LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
sspsv.f
Go to the documentation of this file.
1 *> \brief <b> SSPSV 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
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sspsv.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sspsv.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sspsv.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSPSV( 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 * REAL AP( * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SSPSV 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 REAL 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 SSPTRF, 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 SSPTRF. 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 REAL 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 realOTHERsolve
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 sspsv( 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  REAL AP( * ), B( ldb, * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. External Functions ..
182  LOGICAL LSAME
183  EXTERNAL lsame
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL ssptrf, ssptrs, 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( 'SSPSV ', -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 ssptrf( 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 ssptrs( uplo, n, nrhs, ap, ipiv, b, ldb, info )
218 *
219  END IF
220  RETURN
221 *
222 * End of SSPSV
223 *
224  END
subroutine ssptrs(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPTRS
Definition: ssptrs.f:117
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sspsv(UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices ...
Definition: sspsv.f:164
subroutine ssptrf(UPLO, N, AP, IPIV, INFO)
SSPTRF
Definition: ssptrf.f:159