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| 1 | 1 | pfleura2 | SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) |
|---|---|---|---|
| 2 | 1 | pfleura2 | * .. Scalar Arguments .. |
| 3 | 1 | pfleura2 | COMPLEX ALPHA |
| 4 | 1 | pfleura2 | INTEGER INCX,INCY,N |
| 5 | 1 | pfleura2 | CHARACTER UPLO |
| 6 | 1 | pfleura2 | * .. |
| 7 | 1 | pfleura2 | * .. Array Arguments .. |
| 8 | 1 | pfleura2 | COMPLEX AP(*),X(*),Y(*) |
| 9 | 1 | pfleura2 | * .. |
| 10 | 1 | pfleura2 | * |
| 11 | 1 | pfleura2 | * Purpose |
| 12 | 1 | pfleura2 | * ======= |
| 13 | 1 | pfleura2 | * |
| 14 | 1 | pfleura2 | * CHPR2 performs the hermitian rank 2 operation |
| 15 | 1 | pfleura2 | * |
| 16 | 1 | pfleura2 | * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, |
| 17 | 1 | pfleura2 | * |
| 18 | 1 | pfleura2 | * where alpha is a scalar, x and y are n element vectors and A is an |
| 19 | 1 | pfleura2 | * n by n hermitian matrix, supplied in packed form. |
| 20 | 1 | pfleura2 | * |
| 21 | 1 | pfleura2 | * Arguments |
| 22 | 1 | pfleura2 | * ========== |
| 23 | 1 | pfleura2 | * |
| 24 | 1 | pfleura2 | * UPLO - CHARACTER*1. |
| 25 | 1 | pfleura2 | * On entry, UPLO specifies whether the upper or lower |
| 26 | 1 | pfleura2 | * triangular part of the matrix A is supplied in the packed |
| 27 | 1 | pfleura2 | * array AP as follows: |
| 28 | 1 | pfleura2 | * |
| 29 | 1 | pfleura2 | * UPLO = 'U' or 'u' The upper triangular part of A is |
| 30 | 1 | pfleura2 | * supplied in AP. |
| 31 | 1 | pfleura2 | * |
| 32 | 1 | pfleura2 | * UPLO = 'L' or 'l' The lower triangular part of A is |
| 33 | 1 | pfleura2 | * supplied in AP. |
| 34 | 1 | pfleura2 | * |
| 35 | 1 | pfleura2 | * Unchanged on exit. |
| 36 | 1 | pfleura2 | * |
| 37 | 1 | pfleura2 | * N - INTEGER. |
| 38 | 1 | pfleura2 | * On entry, N specifies the order of the matrix A. |
| 39 | 1 | pfleura2 | * N must be at least zero. |
| 40 | 1 | pfleura2 | * Unchanged on exit. |
| 41 | 1 | pfleura2 | * |
| 42 | 1 | pfleura2 | * ALPHA - COMPLEX . |
| 43 | 1 | pfleura2 | * On entry, ALPHA specifies the scalar alpha. |
| 44 | 1 | pfleura2 | * Unchanged on exit. |
| 45 | 1 | pfleura2 | * |
| 46 | 1 | pfleura2 | * X - COMPLEX array of dimension at least |
| 47 | 1 | pfleura2 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
| 48 | 1 | pfleura2 | * Before entry, the incremented array X must contain the n |
| 49 | 1 | pfleura2 | * element vector x. |
| 50 | 1 | pfleura2 | * Unchanged on exit. |
| 51 | 1 | pfleura2 | * |
| 52 | 1 | pfleura2 | * INCX - INTEGER. |
| 53 | 1 | pfleura2 | * On entry, INCX specifies the increment for the elements of |
| 54 | 1 | pfleura2 | * X. INCX must not be zero. |
| 55 | 1 | pfleura2 | * Unchanged on exit. |
| 56 | 1 | pfleura2 | * |
| 57 | 1 | pfleura2 | * Y - COMPLEX array of dimension at least |
| 58 | 1 | pfleura2 | * ( 1 + ( n - 1 )*abs( INCY ) ). |
| 59 | 1 | pfleura2 | * Before entry, the incremented array Y must contain the n |
| 60 | 1 | pfleura2 | * element vector y. |
