1 SUBROUTINE DSYR2F ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
2 * .. Scalar Arguments ..
4 INTEGER INCX, INCY, LDA, N
6 * .. Array Arguments ..
7 DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
13 * DSYR2 performs the symmetric rank 2 operation
15 * A := alpha*x*y' + alpha*y*x' + A,
17 * where alpha is a scalar, x and y are n element vectors and A is an n
18 * by n symmetric matrix.
24 * On entry, UPLO specifies whether the upper or lower
25 * triangular part of the array A is to be referenced as
28 * UPLO = 'U' or 'u' Only the upper triangular part of A
29 * is to be referenced.
31 * UPLO = 'L' or 'l' Only the lower triangular part of A
32 * is to be referenced.
37 * On entry, N specifies the order of the matrix A.
38 * N must be at least zero.
41 * ALPHA - DOUBLE PRECISION.
42 * On entry, ALPHA specifies the scalar alpha.
45 * X - DOUBLE PRECISION array of dimension at least
46 * ( 1 + ( n - 1 )*abs( INCX ) ).
47 * Before entry, the incremented array X must contain the n
52 * On entry, INCX specifies the increment for the elements of
53 * X. INCX must not be zero.
56 * Y - DOUBLE PRECISION array of dimension at least
57 * ( 1 + ( n - 1 )*abs( INCY ) ).
58 * Before entry, the incremented array Y must contain the n
63 * On entry, INCY specifies the increment for the elements of
64 * Y. INCY must not be zero.
67 * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
68 * Before entry with UPLO = 'U' or 'u', the leading n by n
69 * upper triangular part of the array A must contain the upper
70 * triangular part of the symmetric matrix and the strictly
71 * lower triangular part of A is not referenced. On exit, the
72 * upper triangular part of the array A is overwritten by the
73 * upper triangular part of the updated matrix.
74 * Before entry with UPLO = 'L' or 'l', the leading n by n
75 * lower triangular part of the array A must contain the lower
76 * triangular part of the symmetric matrix and the strictly
77 * upper triangular part of A is not referenced. On exit, the
78 * lower triangular part of the array A is overwritten by the
79 * lower triangular part of the updated matrix.
82 * On entry, LDA specifies the first dimension of A as declared
83 * in the calling (sub) program. LDA must be at least
88 * Level 2 Blas routine.
90 * -- Written on 22-October-1986.
91 * Jack Dongarra, Argonne National Lab.
92 * Jeremy Du Croz, Nag Central Office.
93 * Sven Hammarling, Nag Central Office.
94 * Richard Hanson, Sandia National Labs.
99 PARAMETER ( ZERO = 0.0D+0 )
100 * .. Local Scalars ..
101 DOUBLE PRECISION TEMP1, TEMP2
102 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
103 * .. External Functions ..
106 * .. External Subroutines ..
108 * .. Intrinsic Functions ..
111 * .. Executable Statements ..
113 * Test the input parameters.
116 IF ( .NOT.LSAME( UPLO, 'U' ).AND.
117 $ .NOT.LSAME( UPLO, 'L' ) )THEN
119 ELSE IF( N.LT.0 )THEN
121 ELSE IF( INCX.EQ.0 )THEN
123 ELSE IF( INCY.EQ.0 )THEN
125 ELSE IF( LDA.LT.MAX( 1, N ) )THEN
129 CALL XERBLA( 'DSYR2 ', INFO )
133 * Quick return if possible.
135 IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
138 * Set up the start points in X and Y if the increments are not both
141 IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
145 KX = 1 - ( N - 1 )*INCX
150 KY = 1 - ( N - 1 )*INCY
156 * Start the operations. In this version the elements of A are
157 * accessed sequentially with one pass through the triangular part
160 IF( LSAME( UPLO, 'U' ) )THEN
162 * Form A when A is stored in the upper triangle.
164 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
166 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
170 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
176 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
177 TEMP1 = ALPHA*Y( JY )
178 TEMP2 = ALPHA*X( JX )
182 A( I, J ) = A( I, J ) + X( IX )*TEMP1
194 * Form A when A is stored in the lower triangle.
196 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
198 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
202 A( I, J ) = A( I, J ) + X( I )*TEMP1 + Y( I )*TEMP2
208 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
209 TEMP1 = ALPHA*Y( JY )
210 TEMP2 = ALPHA*X( JX )
214 A( I, J ) = A( I, J ) + X( IX )*TEMP1