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