1 SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
2 * .. Scalar Arguments ..
3 REAL ALPHA
4 INTEGER INCX,N
5 CHARACTER UPLO
6 * ..
7 * .. Array Arguments ..
8 COMPLEX AP(*),X(*)
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * CHPR performs the hermitian rank 1 operation
15 *
16 * A := alpha*x*x**H + 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 - REAL .
43 * On entry, ALPHA specifies the scalar alpha.
44 * Unchanged on exit.
45 *
46 * X - COMPLEX 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 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 * Further Details
78 * ===============
79 *
80 * Level 2 Blas routine.
81 *
82 * -- Written on 22-October-1986.
83 * Jack Dongarra, Argonne National Lab.
84 * Jeremy Du Croz, Nag Central Office.
85 * Sven Hammarling, Nag Central Office.
86 * Richard Hanson, Sandia National Labs.
87 *
88 * =====================================================================
89 *
90 * .. Parameters ..
91 COMPLEX ZERO
92 PARAMETER (ZERO= (0.0E+0,0.0E+0))
93 * ..
94 * .. Local Scalars ..
95 COMPLEX TEMP
96 INTEGER I,INFO,IX,J,JX,K,KK,KX
97 * ..
98 * .. External Functions ..
99 LOGICAL LSAME
100 EXTERNAL LSAME
101 * ..
102 * .. External Subroutines ..
103 EXTERNAL XERBLA
104 * ..
105 * .. Intrinsic Functions ..
106 INTRINSIC CONJG,REAL
107 * ..
108 *
109 * Test the input parameters.
110 *
111 INFO = 0
112 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
113 INFO = 1
114 ELSE IF (N.LT.0) THEN
115 INFO = 2
116 ELSE IF (INCX.EQ.0) THEN
117 INFO = 5
118 END IF
119 IF (INFO.NE.0) THEN
120 CALL XERBLA('CHPR ',INFO)
121 RETURN
122 END IF
123 *
124 * Quick return if possible.
125 *
126 IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
127 *
128 * Set the start point in X if the increment is not unity.
129 *
130 IF (INCX.LE.0) THEN
131 KX = 1 - (N-1)*INCX
132 ELSE IF (INCX.NE.1) THEN
133 KX = 1
134 END IF
135 *
136 * Start the operations. In this version the elements of the array AP
137 * are accessed sequentially with one pass through AP.
138 *
139 KK = 1
140 IF (LSAME(UPLO,'U')) THEN
141 *
142 * Form A when upper triangle is stored in AP.
143 *
144 IF (INCX.EQ.1) THEN
145 DO 20 J = 1,N
146 IF (X(J).NE.ZERO) THEN
147 TEMP = ALPHA*CONJG(X(J))
148 K = KK
149 DO 10 I = 1,J - 1
150 AP(K) = AP(K) + X(I)*TEMP
151 K = K + 1
152 10 CONTINUE
153 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
154 ELSE
155 AP(KK+J-1) = REAL(AP(KK+J-1))
156 END IF
157 KK = KK + J
158 20 CONTINUE
159 ELSE
160 JX = KX
161 DO 40 J = 1,N
162 IF (X(JX).NE.ZERO) THEN
163 TEMP = ALPHA*CONJG(X(JX))
164 IX = KX
165 DO 30 K = KK,KK + J - 2
166 AP(K) = AP(K) + X(IX)*TEMP
167 IX = IX + INCX
168 30 CONTINUE
169 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
170 ELSE
171 AP(KK+J-1) = REAL(AP(KK+J-1))
172 END IF
173 JX = JX + INCX
174 KK = KK + J
175 40 CONTINUE
176 END IF
177 ELSE
178 *
179 * Form A when lower triangle is stored in AP.
180 *
181 IF (INCX.EQ.1) THEN
182 DO 60 J = 1,N
183 IF (X(J).NE.ZERO) THEN
184 TEMP = ALPHA*CONJG(X(J))
185 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J))
186 K = KK + 1
187 DO 50 I = J + 1,N
188 AP(K) = AP(K) + X(I)*TEMP
189 K = K + 1
190 50 CONTINUE
191 ELSE
192 AP(KK) = REAL(AP(KK))
193 END IF
194 KK = KK + N - J + 1
195 60 CONTINUE
196 ELSE
197 JX = KX
198 DO 80 J = 1,N
199 IF (X(JX).NE.ZERO) THEN
200 TEMP = ALPHA*CONJG(X(JX))
201 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX))
202 IX = JX
203 DO 70 K = KK + 1,KK + N - J
204 IX = IX + INCX
205 AP(K) = AP(K) + X(IX)*TEMP
206 70 CONTINUE
207 ELSE
208 AP(KK) = REAL(AP(KK))
209 END IF
210 JX = JX + INCX
211 KK = KK + N - J + 1
212 80 CONTINUE
213 END IF
214 END IF
215 *
216 RETURN
217 *
218 * End of CHPR .
