LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
sspr.f
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1 *> \brief \b SSPR
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 SSPR(UPLO,N,ALPHA,X,INCX,AP)
12 *
13 * .. Scalar Arguments ..
14 * REAL ALPHA
15 * INTEGER INCX,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * REAL AP(*),X(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> SSPR performs the symmetric rank 1 operation
29 *>
30 *> A := alpha*x*x**T + A,
31 *>
32 *> where alpha is a real scalar, x is an n element vector and A is an
33 *> n by n symmetric matrix, supplied in packed form.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] UPLO
40 *> \verbatim
41 *> UPLO is CHARACTER*1
42 *> On entry, UPLO specifies whether the upper or lower
43 *> triangular part of the matrix A is supplied in the packed
44 *> array AP as follows:
45 *>
46 *> UPLO = 'U' or 'u' The upper triangular part of A is
47 *> supplied in AP.
48 *>
49 *> UPLO = 'L' or 'l' The lower triangular part of A is
50 *> supplied in AP.
51 *> \endverbatim
52 *>
53 *> \param[in] N
54 *> \verbatim
55 *> N is INTEGER
56 *> On entry, N specifies the order of the matrix A.
57 *> N must be at least zero.
58 *> \endverbatim
59 *>
60 *> \param[in] ALPHA
61 *> \verbatim
62 *> ALPHA is REAL
63 *> On entry, ALPHA specifies the scalar alpha.
64 *> \endverbatim
65 *>
66 *> \param[in] X
67 *> \verbatim
68 *> X is REAL array, dimension at least
69 *> ( 1 + ( n - 1 )*abs( INCX ) ).
70 *> Before entry, the incremented array X must contain the n
71 *> element vector x.
72 *> \endverbatim
73 *>
74 *> \param[in] INCX
75 *> \verbatim
76 *> INCX is INTEGER
77 *> On entry, INCX specifies the increment for the elements of
78 *> X. INCX must not be zero.
79 *> \endverbatim
80 *>
81 *> \param[in,out] AP
82 *> \verbatim
83 *> AP is REAL array, dimension at least
84 *> ( ( n*( n + 1 ) )/2 ).
85 *> Before entry with UPLO = 'U' or 'u', the array AP must
86 *> contain the upper triangular part of the symmetric matrix
87 *> packed sequentially, column by column, so that AP( 1 )
88 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
89 *> and a( 2, 2 ) respectively, and so on. On exit, the array
90 *> AP is overwritten by the upper triangular part of the
91 *> updated matrix.
92 *> Before entry with UPLO = 'L' or 'l', the array AP must
93 *> contain the lower triangular part of the symmetric matrix
94 *> packed sequentially, column by column, so that AP( 1 )
95 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
96 *> and a( 3, 1 ) respectively, and so on. On exit, the array
97 *> AP is overwritten by the lower triangular part of the
98 *> updated matrix.
99 *> \endverbatim
100 *
101 * Authors:
102 * ========
103 *
104 *> \author Univ. of Tennessee
105 *> \author Univ. of California Berkeley
106 *> \author Univ. of Colorado Denver
107 *> \author NAG Ltd.
108 *
109 *> \ingroup single_blas_level2
110 *
111 *> \par Further Details:
112 * =====================
113 *>
114 *> \verbatim
115 *>
116 *> Level 2 Blas routine.
117 *>
118 *> -- Written on 22-October-1986.
119 *> Jack Dongarra, Argonne National Lab.
120 *> Jeremy Du Croz, Nag Central Office.
121 *> Sven Hammarling, Nag Central Office.
122 *> Richard Hanson, Sandia National Labs.
123 *> \endverbatim
124 *>
125 * =====================================================================
126  SUBROUTINE sspr(UPLO,N,ALPHA,X,INCX,AP)
127 *
128 * -- Reference BLAS level2 routine --
129 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 *
132 * .. Scalar Arguments ..
133  REAL ALPHA
134  INTEGER INCX,N
135  CHARACTER UPLO
136 * ..
137 * .. Array Arguments ..
138  REAL AP(*),X(*)
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL ZERO
145  parameter(zero=0.0e+0)
146 * ..
147 * .. Local Scalars ..
148  REAL TEMP
149  INTEGER I,INFO,IX,J,JX,K,KK,KX
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  EXTERNAL lsame
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL xerbla
157 * ..
158 *
159 * Test the input parameters.
160 *
161  info = 0
162  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
163  info = 1
164  ELSE IF (n.LT.0) THEN
165  info = 2
166  ELSE IF (incx.EQ.0) THEN
167  info = 5
168  END IF
169  IF (info.NE.0) THEN
170  CALL xerbla('SSPR ',info)
171  RETURN
172  END IF
173 *
174 * Quick return if possible.
175 *
176  IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
177 *
178 * Set the start point in X if the increment is not unity.
179 *
180  IF (incx.LE.0) THEN
181  kx = 1 - (n-1)*incx
182  ELSE IF (incx.NE.1) THEN
183  kx = 1
184  END IF
185 *
186 * Start the operations. In this version the elements of the array AP
187 * are accessed sequentially with one pass through AP.
188 *
189  kk = 1
190  IF (lsame(uplo,'U')) THEN
191 *
192 * Form A when upper triangle is stored in AP.
193 *
194  IF (incx.EQ.1) THEN
195  DO 20 j = 1,n
196  IF (x(j).NE.zero) THEN
197  temp = alpha*x(j)
198  k = kk
199  DO 10 i = 1,j
200  ap(k) = ap(k) + x(i)*temp
201  k = k + 1
202  10 CONTINUE
203  END IF
204  kk = kk + j
205  20 CONTINUE
206  ELSE
207  jx = kx
208  DO 40 j = 1,n
209  IF (x(jx).NE.zero) THEN
210  temp = alpha*x(jx)
211  ix = kx
212  DO 30 k = kk,kk + j - 1
213  ap(k) = ap(k) + x(ix)*temp
214  ix = ix + incx
215  30 CONTINUE
216  END IF
217  jx = jx + incx
218  kk = kk + j
219  40 CONTINUE
220  END IF
221  ELSE
222 *
223 * Form A when lower triangle is stored in AP.
224 *
225  IF (incx.EQ.1) THEN
226  DO 60 j = 1,n
227  IF (x(j).NE.zero) THEN
228  temp = alpha*x(j)
229  k = kk
230  DO 50 i = j,n
231  ap(k) = ap(k) + x(i)*temp
232  k = k + 1
233  50 CONTINUE
234  END IF
235  kk = kk + n - j + 1
236  60 CONTINUE
237  ELSE
238  jx = kx
239  DO 80 j = 1,n
240  IF (x(jx).NE.zero) THEN
241  temp = alpha*x(jx)
242  ix = jx
243  DO 70 k = kk,kk + n - j
244  ap(k) = ap(k) + x(ix)*temp
245  ix = ix + incx
246  70 CONTINUE
247  END IF
248  jx = jx + incx
249  kk = kk + n - j + 1
250  80 CONTINUE
251  END IF
252  END IF
253 *
254  RETURN
255 *
256 * End of SSPR
257 *
258  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sspr(UPLO, N, ALPHA, X, INCX, AP)
SSPR
Definition: sspr.f:127