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1: *> \brief <b> DSPSV 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 DSPSV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspsv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspsv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspsv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * DOUBLE PRECISION AP( * ), B( LDB, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DSPSV computes the solution to a real system of linear equations
39: *> A * X = B,
40: *> where A is an N-by-N symmetric matrix stored in packed format and X
41: *> and B are N-by-NRHS matrices.
42: *>
43: *> The diagonal pivoting method is used to factor A as
44: *> A = U * D * U**T, if UPLO = 'U', or
45: *> A = L * D * L**T, if UPLO = 'L',
46: *> where U (or L) is a product of permutation and unit upper (lower)
47: *> triangular matrices, D is symmetric and block diagonal with 1-by-1
48: *> and 2-by-2 diagonal blocks. The factored form of A is then used to
49: *> solve the system of equations A * X = B.
50: *> \endverbatim
51: *
52: * Arguments:
53: * ==========
54: *
55: *> \param[in] UPLO
56: *> \verbatim
57: *> UPLO is CHARACTER*1
58: *> = 'U': Upper triangle of A is stored;
59: *> = 'L': Lower triangle of A is stored.
60: *> \endverbatim
61: *>
62: *> \param[in] N
63: *> \verbatim
64: *> N is INTEGER
65: *> The number of linear equations, i.e., the order of the
66: *> matrix A. N >= 0.
67: *> \endverbatim
68: *>
69: *> \param[in] NRHS
70: *> \verbatim
71: *> NRHS is INTEGER
72: *> The number of right hand sides, i.e., the number of columns
73: *> of the matrix B. NRHS >= 0.
74: *> \endverbatim
75: *>
76: *> \param[in,out] AP
77: *> \verbatim
78: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
79: *> On entry, the upper or lower triangle of the symmetric matrix
80: *> A, packed columnwise in a linear array. The j-th column of A
81: *> is stored in the array AP as follows:
82: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
83: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
84: *> See below for further details.
85: *>
86: *> On exit, the block diagonal matrix D and the multipliers used
87: *> to obtain the factor U or L from the factorization
88: *> A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
89: *> a packed triangular matrix in the same storage format as A.
90: *> \endverbatim
91: *>
92: *> \param[out] IPIV
93: *> \verbatim
94: *> IPIV is INTEGER array, dimension (N)
95: *> Details of the interchanges and the block structure of D, as
96: *> determined by DSPTRF. If IPIV(k) > 0, then rows and columns
97: *> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
98: *> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
99: *> then rows and columns k-1 and -IPIV(k) were interchanged and
100: *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
101: *> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
102: *> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
103: *> diagonal block.
104: *> \endverbatim
105: *>
106: *> \param[in,out] B
107: *> \verbatim
108: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
109: *> On entry, the N-by-NRHS right hand side matrix B.
110: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
111: *> \endverbatim
112: *>
113: *> \param[in] LDB
114: *> \verbatim
115: *> LDB is INTEGER
116: *> The leading dimension of the array B. LDB >= max(1,N).
117: *> \endverbatim
118: *>
119: *> \param[out] INFO
120: *> \verbatim
121: *> INFO is INTEGER
122: *> = 0: successful exit
123: *> < 0: if INFO = -i, the i-th argument had an illegal value
124: *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
125: *> has been completed, but the block diagonal matrix D is
126: *> exactly singular, so the solution could not be
127: *> computed.
128: *> \endverbatim
129: *
130: * Authors:
131: * ========
132: *
133: *> \author Univ. of Tennessee
134: *> \author Univ. of California Berkeley
135: *> \author Univ. of Colorado Denver
136: *> \author NAG Ltd.
137: *
138: *> \date November 2011
139: *
140: *> \ingroup doubleOTHERsolve
141: *
142: *> \par Further Details:
143: * =====================
144: *>
145: *> \verbatim
146: *>
147: *> The packed storage scheme is illustrated by the following example
148: *> when N = 4, UPLO = 'U':
149: *>
150: *> Two-dimensional storage of the symmetric matrix A:
151: *>
152: *> a11 a12 a13 a14
153: *> a22 a23 a24
154: *> a33 a34 (aij = aji)
155: *> a44
156: *>
157: *> Packed storage of the upper triangle of A:
158: *>
159: *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
160: *> \endverbatim
161: *>
162: * =====================================================================
163: SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
164: *
165: * -- LAPACK driver routine (version 3.4.0) --
166: * -- LAPACK is a software package provided by Univ. of Tennessee, --
167: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168: * November 2011
169: *
170: * .. Scalar Arguments ..
171: CHARACTER UPLO
172: INTEGER INFO, LDB, N, NRHS
173: * ..
174: * .. Array Arguments ..
175: INTEGER IPIV( * )
176: DOUBLE PRECISION AP( * ), B( LDB, * )
177: * ..
178: *
179: * =====================================================================
180: *
181: * .. External Functions ..
182: LOGICAL LSAME
183: EXTERNAL LSAME
184: * ..
185: * .. External Subroutines ..
186: EXTERNAL DSPTRF, DSPTRS, XERBLA
187: * ..
188: * .. Intrinsic Functions ..
189: INTRINSIC MAX
190: * ..
191: * .. Executable Statements ..
192: *
193: * Test the input parameters.
194: *
195: INFO = 0
196: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
197: INFO = -1
198: ELSE IF( N.LT.0 ) THEN
199: INFO = -2
200: ELSE IF( NRHS.LT.0 ) THEN
201: INFO = -3
202: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
203: INFO = -7
204: END IF
205: IF( INFO.NE.0 ) THEN
206: CALL XERBLA( 'DSPSV ', -INFO )
207: RETURN
208: END IF
209: *
210: * Compute the factorization A = U*D*U**T or A = L*D*L**T.
211: *
212: CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
213: IF( INFO.EQ.0 ) THEN
214: *
215: * Solve the system A*X = B, overwriting B with X.
216: *
217: CALL DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
218: *
219: END IF
220: RETURN
221: *
222: * End of DSPSV
223: *
224: END
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