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*conjg( 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, 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
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