *> \endverbatim
105 *>
106 *> \param[in,out] B
107 *> \verbatim
108 *> B is COMPLEX array, dimension (LDB,NRHS)
109 *> On entry, the N-by-NRHS right hand side matrix B.
110 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
111 *> \endverbatim
112 *>
113 *> \param[in] LDB
114 *> \verbatim
115 *> LDB is INTEGER
116 *> The leading dimension of the array B. LDB >= max(1,N).
117 *> \endverbatim
118 *>
119 *> \param[out] INFO
120 *> \verbatim
121 *> INFO is INTEGER
122 *> = 0: successful exit
123 *> < 0: if INFO = -i, the i-th argument had an illegal value
124 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
125 *> has been completed, but the block diagonal matrix D is
126 *> exactly singular, so the solution could not be
127 *> computed.
128 *> \endverbatim
129 *
130 * Authors:
131 * ========
132 *
133 *> \author Univ. of Tennessee
134 *> \author Univ. of California Berkeley
135 *> \author Univ. of Colorado Denver
136 *> \author NAG Ltd.
137 *
138 *> \ingroup complexOTHERsolve
139 *
140 *> \par Further Details:
141 * =====================
142 *>
143 *> \verbatim
144 *>
145 *> The packed storage scheme is illustrated by the following example
146 *> when N = 4, UPLO = 'U':
147 *>
148 *> Two-dimensional storage of the symmetric matrix A:
149 *>
150 *> a11 a12 a13 a14
151 *> a22 a23 a24
152 *> a33 a34 (aij = aji)
153 *> a44
154 *>
155 *> Packed storage of the upper triangle of A:
156 *>
157 *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
158 *> \endverbatim
159 *>
160 * =====================================================================
161  SUBROUTINE cspsv( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
162 *
163 * -- LAPACK driver routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER UPLO
169  INTEGER INFO, LDB, N, NRHS
170 * ..
171 * .. Array Arguments ..
172  INTEGER IPIV( * )
173  COMPLEX AP( * ), B( LDB, * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. External Functions ..
179  LOGICAL LSAME
180  EXTERNAL lsame
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL csptrf, csptrs, xerbla
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Test the input parameters.
191 *
192  info = 0
193  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194  info = -1
195  ELSE IF( n.LT.0 ) THEN
196  info = -2
197  ELSE IF( nrhs.LT.0 ) THEN
198  info = -3
199  ELSE IF( ldb.LT.max( 1, n ) ) THEN
200  info = -7
201  END IF
202  IF( info.NE.0 ) THEN
203  CALL xerbla( 'CSPSV ', -info )
204  RETURN
205  END IF
206 *
207 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
208 *
209  CALL csptrf( uplo, n, ap, ipiv, info )
210  IF( info.EQ.0 ) THEN
211 *
212 * Solve the system A*X = B, overwriting B with X.
213 *
214  CALL csptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
215 *
216  END IF
217  RETURN
218 *
219 * End of CSPSV
220 *
221  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine csptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CSPTRS
Definition: csptrs.f:115
subroutine csptrf(UPLO, N, AP, IPIV, INFO)
CSPTRF
Definition: csptrf.f:158
subroutine cspsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: cspsv.f:162