1 SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INCX, N
11 COMPLEX*16 ALPHA
12 * ..
13 * .. Array Arguments ..
14 COMPLEX*16 AP( * ), X( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZSPR performs the symmetric rank 1 operation
21 *
22 * A := alpha*x*x**H + A,
23 *
24 * where alpha is a complex scalar, x is an n element vector and A is an
25 * n by n symmetric matrix, supplied in packed form.
26 *
27 * Arguments
28 * ==========
29 *
30 * UPLO (input) CHARACTER*1
31 * On entry, UPLO specifies whether the upper or lower
32 * triangular part of the matrix A is supplied in the packed
33 * array AP as follows:
34 *
35 * UPLO = 'U' or 'u' The upper triangular part of A is
36 * supplied in AP.
37 *
38 * UPLO = 'L' or 'l' The lower triangular part of A is
39 * supplied in AP.
40 *
41 * Unchanged on exit.
42 *
43 * N (input) INTEGER
44 * On entry, N specifies the order of the matrix A.
45 * N must be at least zero.
46 * Unchanged on exit.
47 *
48 * ALPHA (input) COMPLEX*16
49 * On entry, ALPHA specifies the scalar alpha.
50 * Unchanged on exit.
51 *
52 * X (input) COMPLEX*16 array, dimension at least
53 * ( 1 + ( N - 1 )*abs( INCX ) ).
54 * Before entry, the incremented array X must contain the N-
55 * element vector x.
56 * Unchanged on exit.
57 *
58 * INCX (input) INTEGER
59 * On entry, INCX specifies the increment for the elements of
60 * X. INCX must not be zero.
61 * Unchanged on exit.
62 *
63 * AP (input/output) COMPLEX*16 array, dimension at least
64 * ( ( N*( N + 1 ) )/2 ).
65 * Before entry, with UPLO = 'U' or 'u', the array AP must
66 * contain the upper triangular part of the symmetric matrix
67 * packed sequentially, column by column, so that AP( 1 )
68 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
69 * and a( 2, 2 ) respectively, and so on. On exit, the array
70 * AP is overwritten by the upper triangular part of the
71 * updated matrix.
72 * Before entry, with UPLO = 'L' or 'l', the array AP must
73 * contain the lower triangular part of the symmetric matrix
74 * packed sequentially, column by column, so that AP( 1 )
75 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
76 * and a( 3, 1 ) respectively, and so on. On exit, the array
77 * AP is overwritten by the lower triangular part of the
78 * updated matrix.
79 * Note that the imaginary parts of the diagonal elements need
80 * not be set, they are assumed to be zero, and on exit they
81 * are set to zero.
82 *
83 * =====================================================================
84 *
85 * .. Parameters ..
86 COMPLEX*16 ZERO
87 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
88 * ..
89 * .. Local Scalars ..
90 INTEGER I, INFO, IX, J, JX, K, KK, KX
91 COMPLEX*16 TEMP
92 * ..
93 * .. External Functions ..
94 LOGICAL LSAME
95 EXTERNAL LSAME
96 * ..
97 * .. External Subroutines ..
98 EXTERNAL XERBLA
99 * ..
100 * .. Executable Statements ..
101 *
102 * Test the input parameters.
103 *
104 INFO = 0
105 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
106 INFO = 1
107 ELSE IF( N.LT.0 ) THEN
108 INFO = 2
109 ELSE IF( INCX.EQ.0 ) THEN
110 INFO = 5
111 END IF
112 IF( INFO.NE.0 ) THEN
113 CALL XERBLA( 'ZSPR ', INFO )
114 RETURN
115 END IF
116 *
117 * Quick return if possible.
118 *
119 IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
120 $ RETURN
121 *
122 * Set the start point in X if the increment is not unity.
123 *
124 IF( INCX.LE.0 ) THEN
125 KX = 1 - ( N-1 )*INCX
126 ELSE IF( INCX.NE.1 ) THEN
127 KX = 1
128 END IF
129 *
130 * Start the operations. In this version the elements of the array AP
131 * are accessed sequentially with one pass through AP.
132 *
133 KK = 1
134 IF( LSAME( UPLO, 'U' ) ) THEN
135 *
136 * Form A when upper triangle is stored in AP.
