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
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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
194