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source: branches/2789_MathNetNumerics-Exploration/HeuristicLab.Algorithms.DataAnalysis.Experimental/sbart/zhpr.f @ 17185

Last change on this file since 17185 was 15457, checked in by gkronber, 7 years ago

#2789 added Finbarr O'Sullivan smoothing spline code

File size: 6.6 KB
Line 
1      SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
2*     .. Scalar Arguments ..
3      DOUBLE PRECISION ALPHA
4      INTEGER INCX,N
5      CHARACTER UPLO
6*     ..
7*     .. Array Arguments ..
8      DOUBLE COMPLEX AP(*),X(*)
9*     ..
10*
11*  Purpose
12*  =======
13*
14*  ZHPR    performs the hermitian rank 1 operation
15*
16*     A := alpha*x*conjg( x' ) + A,
17*
18*  where alpha is a real scalar, x is an n element vector and A is an
19*  n by n hermitian matrix, supplied in packed form.
20*
21*  Arguments
22*  ==========
23*
24*  UPLO   - CHARACTER*1.
25*           On entry, UPLO specifies whether the upper or lower
26*           triangular part of the matrix A is supplied in the packed
27*           array AP as follows:
28*
29*              UPLO = 'U' or 'u'   The upper triangular part of A is
30*                                  supplied in AP.
31*
32*              UPLO = 'L' or 'l'   The lower triangular part of A is
33*                                  supplied in AP.
34*
35*           Unchanged on exit.
36*
37*  N      - INTEGER.
38*           On entry, N specifies the order of the matrix A.
39*           N must be at least zero.
40*           Unchanged on exit.
41*
42*  ALPHA  - DOUBLE PRECISION.
43*           On entry, ALPHA specifies the scalar alpha.
44*           Unchanged on exit.
45*
46*  X      - COMPLEX*16       array of dimension at least
47*           ( 1 + ( n - 1 )*abs( INCX ) ).
48*           Before entry, the incremented array X must contain the n
49*           element vector x.
50*           Unchanged on exit.
51*
52*  INCX   - INTEGER.
53*           On entry, INCX specifies the increment for the elements of
54*           X. INCX must not be zero.
55*           Unchanged on exit.
56*
57*  AP     - COMPLEX*16       array of DIMENSION at least
58*           ( ( n*( n + 1 ) )/2 ).
59*           Before entry with  UPLO = 'U' or 'u', the array AP must
60*           contain the upper triangular part of the hermitian matrix
61*           packed sequentially, column by column, so that AP( 1 )
62*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
63*           and a( 2, 2 ) respectively, and so on. On exit, the array
64*           AP is overwritten by the upper triangular part of the
65*           updated matrix.
66*           Before entry with UPLO = 'L' or 'l', the array AP must
67*           contain the lower triangular part of the hermitian matrix
68*           packed sequentially, column by column, so that AP( 1 )
69*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
70*           and a( 3, 1 ) respectively, and so on. On exit, the array
71*           AP is overwritten by the lower triangular part of the
72*           updated matrix.
73*           Note that the imaginary parts of the diagonal elements need
74*           not be set, they are assumed to be zero, and on exit they
75*           are set to zero.
76*
77*
78*  Level 2 Blas routine.
79*
80*  -- Written on 22-October-1986.
81*     Jack Dongarra, Argonne National Lab.
82*     Jeremy Du Croz, Nag Central Office.
83*     Sven Hammarling, Nag Central Office.
84*     Richard Hanson, Sandia National Labs.
85*
86*
87*     .. Parameters ..
88      DOUBLE COMPLEX ZERO
89      PARAMETER (ZERO= (0.0D+0,0.0D+0))
90*     ..
91*     .. Local Scalars ..
92      DOUBLE COMPLEX TEMP
93      INTEGER I,INFO,IX,J,JX,K,KK,KX
94*     ..
95*     .. External Functions ..
96      LOGICAL LSAME
97      EXTERNAL LSAME
98*     ..
99*     .. External Subroutines ..
100      EXTERNAL XERBLA
101*     ..