| 61 | 1 | pfleura2 | * Unchanged on exit. |
| 62 | 1 | pfleura2 | * |
| 63 | 1 | pfleura2 | * INCY - INTEGER. |
| 64 | 1 | pfleura2 | * On entry, INCY specifies the increment for the elements of |
| 65 | 1 | pfleura2 | * Y. INCY must not be zero. |
| 66 | 1 | pfleura2 | * Unchanged on exit. |
| 67 | 1 | pfleura2 | * |
| 68 | 1 | pfleura2 | * AP - COMPLEX array of DIMENSION at least |
| 69 | 1 | pfleura2 | * ( ( n*( n + 1 ) )/2 ). |
| 70 | 1 | pfleura2 | * Before entry with UPLO = 'U' or 'u', the array AP must |
| 71 | 1 | pfleura2 | * contain the upper triangular part of the hermitian matrix |
| 72 | 1 | pfleura2 | * packed sequentially, column by column, so that AP( 1 ) |
| 73 | 1 | pfleura2 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) |
| 74 | 1 | pfleura2 | * and a( 2, 2 ) respectively, and so on. On exit, the array |
| 75 | 1 | pfleura2 | * AP is overwritten by the upper triangular part of the |
| 76 | 1 | pfleura2 | * updated matrix. |
| 77 | 1 | pfleura2 | * Before entry with UPLO = 'L' or 'l', the array AP must |
| 78 | 1 | pfleura2 | * contain the lower triangular part of the hermitian matrix |
| 79 | 1 | pfleura2 | * packed sequentially, column by column, so that AP( 1 ) |
| 80 | 1 | pfleura2 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) |
| 81 | 1 | pfleura2 | * and a( 3, 1 ) respectively, and so on. On exit, the array |
| 82 | 1 | pfleura2 | * AP is overwritten by the lower triangular part of the |
| 83 | 1 | pfleura2 | * updated matrix. |
| 84 | 1 | pfleura2 | * Note that the imaginary parts of the diagonal elements need |
| 85 | 1 | pfleura2 | * not be set, they are assumed to be zero, and on exit they |
| 86 | 1 | pfleura2 | * are set to zero. |
| 87 | 1 | pfleura2 | * |
| 88 | 1 | pfleura2 | * |
| 89 | 1 | pfleura2 | * Level 2 Blas routine. |
| 90 | 1 | pfleura2 | * |
| 91 | 1 | pfleura2 | * -- Written on 22-October-1986. |
| 92 | 1 | pfleura2 | * Jack Dongarra, Argonne National Lab. |
| 93 | 1 | pfleura2 | * Jeremy Du Croz, Nag Central Office. |
| 94 | 1 | pfleura2 | * Sven Hammarling, Nag Central Office. |
| 95 | 1 | pfleura2 | * Richard Hanson, Sandia National Labs. |
| 96 | 1 | pfleura2 | * |
| 97 | 1 | pfleura2 | * |
| 98 | 1 | pfleura2 | * .. Parameters .. |
| 99 | 1 | pfleura2 | COMPLEX ZERO |
| 100 | 1 | pfleura2 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
| 101 | 1 | pfleura2 | * .. |
| 102 | 1 | pfleura2 | * .. Local Scalars .. |
| 103 | 1 | pfleura2 | COMPLEX TEMP1,TEMP2 |
| 104 | 1 | pfleura2 | INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY |
| 105 | 1 | pfleura2 | * .. |
| 106 | 1 | pfleura2 | * .. External Functions .. |
| 107 | 1 | pfleura2 | LOGICAL LSAME |
| 108 | 1 | pfleura2 | EXTERNAL LSAME |
| 109 | 1 | pfleura2 | * .. |
| 110 | 1 | pfleura2 | * .. External Subroutines .. |
| 111 | 1 | pfleura2 | EXTERNAL XERBLA |
| 112 | 1 | pfleura2 | * .. |
| 113 | 1 | pfleura2 | * .. Intrinsic Functions .. |
| 114 | 1 | pfleura2 | INTRINSIC CONJG,REAL |
| 115 | 1 | pfleura2 | * .. |
| 116 | 1 | pfleura2 | * |
