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
