LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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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
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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 principal minor of order i
114*> of A is not positive, so the factorization could not
115*> be 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*> \ingroup posv
127*
128* =====================================================================
129 SUBROUTINE sposv( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
130*
131* -- LAPACK driver routine --
132* -- LAPACK is a software package provided by Univ. of Tennessee, --
133* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135* .. Scalar Arguments ..
136 CHARACTER UPLO
137 INTEGER INFO, LDA, LDB, N, NRHS
138* ..
139* .. Array Arguments ..
140 REAL A( LDA, * ), B( LDB, * )
141* ..
142*
143* =====================================================================
144*
145* .. External Functions ..
146 LOGICAL LSAME
147 EXTERNAL lsame
148* ..
149* .. External Subroutines ..
150 EXTERNAL spotrf, spotrs, xerbla
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC max
154* ..
155* .. Executable Statements ..
156*
157* Test the input parameters.
158*
159 info = 0
160 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
161 info = -1
162 ELSE IF( n.LT.0 ) THEN
163 info = -2
164 ELSE IF( nrhs.LT.0 ) THEN
165 info = -3
166 ELSE IF( lda.LT.max( 1, n ) ) THEN
167 info = -5
168 ELSE IF( ldb.LT.max( 1, n ) ) THEN
169 info = -7
170 END IF
171 IF( info.NE.0 ) THEN
172 CALL xerbla( 'SPOSV ', -info )
173 RETURN
174 END IF
175*
176* Compute the Cholesky factorization A = U**T*U or A = L*L**T.
177*
178 CALL spotrf( uplo, n, a, lda, info )
179 IF( info.EQ.0 ) THEN
180*
181* Solve the system A*X = B, overwriting B with X.
182*
183 CALL spotrs( uplo, n, nrhs, a, lda, b, ldb, info )
184*
185 END IF
186 RETURN
187*
188* End of SPOSV
189*
190 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine sposv(uplo, n, nrhs, a, lda, b, ldb, info)
SPOSV computes the solution to system of linear equations A * X = B for PO matrices
Definition sposv.f:130
subroutine spotrf(uplo, n, a, lda, info)
SPOTRF
Definition spotrf.f:107
subroutine spotrs(uplo, n, nrhs, a, lda, b, ldb, info)
SPOTRS
Definition spotrs.f:110