1*> \brief \b DPOT01
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
12*
13*       .. Scalar Arguments ..
14*       CHARACTER          UPLO
15*       INTEGER            LDA, LDAFAC, N
16*       DOUBLE PRECISION   RESID
17*       ..
18*       .. Array Arguments ..
19*       DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
20*       ..
21*
22*
23*> \par Purpose:
24*  =============
25*>
26*> \verbatim
27*>
28*> DPOT01 reconstructs a symmetric positive definite matrix  A  from
29*> its L*L' or U'*U factorization and computes the residual
30*>    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
31*>    norm( U'*U - A ) / ( N * norm(A) * EPS ),
32*> where EPS is the machine epsilon.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] UPLO
39*> \verbatim
40*>          UPLO is CHARACTER*1
41*>          Specifies whether the upper or lower triangular part of the
42*>          symmetric matrix A is stored:
43*>          = 'U':  Upper triangular
44*>          = 'L':  Lower triangular
45*> \endverbatim
46*>
47*> \param[in] N
48*> \verbatim
49*>          N is INTEGER
50*>          The number of rows and columns of the matrix A.  N >= 0.
51*> \endverbatim
52*>
53*> \param[in] A
54*> \verbatim
55*>          A is DOUBLE PRECISION array, dimension (LDA,N)
56*>          The original symmetric matrix A.
57*> \endverbatim
58*>
59*> \param[in] LDA
60*> \verbatim
61*>          LDA is INTEGER
62*>          The leading dimension of the array A.  LDA >= max(1,N)
63*> \endverbatim
64*>
65*> \param[in,out] AFAC
66*> \verbatim
67*>          AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
68*>          On entry, the factor L or U from the L * L**T or U**T * U
69*>          factorization of A.
70*>          Overwritten with the reconstructed matrix, and then with
71*>          the difference L * L**T - A (or U**T * U - A).
72*> \endverbatim
73*>
74*> \param[in] LDAFAC
75*> \verbatim
76*>          LDAFAC is INTEGER
77*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
78*> \endverbatim
79*>
80*> \param[out] RWORK
81*> \verbatim
82*>          RWORK is DOUBLE PRECISION array, dimension (N)
83*> \endverbatim
84*>
85*> \param[out] RESID
86*> \verbatim
87*>          RESID is DOUBLE PRECISION
88*>          If UPLO = 'L', norm(L * L**T - A) / ( N * norm(A) * EPS )
89*>          If UPLO = 'U', norm(U**T * U - A) / ( N * norm(A) * EPS )
90*> \endverbatim
91*
92*  Authors:
93*  ========
94*
95*> \author Univ. of Tennessee
96*> \author Univ. of California Berkeley
97*> \author Univ. of Colorado Denver
98*> \author NAG Ltd.
99*
100*> \ingroup double_lin
101*
102*  =====================================================================
103      SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID )
104*
105*  -- LAPACK test routine --
106*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
107*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108*
109*     .. Scalar Arguments ..
110      CHARACTER          UPLO
111      INTEGER            LDA, LDAFAC, N
112      DOUBLE PRECISION   RESID
113*     ..
114*     .. Array Arguments ..
115      DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
116*     ..
117*
118*  =====================================================================
119*
120*     .. Parameters ..
121      DOUBLE PRECISION   ZERO, ONE
122      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
123*     ..
124*     .. Local Scalars ..
125      INTEGER            I, J, K
126      DOUBLE PRECISION   ANORM, EPS, T
127*     ..
128*     .. External Functions ..
129      LOGICAL            LSAME
130      DOUBLE PRECISION   DDOT, DLAMCH, DLANSY
131      EXTERNAL           LSAME, DDOT, DLAMCH, DLANSY
132*     ..
133*     .. External Subroutines ..
134      EXTERNAL           DSCAL, DSYR, DTRMV
135*     ..
136*     .. Intrinsic Functions ..
137      INTRINSIC          DBLE
138*     ..
139*     .. Executable Statements ..
140*
141*     Quick exit if N = 0.
142*
143      IF( N.LE.0 ) THEN
144         RESID = ZERO
145         RETURN
146      END IF
147*
148*     Exit with RESID = 1/EPS if ANORM = 0.
149*
150      EPS = DLAMCH( 'Epsilon' )
151      ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
152      IF( ANORM.LE.ZERO ) THEN
153         RESID = ONE / EPS
154         RETURN
155      END IF
156*
157*     Compute the product U**T * U, overwriting U.
158*
159      IF( LSAME( UPLO, 'U' ) ) THEN
160         DO 10 K = N, 1, -1
161*
162*           Compute the (K,K) element of the result.
163*
164            T = DDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
165            AFAC( K, K ) = T
166*
167*           Compute the rest of column K.
168*
169            CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
170     $                  LDAFAC, AFAC( 1, K ), 1 )
171*
172   10    CONTINUE
173*
174*     Compute the product L * L**T, overwriting L.
175*
176      ELSE
177         DO 20 K = N, 1, -1
178*
179*           Add a multiple of column K of the factor L to each of
180*           columns K+1 through N.
181*
182            IF( K+1.LE.N )
183     $         CALL DSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
184     $                    AFAC( K+1, K+1 ), LDAFAC )
185*
186*           Scale column K by the diagonal element.
187*
188            T = AFAC( K, K )
189            CALL DSCAL( N-K+1, T, AFAC( K, K ), 1 )
190*
191   20    CONTINUE
192      END IF
193*
194*     Compute the difference L * L**T - A (or U**T * U - A).
195*
196      IF( LSAME( UPLO, 'U' ) ) THEN
197         DO 40 J = 1, N
198            DO 30 I = 1, J
199               AFAC( I, J ) = AFAC( I, J ) - A( I, J )
200   30       CONTINUE
201   40    CONTINUE
202      ELSE
203         DO 60 J = 1, N
204            DO 50 I = J, N
205               AFAC( I, J ) = AFAC( I, J ) - A( I, J )
206   50       CONTINUE
207   60    CONTINUE
208      END IF
209*
210*     Compute norm(L*U - A) / ( N * norm(A) * EPS )
211*
212      RESID = DLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK )
213*
214      RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
215*
216      RETURN
217*
218*     End of DPOT01
219*
220      END
221