| 117 | 1 | pfleura2 | * Test the input parameters. |
| 118 | 1 | pfleura2 | * |
| 119 | 1 | pfleura2 | INFO = 0 |
| 120 | 1 | pfleura2 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
| 121 | 1 | pfleura2 | INFO = 1 |
| 122 | 1 | pfleura2 | ELSE IF (N.LT.0) THEN |
| 123 | 1 | pfleura2 | INFO = 2 |
| 124 | 1 | pfleura2 | ELSE IF (INCX.EQ.0) THEN |
| 125 | 1 | pfleura2 | INFO = 5 |
| 126 | 1 | pfleura2 | ELSE IF (INCY.EQ.0) THEN |
| 127 | 1 | pfleura2 | INFO = 7 |
| 128 | 1 | pfleura2 | END IF |
| 129 | 1 | pfleura2 | IF (INFO.NE.0) THEN |
| 130 | 1 | pfleura2 | CALL XERBLA('CHPR2 ',INFO)
|
| 131 | 1 | pfleura2 | RETURN |
| 132 | 1 | pfleura2 | END IF |
| 133 | 1 | pfleura2 | * |
| 134 | 1 | pfleura2 | * Quick return if possible. |
| 135 | 1 | pfleura2 | * |
| 136 | 1 | pfleura2 | IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN |
| 137 | 1 | pfleura2 | * |
| 138 | 1 | pfleura2 | * Set up the start points in X and Y if the increments are not both |
| 139 | 1 | pfleura2 | * unity. |
| 140 | 1 | pfleura2 | * |
| 141 | 1 | pfleura2 | IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN |
| 142 | 1 | pfleura2 | IF (INCX.GT.0) THEN |
| 143 | 1 | pfleura2 | KX = 1 |
| 144 | 1 | pfleura2 | ELSE |
| 145 | 1 | pfleura2 | KX = 1 - (N-1)*INCX |
| 146 | 1 | pfleura2 | END IF |
| 147 | 1 | pfleura2 | IF (INCY.GT.0) THEN |
| 148 | 1 | pfleura2 | KY = 1 |
| 149 | 1 | pfleura2 | ELSE |
| 150 | 1 | pfleura2 | KY = 1 - (N-1)*INCY |
| 151 | 1 | pfleura2 | END IF |
| 152 | 1 | pfleura2 | JX = KX |
| 153 | 1 | pfleura2 | JY = KY |
| 154 | 1 | pfleura2 | END IF |
| 155 | 1 | pfleura2 | * |
| 156 | 1 | pfleura2 | * Start the operations. In this version the elements of the array AP |
| 157 | 1 | pfleura2 | * are accessed sequentially with one pass through AP. |
| 158 | 1 | pfleura2 | * |
| 159 | 1 | pfleura2 | KK = 1 |
| 160 | 1 | pfleura2 | IF (LSAME(UPLO,'U')) THEN |
| 161 | 1 | pfleura2 | * |
| 162 | 1 | pfleura2 | * Form A when upper triangle is stored in AP. |
| 163 | 1 | pfleura2 | * |
| 164 | 1 | pfleura2 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
| 165 | 1 | pfleura2 | DO 20 J = 1,N |
| 166 | 1 | pfleura2 | IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
| 167 | 1 | pfleura2 | TEMP1 = ALPHA*CONJG(Y(J)) |
| 168 | 1 | pfleura2 | TEMP2 = CONJG(ALPHA*X(J)) |
| 169 | 1 | pfleura2 | K = KK |
| 170 | 1 | pfleura2 | DO 10 I = 1,J - 1 |
| 171 | 1 | pfleura2 | AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 |
| 172 | 1 | pfleura2 | K = K + 1 |
| 173 | 1 | pfleura2 | 10 CONTINUE |
| 174 | 1 | pfleura2 | AP(KK+J-1) = REAL(AP(KK+J-1)) + |
| 175 | 1 | pfleura2 | + REAL(X(J)*TEMP1+Y(J)*TEMP2) |
| 176 | 1 | pfleura2 | ELSE |
| 177 | 1 | pfleura2 | AP(KK+J-1) = REAL(AP(KK+J-1)) |
| 178 | 1 | pfleura2 | END IF |
| 179 | 1 | pfleura2 | KK = KK + J |
| 180 | 1 | pfleura2 | 20 CONTINUE |
| 181 | 1 | pfleura2 | ELSE |
| 182 | 1 | pfleura2 | DO 40 J = 1,N |
| 183 | 1 | pfleura2 | IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
| 184 | 1 | pfleura2 | TEMP1 = ALPHA*CONJG(Y(JY)) |
