1 SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 2* .. Scalar Arguments .. 3 DOUBLE PRECISION ALPHA 4 INTEGER INCX,INCY,N 5 CHARACTER UPLO 6* .. 7* .. Array Arguments .. 8 DOUBLE PRECISION AP(*),X(*),Y(*) 9* .. 10* 11* Purpose 12* ======= 13* 14* DSPR2 performs the symmetric rank 2 operation 15* 16* A := alpha*x*y' + alpha*y*x' + A, 17* 18* where alpha is a scalar, x and y are n element vectors and A is an 19* n by n symmetric 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 - DOUBLE PRECISION. 43* On entry, ALPHA specifies the scalar alpha. 44* Unchanged on exit. 45* 46* X - DOUBLE PRECISION 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* Y - DOUBLE PRECISION array of dimension at least 58* ( 1 + ( n - 1 )*abs( INCY ) ). 59* Before entry, the incremented array Y must contain the n 60* element vector y. 61* Unchanged on exit. 62* 63* INCY - INTEGER. 64* On entry, INCY specifies the increment for the elements of 65* Y. INCY must not be zero. 66* Unchanged on exit. 67* 68* AP - DOUBLE PRECISION array of DIMENSION at least 69* ( ( n*( n + 1 ) )/2 ). 70* Before entry with UPLO = 'U' or 'u', the array AP must 71* contain the upper triangular part of the symmetric matrix 72* packed sequentially, column by column, so that AP( 1 ) 73* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 74* and a( 2, 2 ) respectively, and so on. On exit, the array 75* AP is overwritten by the upper triangular part of the 76* updated matrix. 77* Before entry with UPLO = 'L' or 'l', the array AP must 78* contain the lower triangular part of the symmetric matrix 79* packed sequentially, column by column, so that AP( 1 ) 80* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 81* and a( 3, 1 ) respectively, and so on. On exit, the array 82* AP is overwritten by the lower triangular part of the 83* updated matrix. 84* 85* Further Details 86* =============== 87* 88* Level 2 Blas routine. 89* 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. 95* 96* ===================================================================== 97* 98* .. Parameters .. 99 DOUBLE PRECISION ZERO 100 PARAMETER (ZERO=0.0D+0) 101* .. 102* .. Local Scalars .. 103 DOUBLE PRECISION TEMP1,TEMP2 104 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 105* .. 106* .. External Functions .. 107 LOGICAL LSAME 108 EXTERNAL LSAME 109* .. 110* .. External Subroutines .. 111 EXTERNAL XERBLA 112* .. 113* 114* Test the input parameters. 115* 116 INFO = 0 117 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 118 INFO = 1 119 ELSE IF (N.LT.0) THEN 120 INFO = 2 121 ELSE IF (INCX.EQ.0) THEN 122 INFO = 5 123 ELSE IF (INCY.EQ.0) THEN 124 INFO = 7 125 END IF 126 IF (INFO.NE.0) THEN 127 CALL XERBLA('DSPR2 ',INFO) 128 RETURN 129 END IF 130* 131* Quick return if possible. 132* 133 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 134* 135* Set up the start points in X and Y if the increments are not both 136* unity. 137* 138 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 139 IF (INCX.GT.0) THEN 140 KX = 1 141 ELSE 142 KX = 1 - (N-1)*INCX 143 END IF 144 IF (INCY.GT.0) THEN 145 KY = 1 146 ELSE 147 KY = 1 - (N-1)*INCY 148 END IF 149 JX = KX 150 JY = KY 151 END IF 152* 153* Start the operations. In this version the elements of the array AP 154* are accessed sequentially with one pass through AP. 155* 156 KK = 1 157 IF (LSAME(UPLO,'U')) THEN 158* 159* Form A when upper triangle is stored in AP. 160* 161 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 162 DO 20 J = 1,N 163 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 164 TEMP1 = ALPHA*Y(J) 165 TEMP2 = ALPHA*X(J) 166 K = KK 167 DO 10 I = 1,J 168 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 169 K = K + 1 170 10 CONTINUE 171 END IF 172 KK = KK + J 173 20 CONTINUE 174 ELSE 175 DO 40 J = 1,N 176 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 177 TEMP1 = ALPHA*Y(JY) 178 TEMP2 = ALPHA*X(JX) 179 IX = KX 180 IY = KY 181 DO 30 K = KK,KK + J - 1 182 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 183 IX = IX + INCX 184 IY = IY + INCY 185 30 CONTINUE 186 END IF 187 JX = JX + INCX 188 JY = JY + INCY 189 KK = KK + J 190 40 CONTINUE 191 END IF 192 ELSE 193* 194* Form A when lower triangle is stored in AP. 195* 196 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 197 DO 60 J = 1,N 198 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 199 TEMP1 = ALPHA*Y(J) 200 TEMP2 = ALPHA*X(J) 201 K = KK 202 DO 50 I = J,N 203 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 204 K = K + 1 205 50 CONTINUE 206 END IF 207 KK = KK + N - J + 1 208 60 CONTINUE 209 ELSE 210 DO 80 J = 1,N 211 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 212 TEMP1 = ALPHA*Y(JY) 213 TEMP2 = ALPHA*X(JX) 214 IX = JX 215 IY = JY 216 DO 70 K = KK,KK + N - J 217 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 218 IX = IX + INCX 219 IY = IY + INCY 220 70 CONTINUE 221 END IF 222 JX = JX + INCX 223 JY = JY + INCY 224 KK = KK + N - J + 1 225 80 CONTINUE 226 END IF 227 END IF 228* 229 RETURN 230* 231* End of DSPR2 . 232* 233 END 234