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
