LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
cppsv.f
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1 *> \brief <b> CPPSV 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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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDB, N, NRHS
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX AP( * ), B( LDB, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CPPSV 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 matrix stored in
40 *> packed format and X 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 matrix and L is a lower triangular
46 *> matrix. The factored form of A is then used to solve the system of
47 *> equations A * X = B.
48 *> \endverbatim
49 *
50 * Arguments:
51 * ==========
52 *
53 *> \param[in] UPLO
54 *> \verbatim
55 *> UPLO is CHARACTER*1
56 *> = 'U': Upper triangle of A is stored;
57 *> = 'L': Lower triangle of A is stored.
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The number of linear equations, i.e., the order of the
64 *> matrix A. N >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in] NRHS
68 *> \verbatim
69 *> NRHS is INTEGER
70 *> The number of right hand sides, i.e., the number of columns
71 *> of the matrix B. NRHS >= 0.
72 *> \endverbatim
73 *>
74 *> \param[in,out] AP
75 *> \verbatim
76 *> AP is COMPLEX array, dimension (N*(N+1)/2)
77 *> On entry, the upper or lower triangle of the Hermitian matrix
78 *> A, packed columnwise in a linear array. The j-th column of A
79 *> is stored in the array AP as follows:
80 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
81 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
82 *> See below for further details.
83 *>
84 *> On exit, if INFO = 0, the factor U or L from the Cholesky
85 *> factorization A = U**H*U or A = L*L**H, in the same storage
86 *> format as A.
87 *> \endverbatim
88 *>
89 *> \param[in,out] B
90 *> \verbatim
91 *> B is COMPLEX array, dimension (LDB,NRHS)
92 *> On entry, the N-by-NRHS right hand side matrix B.
93 *> On exit, if INFO = 0, the N-by-NRHS 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 *> > 0: if INFO = i, the leading minor of order i of A is not
108 *> positive definite, so the factorization could not be
109 *> completed, and the solution has not been computed.
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \ingroup complexOTHERsolve
121 *
122 *> \par Further Details:
123 * =====================
124 *>
125 *> \verbatim
126 *>
127 *> The packed storage scheme is illustrated by the following example
128 *> when N = 4, UPLO = 'U':
129 *>
130 *> Two-dimensional storage of the Hermitian matrix A:
131 *>
132 *> a11 a12 a13 a14
133 *> a22 a23 a24
134 *> a33 a34 (aij = conjg(aji))
135 *> a44
136 *>
137 *> Packed storage of the upper triangle of A:
138 *>
139 *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
140 *> \endverbatim
141 *>
142 * =====================================================================
143  SUBROUTINE cppsv( UPLO, N, NRHS, AP, B, LDB, INFO )
144 *
145 * -- LAPACK driver routine --
146 * -- LAPACK is a software package provided by Univ. of Tennessee, --
147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148 *
149 * .. Scalar Arguments ..
150  CHARACTER UPLO
151  INTEGER INFO, LDB, N, NRHS
152 * ..
153 * .. Array Arguments ..
154  COMPLEX AP( * ), B( LDB, * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL cpptrf, cpptrs, xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC max
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173  info = 0
174  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175  info = -1
176  ELSE IF( n.LT.0 ) THEN
177  info = -2
178  ELSE IF( nrhs.LT.0 ) THEN
179  info = -3
180  ELSE IF( ldb.LT.max( 1, n ) ) THEN
181  info = -6
182  END IF
183  IF( info.NE.0 ) THEN
184  CALL xerbla( 'CPPSV ', -info )
185  RETURN
186  END IF
187 *
188 * Compute the Cholesky factorization A = U**H *U or A = L*L**H.
189 *
190  CALL cpptrf( uplo, n, ap, info )
191  IF( info.EQ.0 ) THEN
192 *
193 * Solve the system A*X = B, overwriting B with X.
194 *
195  CALL cpptrs( uplo, n, nrhs, ap, b, ldb, info )
196 *
197  END IF
198  RETURN
199 *
200 * End of CPPSV
201 *
202  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cpptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
CPPTRS
Definition: cpptrs.f:108
subroutine cpptrf(UPLO, N, AP, INFO)
CPPTRF
Definition: cpptrf.f:119
subroutine cppsv(UPLO, N, NRHS, AP, B, LDB, INFO)
CPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
Definition: cppsv.f:144