1 SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP) 2 * .. Scalar Arguments .. 3 REAL ALPHA 4 INTEGER INCX,N 5 CHARACTER UPLO 6 * .. 7 * .. Array Arguments .. 8 COMPLEX AP(*),X(*) 9 * .. 10 * 11 * Purpose 12 * ======= 13 * 14 * CHPR performs the hermitian rank 1 operation 15 * 16 * A := alpha*x*conjg( x' ) + A, 17 * 18 * where alpha is a real scalar, x is an n element vector 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 - REAL . 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 * AP - COMPLEX array of DIMENSION at least 58 * ( ( n*( n + 1 ) )/2 ). 59 * Before entry with UPLO = 'U' or 'u', the array AP must 60 * contain the upper triangular part of the hermitian matrix 61 * packed sequentially, column by column, so that AP( 1 ) 62 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 63 * and a( 2, 2 ) respectively, and so on. On exit, the array 64 * AP is overwritten by the upper triangular part of the 65 * updated matrix. 66 * Before entry with UPLO = 'L' or 'l', the array AP must 67 * contain the lower triangular part of the hermitian matrix 68 * packed sequentially, column by column, so that AP( 1 ) 69 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 70 * and a( 3, 1 ) respectively, and so on. On exit, the array 71 * AP is overwritten by the lower triangular part of the 72 * updated matrix. 73 * Note that the imaginary parts of the diagonal elements need 74 * not be set, they are assumed to be zero, and on exit they 75 * are set to zero. 76 * 77 * Further Details 78 * =============== 79 * 80 * Level 2 Blas routine. 81 * 82 * -- Written on 22-October-1986. 83 * Jack Dongarra, Argonne National Lab. 84 * Jeremy Du Croz, Nag Central Office. 85 * Sven Hammarling, Nag Central Office. 86 * Richard Hanson, Sandia National Labs. 87 * 88 * ===================================================================== 89 * 90 * .. Parameters .. 91 COMPLEX ZERO 92 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 93 * .. 94 * .. Local Scalars .. 95 COMPLEX TEMP 96 INTEGER I,INFO,IX,J,JX,K,KK,KX 97 * .. 98 * .. External Functions .. 99 LOGICAL LSAME 100 EXTERNAL LSAME 101 * .. 102 * .. External Subroutines .. 103 EXTERNAL XERBLA 104 * .. 105 * .. Intrinsic Functions .. 106 INTRINSIC CONJG,REAL 107 * .. 108 * 109 * Test the input parameters. 110 * 111 INFO = 0 112 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 113 INFO = 1 114 ELSE IF (N.LT.0) THEN 115 INFO = 2 116 ELSE IF (INCX.EQ.0) THEN 117 INFO = 5 118 END IF 119 IF (INFO.NE.0) THEN 120 CALL XERBLA('CHPR ',INFO) 121 RETURN 122 END IF 123 * 124 * Quick return if possible. 125 * 126 IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN 127 * 128 * Set the start point in X if the increment is not unity. 129 * 130 IF (INCX.LE.0) THEN 131 KX = 1 - (N-1)*INCX 132 ELSE IF (INCX.NE.1) THEN 133 KX = 1 134 END IF 135 * 136 * Start the operations. In this version the elements of the array AP 137 * are accessed sequentially with one pass through AP. 138 * 139 KK = 1 140 IF (LSAME(UPLO,'U')) THEN 141 * 142 * Form A when upper triangle is stored in AP. 143 * 144 IF (INCX.EQ.1) THEN 145 DO 20 J = 1,N 146 IF (X(J).NE.ZERO) THEN 147 TEMP = ALPHA*CONJG(X(J)) 148 K = KK 149 DO 10 I = 1,J - 1 150 AP(K) = AP(K) + X(I)*TEMP 151 K = K + 1 152 10 CONTINUE 153 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP) 154 ELSE 155 AP(KK+J-1) = REAL(AP(KK+J-1)) 156 END IF 157 KK = KK + J 158 20 CONTINUE 159 ELSE 160 JX = KX 161 DO 40 J = 1,N 162 IF (X(JX).NE.ZERO) THEN 163 TEMP = ALPHA*CONJG(X(JX)) 164 IX = KX 165 DO 30 K = KK,KK + J - 2 166 AP(K) = AP(K) + X(IX)*TEMP 167 IX = IX + INCX 168 30 CONTINUE 169 AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP) 170 ELSE 171 AP(KK+J-1) = REAL(AP(KK+J-1)) 172 END IF 173 JX = JX + INCX 174 KK = KK + J 175 40 CONTINUE 176 END IF 177 ELSE 178 * 179 * Form A when lower triangle is stored in AP. 180 * 181 IF (INCX.EQ.1) THEN 182 DO 60 J = 1,N 183 IF (X(J).NE.ZERO) THEN 184 TEMP = ALPHA*CONJG(X(J)) 185 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J)) 186 K = KK + 1 187 DO 50 I = J + 1,N 188 AP(K) = AP(K) + X(I)*TEMP 189 K = K + 1 190 50 CONTINUE 191 ELSE 192 AP(KK) = REAL(AP(KK)) 193 END IF 194 KK = KK + N - J + 1 195 60 CONTINUE 196 ELSE 197 JX = KX 198 DO 80 J = 1,N 199 IF (X(JX).NE.ZERO) THEN 200 TEMP = ALPHA*CONJG(X(JX)) 201 AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX)) 202 IX = JX 203 DO 70 K = KK + 1,KK + N - J 204 IX = IX + INCX 205 AP(K) = AP(K) + X(IX)*TEMP 206 70 CONTINUE 207 ELSE 208 AP(KK) = REAL(AP(KK)) 209 END IF 210 JX = JX + INCX 211 KK = KK + N - J + 1 212 80 CONTINUE 213 END IF 214 END IF 215 * 216 RETURN 217 * 218 * End of CHPR . 219 * 220 END 221
