1 SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 2 * .. Scalar Arguments .. 3 DOUBLE PRECISION ALPHA,BETA 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 * DSPMV performs the matrix-vector operation 15 * 16 * y := alpha*A*x + beta*y, 17 * 18 * where alpha and beta are scalars, x and y are n element vectors and 19 * A is an 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 * AP - DOUBLE PRECISION array of DIMENSION at least 47 * ( ( n*( n + 1 ) )/2 ). 48 * Before entry with UPLO = 'U' or 'u', the array AP must 49 * contain the upper triangular part of the symmetric matrix 50 * packed sequentially, column by column, so that AP( 1 ) 51 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 52 * and a( 2, 2 ) respectively, and so on. 53 * Before entry with UPLO = 'L' or 'l', the array AP must 54 * contain the lower triangular part of the symmetric matrix 55 * packed sequentially, column by column, so that AP( 1 ) 56 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 57 * and a( 3, 1 ) respectively, and so on. 58 * Unchanged on exit. 59 * 60 * X - DOUBLE PRECISION array of dimension at least 61 * ( 1 + ( n - 1 )*abs( INCX ) ). 62 * Before entry, the incremented array X must contain the n 63 * element vector x. 64 * Unchanged on exit. 65 * 66 * INCX - INTEGER. 67 * On entry, INCX specifies the increment for the elements of 68 * X. INCX must not be zero. 69 * Unchanged on exit. 70 * 71 * BETA - DOUBLE PRECISION. 72 * On entry, BETA specifies the scalar beta. When BETA is 73 * supplied as zero then Y need not be set on input. 74 * Unchanged on exit. 75 * 76 * Y - DOUBLE PRECISION array of dimension at least 77 * ( 1 + ( n - 1 )*abs( INCY ) ). 78 * Before entry, the incremented array Y must contain the n 79 * element vector y. On exit, Y is overwritten by the updated 80 * vector y. 81 * 82 * INCY - INTEGER. 83 * On entry, INCY specifies the increment for the elements of 84 * Y. INCY must not be zero. 85 * Unchanged on exit. 86 * 87 * Further Details 88 * =============== 89 * 90 * Level 2 Blas routine. 91 * 92 * -- Written on 22-October-1986. 93 * Jack Dongarra, Argonne National Lab. 94 * Jeremy Du Croz, Nag Central Office. 95 * Sven Hammarling, Nag Central Office. 96 * Richard Hanson, Sandia National Labs. 97 * 98 * ===================================================================== 99 * 100 * .. Parameters .. 101 DOUBLE PRECISION ONE,ZERO 102 PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) 103 * .. 104 * .. Local Scalars .. 105 DOUBLE PRECISION TEMP1,TEMP2 106 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 107 * .. 108 * .. External Functions .. 109 LOGICAL LSAME 110 EXTERNAL LSAME 111 * .. 112 * .. External Subroutines .. 113 EXTERNAL XERBLA 114 * .. 115 * 116 * Test the input parameters. 117 * 118 INFO = 0 119 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 120 INFO = 1 121 ELSE IF (N.LT.0) THEN 122 INFO = 2 123 ELSE IF (INCX.EQ.0) THEN 124 INFO = 6 125 ELSE IF (INCY.EQ.0) THEN 126 INFO = 9 127 END IF 128 IF (INFO.NE.0) THEN 129 CALL XERBLA('DSPMV ',INFO) 130 RETURN 131 END IF 132 * 133 * Quick return if possible. 134 * 135 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 136 * 137 * Set up the start points in X and Y. 138 * 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 * 150 * Start the operations. In this version the elements of the array AP 151 * are accessed sequentially with one pass through AP. 152 * 153 * First form y := beta*y. 154 * 155 IF (BETA.NE.ONE) THEN 156 IF (INCY.EQ.1) THEN 157 IF (BETA.EQ.ZERO) THEN 158 DO 10 I = 1,N 159 Y(I) = ZERO 160 10 CONTINUE 161 ELSE 162 DO 20 I = 1,N 163 Y(I) = BETA*Y(I) 164 20 CONTINUE 165 END IF 166 ELSE 167 IY = KY 168 IF (BETA.EQ.ZERO) THEN 169 DO 30 I = 1,N 170 Y(IY) = ZERO 171 IY = IY + INCY 172 30 CONTINUE 173 ELSE 174 DO 40 I = 1,N 175 Y(IY) = BETA*Y(IY) 176 IY = IY + INCY 177 40 CONTINUE 178 END IF 179 END IF 180 END IF 181 IF (ALPHA.EQ.ZERO) RETURN 182 KK = 1 183 IF (LSAME(UPLO,'U')) THEN 184 * 185 * Form y when AP contains the upper triangle. 186 * 187 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 188 DO 60 J = 1,N 189 TEMP1 = ALPHA*X(J) 190 TEMP2 = ZERO 191 K = KK 192 DO 50 I = 1,J - 1 193 Y(I) = Y(I) + TEMP1*AP(K) 194 TEMP2 = TEMP2 + AP(K)*X(I) 195 K = K + 1 196 50 CONTINUE 197 Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 198 KK = KK + J 199 60 CONTINUE 200 ELSE 201 JX = KX 202 JY = KY 203 DO 80 J = 1,N 204 TEMP1 = ALPHA*X(JX) 205 TEMP2 = ZERO 206 IX = KX 207 IY = KY 208 DO 70 K = KK,KK + J - 2 209 Y(IY) = Y(IY) + TEMP1*AP(K) 210 TEMP2 = TEMP2 + AP(K)*X(IX) 211 IX = IX + INCX 212 IY = IY + INCY 213 70 CONTINUE 214 Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 215 JX = JX + INCX 216 JY = JY + INCY 217 KK = KK + J 218 80 CONTINUE 219 END IF 220 ELSE 221 * 222 * Form y when AP contains the lower triangle. 223 * 224 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 225 DO 100 J = 1,N 226 TEMP1 = ALPHA*X(J) 227 TEMP2 = ZERO 228 Y(J) = Y(J) + TEMP1*AP(KK) 229 K = KK + 1 230 DO 90 I = J + 1,N 231 Y(I) = Y(I) + TEMP1*AP(K) 232 TEMP2 = TEMP2 + AP(K)*X(I) 233 K = K + 1 234 90 CONTINUE 235 Y(J) = Y(J) + ALPHA*TEMP2 236 KK = KK + (N-J+1) 237 100 CONTINUE 238 ELSE 239 JX = KX 240 JY = KY 241 DO 120 J = 1,N 242 TEMP1 = ALPHA*X(JX) 243 TEMP2 = ZERO 244 Y(JY) = Y(JY) + TEMP1*AP(KK) 245 IX = JX 246 IY = JY 247 DO 110 K = KK + 1,KK + N - J 248 IX = IX + INCX 249 IY = IY + INCY 250 Y(IY) = Y(IY) + TEMP1*AP(K) 251 TEMP2 = TEMP2 + AP(K)*X(IX) 252 110 CONTINUE 253 Y(JY) = Y(JY) + ALPHA*TEMP2 254 JX = JX + INCX 255 JY = JY + INCY 256 KK = KK + (N-J+1) 257 120 CONTINUE 258 END IF 259 END IF 260 * 261 RETURN 262 * 263 * End of DSPMV . 264 * 265 END 266
