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sposv.f
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1 *> \brief <b> SPOSV computes the solution to system of linear equations A * X = B for PO matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SPOSV + dependencies
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sposv.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, LDB, N, NRHS
26 * ..
27 * .. Array Arguments ..
28 * REAL A( LDA, * ), B( LDB, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SPOSV 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 matrix and X and B
40 *> 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 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] A
75 *> \verbatim
76 *> A is REAL array, dimension (LDA,N)
77 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
78 *> N-by-N upper triangular part of A contains the upper
79 *> triangular part of the matrix A, and the strictly lower
80 *> triangular part of A is not referenced. If UPLO = 'L', the
81 *> leading N-by-N lower triangular part of A contains the lower
82 *> triangular part of the matrix A, and the strictly upper
83 *> triangular part of A is not referenced.
84 *>
85 *> On exit, if INFO = 0, the factor U or L from the Cholesky
86 *> factorization A = U**T*U or A = L*L**T.
87 *> \endverbatim
88 *>
89 *> \param[in] LDA
90 *> \verbatim
91 *> LDA is INTEGER
92 *> The leading dimension of the array A. LDA >= max(1,N).
93 *> \endverbatim
94 *>
95 *> \param[in,out] B
96 *> \verbatim
97 *> B is REAL array, dimension (LDB,NRHS)
98 *> On entry, the N-by-NRHS right hand side matrix B.
99 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
100 *> \endverbatim
101 *>
102 *> \param[in] LDB
103 *> \verbatim
104 *> LDB is INTEGER
105 *> The leading dimension of the array B. LDB >= max(1,N).
106 *> \endverbatim
107 *>
108 *> \param[out] INFO
109 *> \verbatim
110 *> INFO is INTEGER
111 *> = 0: successful exit
112 *> < 0: if INFO = -i, the i-th argument had an illegal value
113 *> > 0: if INFO = i, the leading minor of order i of A is not
114 *> positive definite, so the factorization could not be
115 *> completed, and the solution has not been computed.
116 *> \endverbatim
117 *
118 * Authors:
119 * ========
120 *
121 *> \author Univ. of Tennessee
122 *> \author Univ. of California Berkeley
123 *> \author Univ. of Colorado Denver
124 *> \author NAG Ltd.
125 *
126 *> \date November 2011
127 *
128 *> \ingroup realPOsolve
129 *
130 * =====================================================================
131  SUBROUTINE sposv( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
132 *
133 * -- LAPACK driver routine (version 3.4.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * November 2011
137 *
138 * .. Scalar Arguments ..
139  CHARACTER uplo
140  INTEGER info, lda, ldb, n, nrhs
141 * ..
142 * .. Array Arguments ..
143  REAL a( lda, * ), b( ldb, * )
144 * ..
145 *
146 * =====================================================================
147 *
148 * .. External Functions ..
149  LOGICAL lsame
150  EXTERNAL lsame
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL spotrf, spotrs, xerbla
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC max
157 * ..
158 * .. Executable Statements ..
159 *
160 * Test the input parameters.
161 *
162  info = 0
163  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
164  info = -1
165  ELSE IF( n.LT.0 ) THEN
166  info = -2
167  ELSE IF( nrhs.LT.0 ) THEN
168  info = -3
169  ELSE IF( lda.LT.max( 1, n ) ) THEN
170  info = -5
171  ELSE IF( ldb.LT.max( 1, n ) ) THEN
172  info = -7
173  END IF
174  IF( info.NE.0 ) THEN
175  CALL xerbla( 'SPOSV ', -info )
176  RETURN
177  END IF
178 *
179 * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
180 *
181  CALL spotrf( uplo, n, a, lda, info )
182  IF( info.EQ.0 ) THEN
183 *
184 * Solve the system A*X = B, overwriting B with X.
185 *
186  CALL spotrs( uplo, n, nrhs, a, lda, b, ldb, info )
187 *
188  END IF
189  RETURN
190 *
191 * End of SPOSV
192 *
193  END