| 185 | 1 | pfleura2 | TEMP2 = CONJG(ALPHA*X(JX)) |
| 186 | 1 | pfleura2 | IX = KX |
| 187 | 1 | pfleura2 | IY = KY |
| 188 | 1 | pfleura2 | DO 30 K = KK,KK + J - 2 |
| 189 | 1 | pfleura2 | AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
| 190 | 1 | pfleura2 | IX = IX + INCX |
| 191 | 1 | pfleura2 | IY = IY + INCY |
| 192 | 1 | pfleura2 | 30 CONTINUE |
| 193 | 1 | pfleura2 | AP(KK+J-1) = REAL(AP(KK+J-1)) + |
| 194 | 1 | pfleura2 | + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
| 195 | 1 | pfleura2 | ELSE |
| 196 | 1 | pfleura2 | AP(KK+J-1) = REAL(AP(KK+J-1)) |
| 197 | 1 | pfleura2 | END IF |
| 198 | 1 | pfleura2 | JX = JX + INCX |
| 199 | 1 | pfleura2 | JY = JY + INCY |
| 200 | 1 | pfleura2 | KK = KK + J |
| 201 | 1 | pfleura2 | 40 CONTINUE |
| 202 | 1 | pfleura2 | END IF |
| 203 | 1 | pfleura2 | ELSE |
| 204 | 1 | pfleura2 | * |
| 205 | 1 | pfleura2 | * Form A when lower triangle is stored in AP. |
| 206 | 1 | pfleura2 | * |
| 207 | 1 | pfleura2 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
| 208 | 1 | pfleura2 | DO 60 J = 1,N |
| 209 | 1 | pfleura2 | IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
| 210 | 1 | pfleura2 | TEMP1 = ALPHA*CONJG(Y(J)) |
| 211 | 1 | pfleura2 | TEMP2 = CONJG(ALPHA*X(J)) |
| 212 | 1 | pfleura2 | AP(KK) = REAL(AP(KK)) + |
| 213 | 1 | pfleura2 | + REAL(X(J)*TEMP1+Y(J)*TEMP2) |
| 214 | 1 | pfleura2 | K = KK + 1 |
| 215 | 1 | pfleura2 | DO 50 I = J + 1,N |
| 216 | 1 | pfleura2 | AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 |
| 217 | 1 | pfleura2 | K = K + 1 |
| 218 | 1 | pfleura2 | 50 CONTINUE |
| 219 | 1 | pfleura2 | ELSE |
| 220 | 1 | pfleura2 | AP(KK) = REAL(AP(KK)) |
| 221 | 1 | pfleura2 | END IF |
| 222 | 1 | pfleura2 | KK = KK + N - J + 1 |
| 223 | 1 | pfleura2 | 60 CONTINUE |
| 224 | 1 | pfleura2 | ELSE |
| 225 | 1 | pfleura2 | DO 80 J = 1,N |
| 226 | 1 | pfleura2 | IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
| 227 | 1 | pfleura2 | TEMP1 = ALPHA*CONJG(Y(JY)) |
| 228 | 1 | pfleura2 | TEMP2 = CONJG(ALPHA*X(JX)) |
| 229 | 1 | pfleura2 | AP(KK) = REAL(AP(KK)) + |
| 230 | 1 | pfleura2 | + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
| 231 | 1 | pfleura2 | IX = JX |
| 232 | 1 | pfleura2 | IY = JY |
| 233 | 1 | pfleura2 | DO 70 K = KK + 1,KK + N - J |
| 234 | 1 | pfleura2 | IX = IX + INCX |
| 235 | 1 | pfleura2 | IY = IY + INCY |
| 236 | 1 | pfleura2 | AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
| 237 | 1 | pfleura2 | 70 CONTINUE |
| 238 | 1 | pfleura2 | ELSE |
| 239 | 1 | pfleura2 | AP(KK) = REAL(AP(KK)) |
| 240 | 1 | pfleura2 | END IF |
| 241 | 1 | pfleura2 | JX = JX + INCX |
| 242 | 1 | pfleura2 | JY = JY + INCY |
| 243 | 1 | pfleura2 | KK = KK + N - J + 1 |
| 244 | 1 | pfleura2 | 80 CONTINUE |
| 245 | 1 | pfleura2 | END IF |
| 246 | 1 | pfleura2 | END IF |
| 247 | 1 | pfleura2 | * |
| 248 | 1 | pfleura2 | RETURN |
| 249 | 1 | pfleura2 | * |
| 250 | 1 | pfleura2 | * End of CHPR2 . |
| 251 | 1 | pfleura2 | * |
| 252 | 1 | pfleura2 | END |