Annotation of rpl/lapack/lapack/dposv.f, revision 1.11
1.9 bertrand 1: *> \brief <b> DPOSV 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 DPOSV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPOSV( 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: * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPOSV 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doublePOsolve
129: *
130: * =====================================================================
1.1 bertrand 131: SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
132: *
1.9 bertrand 133: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 136: * November 2011
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER UPLO
140: INTEGER INFO, LDA, LDB, N, NRHS
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. External Functions ..
149: LOGICAL LSAME
150: EXTERNAL LSAME
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL DPOTRF, DPOTRS, 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( 'DPOSV ', -INFO )
176: RETURN
177: END IF
178: *
1.8 bertrand 179: * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
1.1 bertrand 180: *
181: CALL DPOTRF( 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 DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
187: *
188: END IF
189: RETURN
190: *
191: * End of DPOSV
192: *
193: END
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