137 *
138 IF( INCX.EQ.1 ) THEN
139 DO 20 J = 1, N
140 IF( X( J ).NE.ZERO ) THEN
141 TEMP = ALPHA*X( J )
142 K = KK
143 DO 10 I = 1, J - 1
144 AP( K ) = AP( K ) + X( I )*TEMP
145 K = K + 1
146 10 CONTINUE
147 AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
148 ELSE
149 AP( KK+J-1 ) = AP( KK+J-1 )
150 END IF
151 KK = KK + J
152 20 CONTINUE
153 ELSE
154 JX = KX
155 DO 40 J = 1, N
156 IF( X( JX ).NE.ZERO ) THEN
157 TEMP = ALPHA*X( JX )
158 IX = KX
159 DO 30 K = KK, KK + J - 2
160 AP( K ) = AP( K ) + X( IX )*TEMP
161 IX = IX + INCX
162 30 CONTINUE
163 AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
164 ELSE
165 AP( KK+J-1 ) = AP( KK+J-1 )
166 END IF
167 JX = JX + INCX
168 KK = KK + J
169 40 CONTINUE
170 END IF
171 ELSE
172 *
173 * Form A when lower triangle is stored in AP.
174 *
175 IF( INCX.EQ.1 ) THEN
176 DO 60 J = 1, N
177 IF( X( J ).NE.ZERO ) THEN
178 TEMP = ALPHA*X( J )
179 AP( KK ) = AP( KK ) + TEMP*X( J )
180 K = KK + 1
181 DO 50 I = J + 1, N
182 AP( K ) = AP( K ) + X( I )*TEMP
183 K = K + 1
184 50 CONTINUE
185 ELSE
186 AP( KK ) = AP( KK )
187 END IF
188 KK = KK + N - J + 1
189 60 CONTINUE
190 ELSE
191 JX = KX
192 DO 80 J = 1, N
193 IF( X( JX ).NE.ZERO ) THEN
194 TEMP = ALPHA*X( JX )
195 AP( KK ) = AP( KK ) + TEMP*X( JX )
196 IX = JX
197 DO 70 K = KK + 1, KK + N - J
198 IX = IX + INCX
199 AP( K ) = AP( K ) + X( IX )*TEMP
200 70 CONTINUE
201 ELSE
202 AP( KK ) = AP( KK )
203 END IF
204 JX = JX + INCX
205 KK = KK + N - J + 1
206 80 CONTINUE
207 END IF
208 END IF
209 *
210 RETURN
211 *
212 * End of ZSPR
213 *
214 END
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER UPLO
10 INTEGER INCX, N
11 COMPLEX*16 ALPHA
12 * ..
13 * .. Array Arguments ..
14 COMPLEX*16 AP( * ), X( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZSPR performs the symmetric rank 1 operation
21 *
22 * A := alpha*x*x**H + A,
23 *
24 * where alpha is a complex scalar, x is an n element vector and A is an
25 * n by n symmetric matrix, supplied in packed form.
26 *
27 * Arguments
28 * ==========
29 *
30 * UPLO (input) CHARACTER*1
31 * On entry, UPLO specifies whether the upper or lower
32 * triangular part of the matrix A is supplied in the packed
33 * array AP as follows:
34 *
35 * UPLO = 'U' or 'u' The upper triangular part of A is
36 * supplied in AP.
37 *
38 * UPLO = 'L' or 'l' The lower triangular part of A is
39 * supplied in AP.
40 *
41 * Unchanged on exit.
42 *
43 * N (input) INTEGER
44 * On entry, N specifies the order of the matrix A.
45 * N must be at least zero.
46 * Unchanged on exit.
47 *
48 * ALPHA (input) COMPLEX*16
49 * On entry, ALPHA specifies the scalar alpha.
50 * Unchanged on exit.
51 *
52 * X (input) COMPLEX*16 array, dimension at least
53 * ( 1 + ( N - 1 )*abs( INCX ) ).
54 * Before entry, the incremented array X must contain the N-
55 * element vector x.
56 * Unchanged on exit.
57 *
58 * INCX (input) INTEGER
59 * On entry, INCX specifies the increment for the elements of
60 * X. INCX must not be zero.
61 * Unchanged on exit.
62 *
63 * AP (input/output) COMPLEX*16 array, dimension at least
64 * ( ( N*( N + 1 ) )/2 ).
65 * Before entry, with UPLO = 'U' or 'u', the array AP must
66 * contain the upper triangular part of the symmetric matrix
67 * packed sequentially, column by column, so that AP( 1 )
68 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
69 * and a( 2, 2 ) respectively, and so on. On exit, the array
70 * AP is overwritten by the upper triangular part of the
71 * updated matrix.