102*     .. Intrinsic Functions ..
103      INTRINSIC DBLE,DCONJG
104*     ..
105*
106*     Test the input parameters.
107*
108      INFO = 0
109      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
110          INFO = 1
111      ELSE IF (N.LT.0) THEN
112          INFO = 2
113      ELSE IF (INCX.EQ.0) THEN
114          INFO = 5
115      END IF
116      IF (INFO.NE.0) THEN
117          CALL XERBLA('ZHPR  ',INFO)
118          RETURN
119      END IF
120*
121*     Quick return if possible.
122*
123      IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
124*
125*     Set the start point in X if the increment is not unity.
126*
127      IF (INCX.LE.0) THEN
128          KX = 1 - (N-1)*INCX
129      ELSE IF (INCX.NE.1) THEN
130          KX = 1
131      END IF
132*
133*     Start the operations. In this version the elements of the array AP
134*     are accessed sequentially with one pass through AP.
135*
136      KK = 1
137      IF (LSAME(UPLO,'U')) THEN
138*
139*        Form  A  when upper triangle is stored in AP.
140*
141          IF (INCX.EQ.1) THEN
142              DO 20 J = 1,N
143                  IF (X(J).NE.ZERO) THEN
144                      TEMP = ALPHA*DCONJG(X(J))
145                      K = KK
146                      DO 10 I = 1,J - 1
147                          AP(K) = AP(K) + X(I)*TEMP
148                          K = K + 1
149   10                 CONTINUE
150                      AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP)
151                  ELSE
152                      AP(KK+J-1) = DBLE(AP(KK+J-1))
153                  END IF
154                  KK = KK + J
155   20         CONTINUE
156          ELSE
157              JX = KX
158              DO 40 J = 1,N
159                  IF (X(JX).NE.ZERO) THEN
160                      TEMP = ALPHA*DCONJG(X(JX))
161                      IX = KX
162                      DO 30 K = KK,KK + J - 2
163                          AP(K) = AP(K) + X(IX)*TEMP
164                          IX = IX + INCX
165   30                 CONTINUE
166                      AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP)
167                  ELSE
168                      AP(KK+J-1) = DBLE(AP(KK+J-1))
169                  END IF
170                  JX = JX + INCX
171                  KK = KK + J
172   40         CONTINUE
173          END IF
174      ELSE
175*
176*        Form  A  when lower triangle is stored in AP.
177*
178          IF (INCX.EQ.1) THEN
179              DO 60 J = 1,N
180                  IF (X(J).NE.ZERO) THEN
181                      TEMP = ALPHA*DCONJG(X(J))
182                      AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J))
183                      K = KK + 1
184                      DO 50 I = J + 1,N
185                          AP(K) = AP(K) + X(I)*TEMP
186                          K = K + 1
187   50                 CONTINUE
188                  ELSE
189                      AP(KK) = DBLE(AP(KK))
190                  END IF
191                  KK = KK + N - J + 1
192   60         CONTINUE
193          ELSE
194              JX = KX
195              DO 80 J = 1,N
196                  IF (X(JX).NE.ZERO) THEN
197                      TEMP = ALPHA*DCONJG(X(JX))
198                      AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX))
199                      IX = JX
200                      DO 70 K = KK + 1,KK + N - J
201                          IX = IX + INCX
202                          AP(K) = AP(K) + X(IX)*TEMP
203   70                 CONTINUE
204                  ELSE
205                      AP(KK) = DBLE(AP(KK))
206                  END IF
207                  JX = JX + INCX
208                  KK = KK + N - J + 1
209   80         CONTINUE
210          END IF
211      END IF
212*
213      RETURN
214*
215*     End of ZHPR  .
216*
217      END
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