|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 00002 * .. Scalar Arguments .. 00003 COMPLEX ALPHA 00004 INTEGER INCX,INCY,N 00005 CHARACTER UPLO 00006 * .. 00007 * .. Array Arguments .. 00008 COMPLEX AP(*),X(*),Y(*) 00009 * .. 00010 * 00011 * Purpose 00012 * ======= 00013 * 00014 * CHPR2 performs the hermitian rank 2 operation 00015 * 00016 * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, 00017 * 00018 * where alpha is a scalar, x and y are n element vectors and A is an 00019 * n by n hermitian matrix, supplied in packed form. 00020 * 00021 * Arguments 00022 * ========== 00023 * 00024 * UPLO - CHARACTER*1. 00025 * On entry, UPLO specifies whether the upper or lower 00026 * triangular part of the matrix A is supplied in the packed 00027 * array AP as follows: 00028 * 00029 * UPLO = 'U' or 'u' The upper triangular part of A is 00030 * supplied in AP. 00031 * 00032 * UPLO = 'L' or 'l' The lower triangular part of A is 00033 * supplied in AP. 00034 * 00035 * Unchanged on exit. 00036 * 00037 * N - INTEGER. 00038 * On entry, N specifies the order of the matrix A. 00039 * N must be at least zero. 00040 * Unchanged on exit. 00041 * 00042 * ALPHA - COMPLEX . 00043 * On entry, ALPHA specifies the scalar alpha. 00044 * Unchanged on exit. 00045 * 00046 * X - COMPLEX array of dimension at least 00047 * ( 1 + ( n - 1 )*abs( INCX ) ). 00048 * Before entry, the incremented array X must contain the n 00049 * element vector x. 00050 * Unchanged on exit. 00051 * 00052 * INCX - INTEGER. 00053 * On entry, INCX specifies the increment for the elements of 00054 * X. INCX must not be zero. 00055 * Unchanged on exit. 00056 * 00057 * Y - COMPLEX array of dimension at least 00058 * ( 1 + ( n - 1 )*abs( INCY ) ). 00059 * Before entry, the incremented array Y must contain the n 00060 * element vector y. 00061 * Unchanged on exit. 00062 * 00063 * INCY - INTEGER. 00064 * On entry, INCY specifies the increment for the elements of 00065 * Y. INCY must not be zero. 00066 * Unchanged on exit. 00067 * 00068 * AP - COMPLEX array of DIMENSION at least 00069 * ( ( n*( n + 1 ) )/2 ). 00070 * Before entry with UPLO = 'U' or 'u', the array AP must 00071 * contain the upper triangular part of the hermitian matrix 00072 * packed sequentially, column by column, so that AP( 1 ) 00073 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 00074 * and a( 2, 2 ) respectively, and so on. On exit, the array 00075 * AP is overwritten by the upper triangular part of the 00076 * updated matrix. 00077 * Before entry with UPLO = 'L' or 'l', the array AP must 00078 * contain the lower triangular part of the hermitian matrix 00079 * packed sequentially, column by column, so that AP( 1 ) 00080 * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 00081 * and a( 3, 1 ) respectively, and so on. On exit, the array 00082 * AP is overwritten by the lower triangular part of the 00083 * updated matrix. 00084 * Note that the imaginary parts of the diagonal elements need 00085 * not be set, they are assumed to be zero, and on exit they 00086 * are set to zero. 00087 * 00088 * Further Details 00089 * =============== 00090 * 00091 * Level 2 Blas routine. 00092 * 00093 * -- Written on 22-October-1986. 00094 * Jack Dongarra, Argonne National Lab. 00095 * Jeremy Du Croz, Nag Central Office. 00096 * Sven Hammarling, Nag Central Office. 00097 * Richard Hanson, Sandia National Labs. 00098 * 00099 * ===================================================================== 00100 * 00101 * .. Parameters .. 00102 COMPLEX ZERO 00103 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00104 * .. 00105 * .. Local Scalars .. 00106 COMPLEX TEMP1,TEMP2 00107 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 00108 * .. 