1*> \brief \b DTPTRS
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DTPTRS + dependencies
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11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtptrs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          DIAG, TRANS, 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*> DTPTRS solves a triangular system of the form
38*>
39*>    A * X = B  or  A**T * X = B,
40*>
41*> where A is a triangular matrix of order N stored in packed format,
42*> and B is an N-by-NRHS matrix.  A check is made to verify that A is
43*> nonsingular.
44*> \endverbatim
45*
46*  Arguments:
47*  ==========
48*
49*> \param[in] UPLO
50*> \verbatim
51*>          UPLO is CHARACTER*1
52*>          = 'U':  A is upper triangular;
53*>          = 'L':  A is lower triangular.
54*> \endverbatim
55*>
56*> \param[in] TRANS
57*> \verbatim
58*>          TRANS is CHARACTER*1
59*>          Specifies the form of the system of equations:
60*>          = 'N':  A * X = B  (No transpose)
61*>          = 'T':  A**T * X = B  (Transpose)
62*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
63*> \endverbatim
64*>
65*> \param[in] DIAG
66*> \verbatim
67*>          DIAG is CHARACTER*1
68*>          = 'N':  A is non-unit triangular;
69*>          = 'U':  A is unit triangular.
70*> \endverbatim
71*>
72*> \param[in] N
73*> \verbatim
74*>          N is INTEGER
75*>          The order of the matrix A.  N >= 0.
76*> \endverbatim
77*>
78*> \param[in] NRHS
79*> \verbatim
80*>          NRHS is INTEGER
81*>          The number of right hand sides, i.e., the number of columns
82*>          of the matrix B.  NRHS >= 0.
83*> \endverbatim
84*>
85*> \param[in] AP
86*> \verbatim
87*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
88*>          The upper or lower triangular matrix A, packed columnwise in
89*>          a linear array.  The j-th column of A is stored in the array
90*>          AP as follows:
91*>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
92*>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
93*> \endverbatim
94*>
95*> \param[in,out] B
96*> \verbatim
97*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
98*>          On entry, the right hand side matrix B.
99*>          On exit, if INFO = 0, the solution matrix X.
100*> \endverbatim
101*>
102*> \param[in] LDB
103*> \verbatim
104*>          LDB is INTEGER
105*>          The leading dimension of the array B.  LDB >= max(1,N).
106*> \endverbatim
107*>
108*> \param[out] INFO
109*> \verbatim
110*>          INFO is INTEGER
111*>          = 0:  successful exit
112*>          < 0:  if INFO = -i, the i-th argument had an illegal value
113*>          > 0:  if INFO = i, the i-th diagonal element of A is zero,
114*>                indicating that the matrix is singular and the
115*>                solutions X have not been computed.
116*> \endverbatim
117*
118*  Authors:
119*  ========
120*
121*> \author Univ. of Tennessee
122*> \author Univ. of California Berkeley
123*> \author Univ. of Colorado Denver
124*> \author NAG Ltd.
125*
126*> \ingroup doubleOTHERcomputational
127*
128*  =====================================================================
129      SUBROUTINE DTPTRS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, INFO )
130*
131*  -- LAPACK computational routine --
132*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
133*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135*     .. Scalar Arguments ..
136      CHARACTER          DIAG, TRANS, UPLO
137      INTEGER            INFO, LDB, N, NRHS
138*     ..
139*     .. Array Arguments ..
140      DOUBLE PRECISION   AP( * ), B( LDB, * )
141*     ..
142*
143*  =====================================================================
144*
145*     .. Parameters ..
146      DOUBLE PRECISION   ZERO
147      PARAMETER          ( ZERO = 0.0D+0 )
148*     ..
149*     .. Local Scalars ..
150      LOGICAL            NOUNIT, UPPER
151      INTEGER            J, JC
152*     ..
153*     .. External Functions ..
154      LOGICAL            LSAME
155      EXTERNAL           LSAME
156*     ..
157*     .. External Subroutines ..
158      EXTERNAL           DTPSV, XERBLA
159*     ..
160*     .. Intrinsic Functions ..
161      INTRINSIC          MAX
162*     ..
163*     .. Executable Statements ..
164*
165*     Test the input parameters.
166*
167      INFO = 0
168      UPPER = LSAME( UPLO, 'U' )
169      NOUNIT = LSAME( DIAG, 'N' )
170      IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
171         INFO = -1
172      ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
173     $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
174         INFO = -2
175      ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
176         INFO = -3
177      ELSE IF( N.LT.0 ) THEN
178         INFO = -4
179      ELSE IF( NRHS.LT.0 ) THEN
180         INFO = -5
181      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
182         INFO = -8
183      END IF
184      IF( INFO.NE.0 ) THEN
185         CALL XERBLA( 'DTPTRS', -INFO )
186         RETURN
187      END IF
188*
189*     Quick return if possible
190*
191      IF( N.EQ.0 )
192     $   RETURN
193*
194*     Check for singularity.
195*
196      IF( NOUNIT ) THEN
197         IF( UPPER ) THEN
198            JC = 1
199            DO 10 INFO = 1, N
200               IF( AP( JC+INFO-1 ).EQ.ZERO )
201     $            RETURN
202               JC = JC + INFO
203   10       CONTINUE
204         ELSE
205            JC = 1
206            DO 20 INFO = 1, N
207               IF( AP( JC ).EQ.ZERO )
208     $            RETURN
209               JC = JC + N - INFO + 1
210   20       CONTINUE
211         END IF
212      END IF
213      INFO = 0
214*
215*     Solve A * x = b  or  A**T * x = b.
216*
217      DO 30 J = 1, NRHS
218         CALL DTPSV( UPLO, TRANS, DIAG, N, AP, B( 1, J ), 1 )
219   30 CONTINUE
220*
221      RETURN
222*
223*     End of DTPTRS
224*
225      END
226