1: *> \brief <b> DPPSV 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: *
8: *> \htmlonly
9: *> Download DPPSV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppsv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dppsv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dppsv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPPSV( 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: * DOUBLE PRECISION AP( * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPPSV 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 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**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] AP
75: *> \verbatim
76: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
77: *> On entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, in the same storage
86: *> format as A.
87: *> \endverbatim
88: *>
89: *> \param[in,out] B
90: *> \verbatim
91: *> B is DOUBLE PRECISION 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 doubleOTHERsolve
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 symmetric 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 DPPSV( 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: DOUBLE PRECISION AP( * ), B( LDB, * )
155: * ..
156: *
157: * =====================================================================
158: *
159: * .. External Functions ..
160: LOGICAL LSAME
161: EXTERNAL LSAME
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL DPPTRF, DPPTRS, 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( 'DPPSV ', -INFO )
185: RETURN
186: END IF
187: *
188: * Compute the Cholesky factorization A = U**T*U or A = L*L**T.
189: *
190: CALL DPPTRF( 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 DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
196: *
197: END IF
198: RETURN
199: *
200: * End of DPPSV
201: *
202: END
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