LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dpptrs.f
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1 *> \brief \b DPPTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DPPTRS( 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 *> DPPTRS solves a system of linear equations A*X = B with a symmetric
38 *> positive definite matrix A in packed storage using the Cholesky
39 *> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
40 *> \endverbatim
41 *
42 * Arguments:
43 * ==========
44 *
45 *> \param[in] UPLO
46 *> \verbatim
47 *> UPLO is CHARACTER*1
48 *> = 'U': Upper triangle of A is stored;
49 *> = 'L': Lower triangle of A is stored.
50 *> \endverbatim
51 *>
52 *> \param[in] N
53 *> \verbatim
54 *> N is INTEGER
55 *> The order of the matrix A. N >= 0.
56 *> \endverbatim
57 *>
58 *> \param[in] NRHS
59 *> \verbatim
60 *> NRHS is INTEGER
61 *> The number of right hand sides, i.e., the number of columns
62 *> of the matrix B. NRHS >= 0.
63 *> \endverbatim
64 *>
65 *> \param[in] AP
66 *> \verbatim
67 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
68 *> The triangular factor U or L from the Cholesky factorization
69 *> A = U**T*U or A = L*L**T, packed columnwise in a linear
70 *> array. The j-th column of U or L is stored in the array AP
71 *> as follows:
72 *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
73 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
74 *> \endverbatim
75 *>
76 *> \param[in,out] B
77 *> \verbatim
78 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
79 *> On entry, the right hand side matrix B.
80 *> On exit, the solution matrix X.
81 *> \endverbatim
82 *>
83 *> \param[in] LDB
84 *> \verbatim
85 *> LDB is INTEGER
86 *> The leading dimension of the array B. LDB >= max(1,N).
87 *> \endverbatim
88 *>
89 *> \param[out] INFO
90 *> \verbatim
91 *> INFO is INTEGER
92 *> = 0: successful exit
93 *> < 0: if INFO = -i, the i-th argument had an illegal value
94 *> \endverbatim
95 *
96 * Authors:
97 * ========
98 *
99 *> \author Univ. of Tennessee
100 *> \author Univ. of California Berkeley
101 *> \author Univ. of Colorado Denver
102 *> \author NAG Ltd.
103 *
104 *> \date November 2011
105 *
106 *> \ingroup doubleOTHERcomputational
107 *
108 * =====================================================================
109  SUBROUTINE dpptrs( UPLO, N, NRHS, AP, B, LDB, INFO )
110 *
111 * -- LAPACK computational routine (version 3.4.0) --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 * November 2011
115 *
116 * .. Scalar Arguments ..
117  CHARACTER UPLO
118  INTEGER INFO, LDB, N, NRHS
119 * ..
120 * .. Array Arguments ..
121  DOUBLE PRECISION AP( * ), B( ldb, * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Local Scalars ..
127  LOGICAL UPPER
128  INTEGER I
129 * ..
130 * .. External Functions ..
131  LOGICAL LSAME
132  EXTERNAL lsame
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL dtpsv, xerbla
136 * ..
137 * .. Intrinsic Functions ..
138  INTRINSIC max
139 * ..
140 * .. Executable Statements ..
141 *
142 * Test the input parameters.
143 *
144  info = 0
145  upper = lsame( uplo, 'U' )
146  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
147  info = -1
148  ELSE IF( n.LT.0 ) THEN
149  info = -2
150  ELSE IF( nrhs.LT.0 ) THEN
151  info = -3
152  ELSE IF( ldb.LT.max( 1, n ) ) THEN
153  info = -6
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'DPPTRS', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( n.EQ.0 .OR. nrhs.EQ.0 )
163  \$ RETURN
164 *
165  IF( upper ) THEN
166 *
167 * Solve A*X = B where A = U**T * U.
168 *
169  DO 10 i = 1, nrhs
170 *
171 * Solve U**T *X = B, overwriting B with X.
172 *
173  CALL dtpsv( 'Upper', 'Transpose', 'Non-unit', n, ap,
174  \$ b( 1, i ), 1 )
175 *
176 * Solve U*X = B, overwriting B with X.
177 *
178  CALL dtpsv( 'Upper', 'No transpose', 'Non-unit', n, ap,
179  \$ b( 1, i ), 1 )
180  10 CONTINUE
181  ELSE
182 *
183 * Solve A*X = B where A = L * L**T.
184 *
185  DO 20 i = 1, nrhs
186 *
187 * Solve L*Y = B, overwriting B with X.
188 *
189  CALL dtpsv( 'Lower', 'No transpose', 'Non-unit', n, ap,
190  \$ b( 1, i ), 1 )
191 *
192 * Solve L**T *X = Y, overwriting B with X.
193 *
194  CALL dtpsv( 'Lower', 'Transpose', 'Non-unit', n, ap,
195  \$ b( 1, i ), 1 )
196  20 CONTINUE
197  END IF
198 *
199  RETURN
200 *
201 * End of DPPTRS
202 *
203  END
subroutine dpptrs(UPLO, N, NRHS, AP, B, LDB, INFO)
DPPTRS
Definition: dpptrs.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dtpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
Definition: dtpsv.f:146