00109 * .. External Functions .. 00110 LOGICAL LSAME 00111 EXTERNAL LSAME 00112 * .. 00113 * .. External Subroutines .. 00114 EXTERNAL XERBLA 00115 * .. 00116 * .. Intrinsic Functions .. 00117 INTRINSIC CONJG,REAL 00118 * .. 00119 * 00120 * Test the input parameters. 00121 * 00122 INFO = 0 00123 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00124 INFO = 1 00125 ELSE IF (N.LT.0) THEN 00126 INFO = 2 00127 ELSE IF (INCX.EQ.0) THEN 00128 INFO = 5 00129 ELSE IF (INCY.EQ.0) THEN 00130 INFO = 7 00131 END IF 00132 IF (INFO.NE.0) THEN 00133 CALL XERBLA('CHPR2 ',INFO) 00134 RETURN 00135 END IF 00136 * 00137 * Quick return if possible. 00138 * 00139 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 00140 * 00141 * Set up the start points in X and Y if the increments are not both 00142 * unity. 00143 * 00144 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 00145 IF (INCX.GT.0) THEN 00146 KX = 1 00147 ELSE 00148 KX = 1 - (N-1)*INCX 00149 END IF 00150 IF (INCY.GT.0) THEN 00151 KY = 1 00152 ELSE 00153 KY = 1 - (N-1)*INCY 00154 END IF 00155 JX = KX 00156 JY = KY 00157 END IF 00158 * 00159 * Start the operations. In this version the elements of the array AP 00160 * are accessed sequentially with one pass through AP. 00161 * 00162 KK = 1 00163 IF (LSAME(UPLO,'U')) THEN 00164 * 00165 * Form A when upper triangle is stored in AP. 00166 * 00167 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00168 DO 20 J = 1,N 00169 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00170 TEMP1 = ALPHA*CONJG(Y(J)) 00171 TEMP2 = CONJG(ALPHA*X(J)) 00172 K = KK 00173 DO 10 I = 1,J - 1 00174 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00175 K = K + 1 00176 10 CONTINUE 00177 AP(KK+J-1) = REAL(AP(KK+J-1)) + 00178 + REAL(X(J)*TEMP1+Y(J)*TEMP2) 00179 ELSE 00180 AP(KK+J-1) = REAL(AP(KK+J-1)) 00181 END IF 00182 KK = KK + J 00183 20 CONTINUE 00184 ELSE 00185 DO 40 J = 1,N 00186 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00187 TEMP1 = ALPHA*CONJG(Y(JY)) 00188 TEMP2 = CONJG(ALPHA*X(JX)) 00189 IX = KX 00190 IY = KY 00191 DO 30 K = KK,KK + J - 2 00192 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00193 IX = IX + INCX 00194 IY = IY + INCY 00195 30 CONTINUE 00196 AP(KK+J-1) = REAL(AP(KK+J-1)) + 00197 + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) 00198 ELSE 00199 AP(KK+J-1) = REAL(AP(KK+J-1)) 00200 END IF 00201 JX = JX + INCX 00202 JY = JY + INCY 00203 KK = KK + J 00204 40 CONTINUE 00205 END IF 00206 ELSE 00207 * 00208 * Form A when lower triangle is stored in AP. 00209 * 00210 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00211 DO 60 J = 1,N 00212 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00213 TEMP1 = ALPHA*CONJG(Y(J)) 00214 TEMP2 = CONJG(ALPHA*X(J)) 00215 AP(KK) = REAL(AP(KK)) + 00216 + REAL(X(J)*TEMP1+Y(J)*TEMP2) 00217 K = KK + 1 00218 DO 50 I = J + 1,N 00219 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00220 K = K + 1 00221 50 CONTINUE 00222 ELSE 00223 AP(KK) = REAL(AP(KK)) 00224 END IF 00225 KK = KK + N - J + 1 00226 60 CONTINUE 00227 ELSE 00228 DO 80 J = 1,N 00229 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00230 TEMP1 = ALPHA*CONJG(Y(JY)) 00231 TEMP2 = CONJG(ALPHA*X(JX)) 00232 AP(KK) = REAL(AP(KK)) + 00233 + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) 00234 IX = JX 00235 IY = JY 00236 DO 70 K = KK + 1,KK + N - J 00237 IX = IX + INCX 00238 IY = IY + INCY 00239 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00240 70 CONTINUE 00241 ELSE 00242 AP(KK) = REAL(AP(KK)) 00243 END IF 00244 JX = JX + INCX 00245 JY = JY + INCY 00246 KK = KK + N - J + 1 00247 80 CONTINUE 00248 END IF 00249 END IF 00250 * 00251 RETURN 00252 * 00253 * End of CHPR2 . 00254 * 00255 END
1.7.3 
