1 SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 2* .. Scalar Arguments .. 3 REAL ALPHA,BETA 4 INTEGER INCX,INCY,N 5 CHARACTER UPLO 6* .. 7* .. Array Arguments .. 8 REAL AP(*),X(*),Y(*) 9* .. 10* 11* Purpose 12* ======= 13* 14* SSPMV 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 - REAL . 43* On entry, ALPHA specifies the scalar alpha. 44* Unchanged on exit. 45* 46* AP - REAL 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 - REAL 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 - REAL . 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 - REAL 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 REAL ONE,ZERO 102 PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) 103* .. 104* .. Local Scalars .. 105 REAL 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('SSPMV ',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 SSPMV . 264* 265 END 266