1 SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 2* .. Scalar Arguments .. 3 DOUBLE COMPLEX ALPHA,BETA 4 INTEGER INCX,INCY,N 5 CHARACTER UPLO 6* .. 7* .. Array Arguments .. 8 DOUBLE COMPLEX AP(*),X(*),Y(*) 9* .. 10* 11* Purpose 12* ======= 13* 14* ZHPMV 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 hermitian 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 - COMPLEX*16 . 43* On entry, ALPHA specifies the scalar alpha. 44* Unchanged on exit. 45* 46* AP - COMPLEX*16 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 hermitian 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 hermitian 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* Note that the imaginary parts of the diagonal elements need 59* not be set and are assumed to be zero. 60* Unchanged on exit. 61* 62* X - COMPLEX*16 array of dimension at least 63* ( 1 + ( n - 1 )*abs( INCX ) ). 64* Before entry, the incremented array X must contain the n 65* element vector x. 66* Unchanged on exit. 67* 68* INCX - INTEGER. 69* On entry, INCX specifies the increment for the elements of 70* X. INCX must not be zero. 71* Unchanged on exit. 72* 73* BETA - COMPLEX*16 . 74* On entry, BETA specifies the scalar beta. When BETA is 75* supplied as zero then Y need not be set on input. 76* Unchanged on exit. 77* 78* Y - COMPLEX*16 array of dimension at least 79* ( 1 + ( n - 1 )*abs( INCY ) ). 80* Before entry, the incremented array Y must contain the n 81* element vector y. On exit, Y is overwritten by the updated 82* vector y. 83* 84* INCY - INTEGER. 85* On entry, INCY specifies the increment for the elements of 86* Y. INCY must not be zero. 87* Unchanged on exit. 88* 89* Further Details 90* =============== 91* 92* Level 2 Blas routine. 93* 94* -- Written on 22-October-1986. 95* Jack Dongarra, Argonne National Lab. 96* Jeremy Du Croz, Nag Central Office. 97* Sven Hammarling, Nag Central Office. 98* Richard Hanson, Sandia National Labs. 99* 100* ===================================================================== 101* 102* .. Parameters .. 103 DOUBLE COMPLEX ONE 104 PARAMETER (ONE= (1.0D+0,0.0D+0)) 105 DOUBLE COMPLEX ZERO 106 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 107* .. 108* .. Local Scalars .. 109 DOUBLE COMPLEX TEMP1,TEMP2 110 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 111* .. 112* .. External Functions .. 113 LOGICAL LSAME 114 EXTERNAL LSAME 115* .. 116* .. External Subroutines .. 117 EXTERNAL XERBLA 118* .. 119* .. Intrinsic Functions .. 120 INTRINSIC DBLE,DCONJG 121* .. 122* 123* Test the input parameters. 124* 125 INFO = 0 126 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 127 INFO = 1 128 ELSE IF (N.LT.0) THEN 129 INFO = 2 130 ELSE IF (INCX.EQ.0) THEN 131 INFO = 6 132 ELSE IF (INCY.EQ.0) THEN 133 INFO = 9 134 END IF 135 IF (INFO.NE.0) THEN 136 CALL XERBLA('ZHPMV ',INFO) 137 RETURN 138 END IF 139* 140* Quick return if possible. 141* 142 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 143* 144* Set up the start points in X and Y. 145* 146 IF (INCX.GT.0) THEN 147 KX = 1 148 ELSE 149 KX = 1 - (N-1)*INCX 150 END IF 151 IF (INCY.GT.0) THEN 152 KY = 1 153 ELSE 154 KY = 1 - (N-1)*INCY 155 END IF 156* 157* Start the operations. In this version the elements of the array AP 158* are accessed sequentially with one pass through AP. 159* 160* First form y := beta*y. 161* 162 IF (BETA.NE.ONE) THEN 163 IF (INCY.EQ.1) THEN 164 IF (BETA.EQ.ZERO) THEN 165 DO 10 I = 1,N 166 Y(I) = ZERO 167 10 CONTINUE 168 ELSE 169 DO 20 I = 1,N 170 Y(I) = BETA*Y(I) 171 20 CONTINUE 172 END IF 173 ELSE 174 IY = KY 175 IF (BETA.EQ.ZERO) THEN 176 DO 30 I = 1,N 177 Y(IY) = ZERO 178 IY = IY + INCY 179 30 CONTINUE 180 ELSE 181 DO 40 I = 1,N 182 Y(IY) = BETA*Y(IY) 183 IY = IY + INCY 184 40 CONTINUE 185 END IF 186 END IF 187 END IF 188 IF (ALPHA.EQ.ZERO) RETURN 189 KK = 1 190 IF (LSAME(UPLO,'U')) THEN 191* 192* Form y when AP contains the upper triangle. 193* 194 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 195 DO 60 J = 1,N 196 TEMP1 = ALPHA*X(J) 197 TEMP2 = ZERO 198 K = KK 199 DO 50 I = 1,J - 1 200 Y(I) = Y(I) + TEMP1*AP(K) 201 TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) 202 K = K + 1 203 50 CONTINUE 204 Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 205 KK = KK + J 206 60 CONTINUE 207 ELSE 208 JX = KX 209 JY = KY 210 DO 80 J = 1,N 211 TEMP1 = ALPHA*X(JX) 212 TEMP2 = ZERO 213 IX = KX 214 IY = KY 215 DO 70 K = KK,KK + J - 2 216 Y(IY) = Y(IY) + TEMP1*AP(K) 217 TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) 218 IX = IX + INCX 219 IY = IY + INCY 220 70 CONTINUE 221 Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 222 JX = JX + INCX 223 JY = JY + INCY 224 KK = KK + J 225 80 CONTINUE 226 END IF 227 ELSE 228* 229* Form y when AP contains the lower triangle. 230* 231 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 232 DO 100 J = 1,N 233 TEMP1 = ALPHA*X(J) 234 TEMP2 = ZERO 235 Y(J) = Y(J) + TEMP1*DBLE(AP(KK)) 236 K = KK + 1 237 DO 90 I = J + 1,N 238 Y(I) = Y(I) + TEMP1*AP(K) 239 TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) 240 K = K + 1 241 90 CONTINUE 242 Y(J) = Y(J) + ALPHA*TEMP2 243 KK = KK + (N-J+1) 244 100 CONTINUE 245 ELSE 246 JX = KX 247 JY = KY 248 DO 120 J = 1,N 249 TEMP1 = ALPHA*X(JX) 250 TEMP2 = ZERO 251 Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK)) 252 IX = JX 253 IY = JY 254 DO 110 K = KK + 1,KK + N - J 255 IX = IX + INCX 256 IY = IY + INCY 257 Y(IY) = Y(IY) + TEMP1*AP(K) 258 TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) 259 110 CONTINUE 260 Y(JY) = Y(JY) + ALPHA*TEMP2 261 JX = JX + INCX 262 JY = JY + INCY 263 KK = KK + (N-J+1) 264 120 CONTINUE 265 END IF 266 END IF 267* 268 RETURN 269* 270* End of ZHPMV . 271* 272 END 273