1 SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 2 * .. Scalar Arguments .. 3 COMPLEX ALPHA 4 INTEGER INCX,INCY,N 5 CHARACTER UPLO 6 * .. 7 * .. Array Arguments .. 8 COMPLEX AP(*),X(*),Y(*) 9 * .. 10 * 11 * Purpose 12 * ======= 13 * 14 * CHPR2 performs the hermitian rank 2 operation 15 * 16 * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, 17 * 18 * where alpha is a scalar, x and y are n element vectors and A is an 19 * 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 . 43 * On entry, ALPHA specifies the scalar alpha. 44 * Unchanged on exit. 45 * 46 * X - COMPLEX 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 - COMPLEX 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 - COMPLEX 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 hermitian 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 hermitian 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 * Note that the imaginary parts of the diagonal elements need 85 * not be set, they are assumed to be zero, and on exit they 86 * are set to zero. 87 * 88 * Further Details 89 * =============== 90 * 91 * Level 2 Blas routine. 92 * 93 * -- Written on 22-October-1986. 94 * Jack Dongarra, Argonne National Lab. 95 * Jeremy Du Croz, Nag Central Office. 96 * Sven Hammarling, Nag Central Office. 97 * Richard Hanson, Sandia National Labs. 98 * 99 * ===================================================================== 100 * 101 * .. Parameters .. 102 COMPLEX ZERO 103 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 104 * .. 105 * .. Local Scalars .. 106 COMPLEX TEMP1,TEMP2 107 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 108 * .. 109 * .. External Functions .. 110 LOGICAL LSAME 111 EXTERNAL LSAME 112 * .. 113 * .. External Subroutines .. 114 EXTERNAL XERBLA 115 * .. 116 * .. Intrinsic Functions .. 117 INTRINSIC CONJG,REAL 118 * .. 119 * 120 * Test the input parameters. 121 * 122 INFO = 0 123 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 124 INFO = 1 125 ELSE IF (N.LT.0) THEN 126 INFO = 2 127 ELSE IF (INCX.EQ.0) THEN 128 INFO = 5 129 ELSE IF (INCY.EQ.0) THEN 130 INFO = 7 131 END IF 132 IF (INFO.NE.0) THEN 133 CALL XERBLA('CHPR2 ',INFO) 134 RETURN 135 END IF 136 * 137 * Quick return if possible. 138 * 139 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 140 * 141 * Set up the start points in X and Y if the increments are not both 142 * unity. 143 * 144 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 145 IF (INCX.GT.0) THEN 146 KX = 1 147 ELSE 148 KX = 1 - (N-1)*INCX 149 END IF 150 IF (INCY.GT.0) THEN 151 KY = 1 152 ELSE 153 KY = 1 - (N-1)*INCY 154 END IF 155 JX = KX 156 JY = KY 157 END IF 158 * 159 * Start the operations. In this version the elements of the array AP 160 * are accessed sequentially with one pass through AP. 161 * 162 KK = 1 163 IF (LSAME(UPLO,'U')) THEN 164 * 165 * Form A when upper triangle is stored in AP. 166 * 167 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 168 DO 20 J = 1,N 169 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 170 TEMP1 = ALPHA*CONJG(Y(J)) 171 TEMP2 = CONJG(ALPHA*X(J)) 172 K = KK 173 DO 10 I = 1,J - 1 174 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 175 K = K + 1 176 10 CONTINUE 177 AP(KK+J-1) = REAL(AP(KK+J-1)) + 178 + REAL(X(J)*TEMP1+Y(J)*TEMP2) 179 ELSE 180 AP(KK+J-1) = REAL(AP(KK+J-1)) 181 END IF 182 KK = KK + J 183 20 CONTINUE 184 ELSE 185 DO 40 J = 1,N 186 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 187 TEMP1 = ALPHA*CONJG(Y(JY)) 188 TEMP2 = CONJG(ALPHA*X(JX)) 189 IX = KX 190 IY = KY 191 DO 30 K = KK,KK + J - 2 192 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 193 IX = IX + INCX 194 IY = IY + INCY 195 30 CONTINUE 196 AP(KK+J-1) = REAL(AP(KK+J-1)) + 197 + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) 198 ELSE 199 AP(KK+J-1) = REAL(AP(KK+J-1)) 200 END IF 201 JX = JX + INCX 202 JY = JY + INCY 203 KK = KK + J 204 40 CONTINUE 205 END IF 206 ELSE 207 * 208 * Form A when lower triangle is stored in AP. 209 * 210 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 211 DO 60 J = 1,N 212 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 213 TEMP1 = ALPHA*CONJG(Y(J)) 214 TEMP2 = CONJG(ALPHA*X(J)) 215 AP(KK) = REAL(AP(KK)) + 216 + REAL(X(J)*TEMP1+Y(J)*TEMP2) 217 K = KK + 1 218 DO 50 I = J + 1,N 219 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 220 K = K + 1 221 50 CONTINUE 222 ELSE 223 AP(KK) = REAL(AP(KK)) 224 END IF 225 KK = KK + N - J + 1 226 60 CONTINUE 227 ELSE 228 DO 80 J = 1,N 229 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 230 TEMP1 = ALPHA*CONJG(Y(JY)) 231 TEMP2 = CONJG(ALPHA*X(JX)) 232 AP(KK) = REAL(AP(KK)) + 233 + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) 234 IX = JX 235 IY = JY 236 DO 70 K = KK + 1,KK + N - J 237 IX = IX + INCX 238 IY = IY + INCY 239 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 240 70 CONTINUE 241 ELSE 242 AP(KK) = REAL(AP(KK)) 243 END IF 244 JX = JX + INCX 245 JY = JY + INCY 246 KK = KK + N - J + 1 247 80 CONTINUE 248 END IF 249 END IF 250 * 251 RETURN 252 * 253 * End of CHPR2 . 254 * 255 END 256
