LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zptsv.f
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1 *> \brief <b> ZPTSV 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 ZPTSV( N, NRHS, D, E, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDB, N, NRHS
25 * ..
26 * .. Array Arguments ..
27 * DOUBLE PRECISION D( * )
28 * COMPLEX*16 B( LDB, * ), E( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> ZPTSV computes the solution to a complex system of linear equations
38 *> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
39 *> matrix, and X and B are N-by-NRHS matrices.
40 *>
41 *> A is factored as A = L*D*L**H, and the factored form of A is then
42 *> used to solve the system of equations.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGER
51 *> The order of the matrix A. N >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] NRHS
55 *> \verbatim
56 *> NRHS is INTEGER
57 *> The number of right hand sides, i.e., the number of columns
58 *> of the matrix B. NRHS >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in,out] D
62 *> \verbatim
63 *> D is DOUBLE PRECISION array, dimension (N)
64 *> On entry, the n diagonal elements of the tridiagonal matrix
65 *> A. On exit, the n diagonal elements of the diagonal matrix
66 *> D from the factorization A = L*D*L**H.
67 *> \endverbatim
68 *>
69 *> \param[in,out] E
70 *> \verbatim
71 *> E is COMPLEX*16 array, dimension (N-1)
72 *> On entry, the (n-1) subdiagonal elements of the tridiagonal
73 *> matrix A. On exit, the (n-1) subdiagonal elements of the
74 *> unit bidiagonal factor L from the L*D*L**H factorization of
75 *> A. E can also be regarded as the superdiagonal of the unit
76 *> bidiagonal factor U from the U**H*D*U factorization of A.
77 *> \endverbatim
78 *>
79 *> \param[in,out] B
80 *> \verbatim
81 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
82 *> On entry, the N-by-NRHS right hand side matrix B.
83 *> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
84 *> \endverbatim
85 *>
86 *> \param[in] LDB
87 *> \verbatim
88 *> LDB is INTEGER
89 *> The leading dimension of the array B. LDB >= max(1,N).
90 *> \endverbatim
91 *>
92 *> \param[out] INFO
93 *> \verbatim
94 *> INFO is INTEGER
95 *> = 0: successful exit
96 *> < 0: if INFO = -i, the i-th argument had an illegal value
97 *> > 0: if INFO = i, the leading minor of order i is not
98 *> positive definite, and the solution has not been
99 *> computed. The factorization has not been completed
100 *> unless i = N.
101 *> \endverbatim
102 *
103 * Authors:
104 * ========
105 *
106 *> \author Univ. of Tennessee
107 *> \author Univ. of California Berkeley
108 *> \author Univ. of Colorado Denver
109 *> \author NAG Ltd.
110 *
111 *> \ingroup complex16PTsolve
112 *
113 * =====================================================================
114  SUBROUTINE zptsv( N, NRHS, D, E, B, LDB, INFO )
115 *
116 * -- LAPACK driver routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  INTEGER INFO, LDB, N, NRHS
122 * ..
123 * .. Array Arguments ..
124  DOUBLE PRECISION D( * )
125  COMPLEX*16 B( LDB, * ), E( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. External Subroutines ..
131  EXTERNAL xerbla, zpttrf, zpttrs
132 * ..
133 * .. Intrinsic Functions ..
134  INTRINSIC max
135 * ..
136 * .. Executable Statements ..
137 *
138 * Test the input parameters.
139 *
140  info = 0
141  IF( n.LT.0 ) THEN
142  info = -1
143  ELSE IF( nrhs.LT.0 ) THEN
144  info = -2
145  ELSE IF( ldb.LT.max( 1, n ) ) THEN
146  info = -6
147  END IF
148  IF( info.NE.0 ) THEN
149  CALL xerbla( 'ZPTSV ', -info )
150  RETURN
151  END IF
152 *
153 * Compute the L*D*L**H (or U**H*D*U) factorization of A.
154 *
155  CALL zpttrf( n, d, e, info )
156  IF( info.EQ.0 ) THEN
157 *
158 * Solve the system A*X = B, overwriting B with X.
159 *
160  CALL zpttrs( 'Lower', n, nrhs, d, e, b, ldb, info )
161  END IF
162  RETURN
163 *
164 * End of ZPTSV
165 *
166  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zpttrs(UPLO, N, NRHS, D, E, B, LDB, INFO)
ZPTTRS
Definition: zpttrs.f:121
subroutine zpttrf(N, D, E, INFO)
ZPTTRF
Definition: zpttrf.f:92
subroutine zptsv(N, NRHS, D, E, B, LDB, INFO)
ZPTSV computes the solution to system of linear equations A * X = B for PT matrices
Definition: zptsv.f:115