72 * Before entry, with UPLO = 'L' or 'l', the array AP must
73 * contain the lower triangular part of the symmetric matrix
74 * packed sequentially, column by column, so that AP( 1 )
75 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
76 * and a( 3, 1 ) respectively, and so on. On exit, the array
77 * AP is overwritten by the lower triangular part of the
78 * updated matrix.
79 * Note that the imaginary parts of the diagonal elements need
80 * not be set, they are assumed to be zero, and on exit they
81 * are set to zero.
82 *
83 * =====================================================================
84 *
85 * .. Parameters ..
86 COMPLEX*16 ZERO
87 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
88 * ..
89 * .. Local Scalars ..
90 INTEGER I, INFO, IX, J, JX, K, KK, KX
91 COMPLEX*16 TEMP
92 * ..
93 * .. External Functions ..
94 LOGICAL LSAME
95 EXTERNAL LSAME
96 * ..
97 * .. External Subroutines ..
98 EXTERNAL XERBLA
99 * ..
100 * .. Executable Statements ..
101 *
102 * Test the input parameters.
103 *
104 INFO = 0
105 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
106 INFO = 1
107 ELSE IF( N.LT.0 ) THEN
108 INFO = 2
109 ELSE IF( INCX.EQ.0 ) THEN
110 INFO = 5
111 END IF
112 IF( INFO.NE.0 ) THEN
113 CALL XERBLA( 'ZSPR ', INFO )
114 RETURN
115 END IF
116 *
117 * Quick return if possible.
118 *
119 IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
120 $ RETURN
121 *
122 * Set the start point in X if the increment is not unity.
123 *
124 IF( INCX.LE.0 ) THEN
125 KX = 1 - ( N-1 )*INCX
126 ELSE IF( INCX.NE.1 ) THEN
127 KX = 1
128 END IF
129 *
130 * Start the operations. In this version the elements of the array AP
131 * are accessed sequentially with one pass through AP.
132 *
133 KK = 1
134 IF( LSAME( UPLO, 'U' ) ) THEN
135 *
136 * Form A when upper triangle is stored in AP.
137 *
138 IF( INCX.EQ.1 ) THEN
139 DO 20 J = 1, N
140 IF( X( J ).NE.ZERO ) THEN
141 TEMP = ALPHA*X( J )
142 K = KK
143 DO 10 I = 1, J - 1
144 AP( K ) = AP( K ) + X( I )*TEMP
145 K = K + 1
146 10 CONTINUE
147 AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
148 ELSE
149 AP( KK+J-1 ) = AP( KK+J-1 )
150 END IF
151 KK = KK + J
152 20 CONTINUE
153 ELSE
154 JX = KX
155 DO 40 J = 1, N
156 IF( X( JX ).NE.ZERO ) THEN
157 TEMP = ALPHA*X( JX )
158 IX = KX
159 DO 30 K = KK, KK + J - 2
160 AP( K ) = AP( K ) + X( IX )*TEMP
161 IX = IX + INCX
162 30 CONTINUE
163 AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
164 ELSE
165 AP( KK+J-1 ) = AP( KK+J-1 )
166 END IF
167 JX = JX + INCX
168 KK = KK + J
169 40 CONTINUE
170 END IF
171 ELSE
172 *
173 * Form A when lower triangle is stored in AP.
174 *
175 IF( INCX.EQ.1 ) THEN
176 DO 60 J = 1, N
177 IF( X( J ).NE.ZERO ) THEN
178 TEMP = ALPHA*X( J )
179 AP( KK ) = AP( KK ) + TEMP*X( J )
180 K = KK + 1
181 DO 50 I = J + 1, N
182 AP( K ) = AP( K ) + X( I )*TEMP
183 K = K + 1
184 50 CONTINUE
185 ELSE
186 AP( KK ) = AP( KK )
187 END IF
188 KK = KK + N - J + 1
189 60 CONTINUE
190 ELSE
191 JX = KX
192 DO 80 J = 1, N
193 IF( X( JX ).NE.ZERO ) THEN
194 TEMP = ALPHA*X( JX )
195 AP( KK ) = AP( KK ) + TEMP*X( JX )
196 IX = JX
197 DO 70 K = KK + 1, KK + N - J
198 IX = IX + INCX
199 AP( K ) = AP( K ) + X( IX )*TEMP
200 70 CONTINUE
201 ELSE
202 AP( KK ) = AP( KK )
203 END IF
204 JX = JX + INCX
205 KK = KK + N - J + 1
206 80 CONTINUE
207 END IF
208 END IF
209 *
210 RETURN
211 *
212 * End of ZSPR
213 *
214 END