LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
dptsv.f
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1 *> \brief <b> DPTSV computes the solution to system of linear equations A * X = B for PT matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDB, N, NRHS
25 * ..
26 * .. Array Arguments ..
27 * DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> DPTSV computes the solution to a real system of linear equations
37 *> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
38 *> matrix, and X and B are N-by-NRHS matrices.
39 *>
40 *> A is factored as A = L*D*L**T, and the factored form of A is then
41 *> used to solve the system of equations.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] N
48 *> \verbatim
49 *> N is INTEGER
50 *> The order of the matrix A. N >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] NRHS
54 *> \verbatim
55 *> NRHS is INTEGER
56 *> The number of right hand sides, i.e., the number of columns
57 *> of the matrix B. NRHS >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in,out] D
61 *> \verbatim
62 *> D is DOUBLE PRECISION array, dimension (N)
63 *> On entry, the n diagonal elements of the tridiagonal matrix
64 *> A. On exit, the n diagonal elements of the diagonal matrix
65 *> D from the factorization A = L*D*L**T.
66 *> \endverbatim
67 *>
68 *> \param[in,out] E
69 *> \verbatim
70 *> E is DOUBLE PRECISION array, dimension (N-1)
71 *> On entry, the (n-1) subdiagonal elements of the tridiagonal
72 *> matrix A. On exit, the (n-1) subdiagonal elements of the
73 *> unit bidiagonal factor L from the L*D*L**T factorization of
74 *> A. (E can also be regarded as the superdiagonal of the unit
75 *> bidiagonal factor U from the U**T*D*U factorization of A.)
76 *> \endverbatim
77 *>
78 *> \param[in,out] B
79 *> \verbatim
80 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
81 *> On entry, the N-by-NRHS right hand side matrix B.
82 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
83 *> \endverbatim
84 *>
85 *> \param[in] LDB
86 *> \verbatim
87 *> LDB is INTEGER
88 *> The leading dimension of the array B. LDB >= max(1,N).
89 *> \endverbatim
90 *>
91 *> \param[out] INFO
92 *> \verbatim
93 *> INFO is INTEGER
94 *> = 0: successful exit
95 *> < 0: if INFO = -i, the i-th argument had an illegal value
96 *> > 0: if INFO = i, the leading minor of order i is not
97 *> positive definite, and the solution has not been
98 *> computed. The factorization has not been completed
99 *> unless i = N.
100 *> \endverbatim
101 *
102 * Authors:
103 * ========
104 *
105 *> \author Univ. of Tennessee
106 *> \author Univ. of California Berkeley
107 *> \author Univ. of Colorado Denver
108 *> \author NAG Ltd.
109 *
110 *> \date December 2016
111 *
112 *> \ingroup doublePTsolve
113 *
114 * =====================================================================
115  SUBROUTINE dptsv( N, NRHS, D, E, B, LDB, INFO )
116 *
117 * -- LAPACK driver routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  INTEGER INFO, LDB, N, NRHS
124 * ..
125 * .. Array Arguments ..
126  DOUBLE PRECISION B( ldb, * ), D( * ), E( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. External Subroutines ..
132  EXTERNAL dpttrf, dpttrs, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC max
136 * ..
137 * .. Executable Statements ..
138 *
139 * Test the input parameters.
140 *
141  info = 0
142  IF( n.LT.0 ) THEN
143  info = -1
144  ELSE IF( nrhs.LT.0 ) THEN
145  info = -2
146  ELSE IF( ldb.LT.max( 1, n ) ) THEN
147  info = -6
148  END IF
149  IF( info.NE.0 ) THEN
150  CALL xerbla( 'DPTSV ', -info )
151  RETURN
152  END IF
153 *
154 * Compute the L*D*L**T (or U**T*D*U) factorization of A.
155 *
156  CALL dpttrf( n, d, e, info )
157  IF( info.EQ.0 ) THEN
158 *
159 * Solve the system A*X = B, overwriting B with X.
160 *
161  CALL dpttrs( n, nrhs, d, e, b, ldb, info )
162  END IF
163  RETURN
164 *
165 * End of DPTSV
166 *
167  END
subroutine dpttrf(N, D, E, INFO)
DPTTRF
Definition: dpttrf.f:93
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dptsv(N, NRHS, D, E, B, LDB, INFO)
DPTSV computes the solution to system of linear equations A * X = B for PT matrices ...
Definition: dptsv.f:116
subroutine dpttrs(N, NRHS, D, E, B, LDB, INFO)
DPTTRS
Definition: dpttrs.f:111