219 *
220 END
2 * .. Scalar Arguments ..
3 REAL ALPHA
4 INTEGER INCX,N
5 CHARACTER UPLO
6 * ..
7 * .. Array Arguments ..
8 COMPLEX AP(*),X(*)
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * CHPR performs the hermitian rank 1 operation
15 *
16 * A := alpha*x*x**H + 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 - REAL .
43 * On entry, ALPHA specifies the scalar alpha.
44 * Unchanged on exit.
45 *
46 * X - COMPLEX 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 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 * Further Details
78 * ===============
79 *
80 * Level 2 Blas routine.
81 *
82 * -- Written on 22-October-1986.
83 * Jack Dongarra, Argonne National Lab.
84 * Jeremy Du Croz, Nag Central Office.
85 * Sven Hammarling, Nag Central Office.
86 * Richard Hanson, Sandia National Labs.
87 *
88 * =====================================================================
89 *
90 * .. Parameters ..
91 COMPLEX ZERO
92 PARAMETER (ZERO= (0.0E+0,0.0E+0))
93 * ..
94 * .. Local Scalars ..
95 COMPLEX TEMP
96 INTEGER I,INFO,IX,J,JX,K,KK,KX
97 * ..
98 * .. External Functions ..
99 LOGICAL LSAME
100 EXTERNAL LSAME
101 * ..
102 * .. External Subroutines ..
103 EXTERNAL XERBLA
104 * ..
105 * .. Intrinsic Functions ..
106 INTRINSIC CONJG,REAL
107 * ..
108 *
109 * Test the input parameters.
110 *
111 INFO = 0
112 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
113 INFO = 1
114 ELSE IF (N.LT.0) THEN
115 INFO = 2
116 ELSE IF (INCX.EQ.0) THEN
117 INFO = 5
118 END IF
119 IF (INFO.NE.0) THEN
120 CALL XERBLA('CHPR ',INFO)
121 RETURN
122 END IF
123 *
124 * Quick return if possible.
125 *
126 IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
127 *
128 * Set the start point in X if the increment is not unity.
129 *
130 IF (INCX.LE.0) THEN
131 KX = 1 - (N-1)*INCX
132 ELSE IF (INCX.NE.1) THEN
133 KX = 1
134 END IF
135 *
136 * Start the operations. In this version the elements of the array AP
137 * are accessed sequentially with one pass through AP.
138 *
139 KK = 1
140 IF (LSAME(UPLO,'U')) THEN
141 *
142 * Form A when upper triangle is stored in AP.
143 *
144 IF (INCX.EQ.1) THEN
145 DO 20 J = 1,N
146 IF (X(J).NE.ZERO) THEN
147 TEMP = ALPHA*CONJG(X(J))
148 K = KK
149 DO 10 I = 1,J - 1
150 AP(K) = AP(K) + X(I)*TEMP
151 K = K + 1
152 10 CONTINUE
153 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
154 ELSE
155 AP(KK+J-1) = REAL(AP(KK+J-1))
156 END IF
157 KK = KK + J
158 20 CONTINUE
159 ELSE
160 JX = KX
161 DO 40 J = 1,N
162 IF (X(JX).NE.ZERO) THEN
163 TEMP = ALPHA*CONJG(X(JX))
164 IX = KX
165 DO 30 K = KK,KK + J - 2
166 AP(K) = AP(K) + X(IX)*TEMP
167 IX = IX + INCX
168 30 CONTINUE
169 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
170 ELSE
171 AP(KK+J-1) = REAL(AP(KK+J-1))
172 END IF
173 JX = JX + INCX
174 KK = KK + J
175 40 CONTINUE
176 END IF
177 ELSE
178 *
179 * Form A when lower triangle is stored in AP.
180 *
181 IF (INCX.EQ.1) THEN
182 DO 60 J = 1,N
183 IF (X(J).NE.ZERO) THEN
184 TEMP = ALPHA*CONJG(X(J))
185 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J))
186 K = KK + 1
187 DO 50 I = J + 1,N
188 AP(K) = AP(K) + X(I)*TEMP
189 K = K + 1
190 50 CONTINUE
191 ELSE
192 AP(KK) = REAL(AP(KK))
193 END IF
194 KK = KK + N - J + 1
195 60 CONTINUE
196 ELSE
197 JX = KX
198 DO 80 J = 1,N
199 IF (X(JX).NE.ZERO) THEN
200 TEMP = ALPHA*CONJG(X(JX))
201 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX))
202 IX = JX
203 DO 70 K = KK + 1,KK + N - J
204 IX = IX + INCX
205 AP(K) = AP(K) + X(IX)*TEMP
206 70 CONTINUE
207 ELSE
208 AP(KK) = REAL(AP(KK))
209 END IF
210 JX = JX + INCX
211 KK = KK + N - J + 1
212 80 CONTINUE
213 END IF
214 END IF
215 *
216 RETURN
217 *
218 * End of CHPR .
219 *
220 END