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1.1 bertrand 1: SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
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, LDA, N
11: COMPLEX*16 ALPHA
12: * ..
13: * .. Array Arguments ..
14: COMPLEX*16 A( LDA, * ), X( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZSYR performs the symmetric rank 1 operation
21: *
22: * A := alpha*x*( x' ) + 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.
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 array A is to be referenced as
33: * follows:
34: *
35: * UPLO = 'U' or 'u' Only the upper triangular part of A
36: * is to be referenced.
37: *
38: * UPLO = 'L' or 'l' Only the lower triangular part of A
39: * is to be referenced.
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: * A (input/output) COMPLEX*16 array, dimension ( LDA, N )
64: * Before entry, with UPLO = 'U' or 'u', the leading n by n
65: * upper triangular part of the array A must contain the upper
66: * triangular part of the symmetric matrix and the strictly
67: * lower triangular part of A is not referenced. On exit, the
68: * upper triangular part of the array A is overwritten by the
69: * upper triangular part of the updated matrix.
70: * Before entry, with UPLO = 'L' or 'l', the leading n by n
71: * lower triangular part of the array A must contain the lower
72: * triangular part of the symmetric matrix and the strictly
73: * upper triangular part of A is not referenced. On exit, the
74: * lower triangular part of the array A is overwritten by the
75: * lower triangular part of the updated matrix.
76: *
77: * LDA (input) INTEGER
78: * On entry, LDA specifies the first dimension of A as declared
79: * in the calling (sub) program. LDA must be at least
80: * max( 1, N ).
81: * Unchanged on exit.
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, KX
91: COMPLEX*16 TEMP
92: * ..
93: * .. External Functions ..
94: LOGICAL LSAME
95: EXTERNAL LSAME
96: * ..
97: * .. External Subroutines ..
98: EXTERNAL XERBLA
99: * ..
100: * .. Intrinsic Functions ..
101: INTRINSIC MAX
102: * ..
103: * .. Executable Statements ..
104: *
105: * Test the input parameters.
106: *
107: INFO = 0
108: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
109: INFO = 1
110: ELSE IF( N.LT.0 ) THEN
111: INFO = 2
112: ELSE IF( INCX.EQ.0 ) THEN
113: INFO = 5
114: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
115: INFO = 7
116: END IF
117: IF( INFO.NE.0 ) THEN
118: CALL XERBLA( 'ZSYR ', INFO )
119: RETURN
120: END IF
121: *
122: * Quick return if possible.
123: *
124: IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
125: $ RETURN
126: *
127: * Set the start point in X if the increment is not unity.
128: *
129: IF( INCX.LE.0 ) THEN
130: KX = 1 - ( N-1 )*INCX
131: ELSE IF( INCX.NE.1 ) THEN
132: KX = 1
133: END IF
134: *
135: * Start the operations. In this version the elements of A are
136: * accessed sequentially with one pass through the triangular part
137: * of A.
138: *
139: IF( LSAME( UPLO, 'U' ) ) THEN
140: *
141: * Form A when A is stored in upper triangle.
142: *
143: IF( INCX.EQ.1 ) THEN
144: DO 20 J = 1, N
145: IF( X( J ).NE.ZERO ) THEN
146: TEMP = ALPHA*X( J )
147: DO 10 I = 1, J
148: A( I, J ) = A( I, J ) + X( I )*TEMP
149: 10 CONTINUE
150: END IF
151: 20 CONTINUE
152: ELSE
153: JX = KX
154: DO 40 J = 1, N
155: IF( X( JX ).NE.ZERO ) THEN
156: TEMP = ALPHA*X( JX )
157: IX = KX
158: DO 30 I = 1, J
159: A( I, J ) = A( I, J ) + X( IX )*TEMP
160: IX = IX + INCX
161: 30 CONTINUE
162: END IF
163: JX = JX + INCX
164: 40 CONTINUE
165: END IF
166: ELSE
167: *
168: * Form A when A is stored in lower triangle.
169: *
170: IF( INCX.EQ.1 ) THEN
171: DO 60 J = 1, N
172: IF( X( J ).NE.ZERO ) THEN
173: TEMP = ALPHA*X( J )
174: DO 50 I = J, N
175: A( I, J ) = A( I, J ) + X( I )*TEMP
176: 50 CONTINUE
177: END IF
178: 60 CONTINUE
179: ELSE
180: JX = KX
181: DO 80 J = 1, N
182: IF( X( JX ).NE.ZERO ) THEN
183: TEMP = ALPHA*X( JX )
184: IX = JX
185: DO 70 I = J, N
186: A( I, J ) = A( I, J ) + X( IX )*TEMP
187: IX = IX + INCX
188: 70 CONTINUE
189: END IF
190: JX = JX + INCX
191: 80 CONTINUE
192: END IF
193: END IF
194: *
195: RETURN
196: *
197: * End of ZSYR
198: *
199: END