00001 SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA) 00002 * .. Scalar Arguments .. 00003 REAL ALPHA 00004 INTEGER INCX,LDA,N 00005 CHARACTER UPLO 00006 * .. 00007 * .. Array Arguments .. 00008 COMPLEX A(LDA,*),X(*) 00009 * .. 00010 * 00011 * Purpose 00012 * ======= 00013 * 00014 * CHER performs the hermitian rank 1 operation 00015 * 00016 * A := alpha*x*conjg( x' ) + A, 00017 * 00018 * where alpha is a real scalar, x is an n element vector and A is an 00019 * n by n hermitian matrix. 00020 * 00021 * Arguments 00022 * ========== 00023 * 00024 * UPLO - CHARACTER*1. 00025 * On entry, UPLO specifies whether the upper or lower 00026 * triangular part of the array A is to be referenced as 00027 * follows: 00028 * 00029 * UPLO = 'U' or 'u' Only the upper triangular part of A 00030 * is to be referenced. 00031 * 00032 * UPLO = 'L' or 'l' Only the lower triangular part of A 00033 * is to be referenced. 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 - REAL . 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 * A - COMPLEX array of DIMENSION ( LDA, n ). 00058 * Before entry with UPLO = 'U' or 'u', the leading n by n 00059 * upper triangular part of the array A must contain the upper 00060 * triangular part of the hermitian matrix and the strictly 00061 * lower triangular part of A is not referenced. On exit, the 00062 * upper triangular part of the array A is overwritten by the 00063 * upper triangular part of the updated matrix. 00064 * Before entry with UPLO = 'L' or 'l', the leading n by n 00065 * lower triangular part of the array A must contain the lower 00066 * triangular part of the hermitian matrix and the strictly 00067 * upper triangular part of A is not referenced. On exit, the 00068 * lower triangular part of the array A is overwritten by the 00069 * lower triangular part of the updated matrix. 00070 * Note that the imaginary parts of the diagonal elements need 00071 * not be set, they are assumed to be zero, and on exit they 00072 * are set to zero. 00073 * 00074 * LDA - INTEGER. 00075 * On entry, LDA specifies the first dimension of A as declared 00076 * in the calling (sub) program. LDA must be at least 00077 * max( 1, n ). 00078 * Unchanged on exit. 00079 * 00080 * Further Details 00081 * =============== 00082 * 00083 * Level 2 Blas routine. 00084 * 00085 * -- Written on 22-October-1986. 00086 * Jack Dongarra, Argonne National Lab. 00087 * Jeremy Du Croz, Nag Central Office. 00088 * Sven Hammarling, Nag Central Office. 00089 * Richard Hanson, Sandia National Labs. 00090 * 00091 * ===================================================================== 00092 * 00093 * .. Parameters .. 00094 COMPLEX ZERO 00095 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00096 * .. 00097 * .. Local Scalars .. 00098 COMPLEX TEMP 00099 INTEGER I,INFO,IX,J,JX,KX 00100 * .. 00101 * .. External Functions .. 00102 LOGICAL LSAME 00103 EXTERNAL LSAME 00104 * .. 00105 * .. External Subroutines .. 00106 EXTERNAL XERBLA 00107 * .. 00108 * .. Intrinsic Functions .. 00109 INTRINSIC CONJG,MAX,REAL 00110 * .. 00111 * 00112 * Test the input parameters. 00113 * 00114 INFO = 0 00115 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00116 INFO = 1 00117 ELSE IF (N.LT.0) THEN 00118 INFO = 2 00119 ELSE IF (INCX.EQ.0) THEN 00120 INFO = 5 00121 ELSE IF (LDA.LT.MAX(1,N)) THEN 00122 INFO = 7 00123 END IF 00124 IF (INFO.NE.0) THEN 00125 CALL XERBLA('CHER ',INFO) 00126 RETURN 00127 END IF 00128 * 00129 * Quick return if possible. 00130 * 00131 IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN 00132 * 00133 * Set the start point in X if the increment is not unity. 00134 * 00135 IF (INCX.LE.0) THEN 00136 KX = 1 - (N-1)*INCX 00137 ELSE IF (INCX.NE.1) THEN 00138 KX = 1 00139 END IF 00140 * 00141 * Start the operations. In this version the elements of A are 00142 * accessed sequentially with one pass through the triangular part 00143 * of A. 00144 * 00145 IF (LSAME(UPLO,'U')) THEN 00146 * 00147 * Form A when A is stored in upper triangle. 00148 * 00149 IF (INCX.EQ.1) THEN 00150 DO 20 J = 1,N 00151 IF (X(J).NE.ZERO) THEN 00152 TEMP = ALPHA*CONJG(X(J)) 00153 DO 10 I = 1,J - 1 00154 A(I,J) = A(I,J) + X(I)*TEMP 00155 10 CONTINUE 00156 A(J,J) = REAL(A(J,J)) + REAL(X(J)*TEMP) 00157 ELSE 00158 A(J,J) = REAL(A(J,J)) 00159 END IF 00160 20 CONTINUE 00161 ELSE 00162 JX = KX 00163 DO 40 J = 1,N 00164 IF (X(JX).NE.ZERO) THEN 00165 TEMP = ALPHA*CONJG(X(JX)) 00166 IX = KX 00167 DO 30 I = 1,J - 1 00168 A(I,J) = A(I,J) + X(IX)*TEMP 00169 IX = IX + INCX 00170 30 CONTINUE 00171 A(J,J) = REAL(A(J,J)) + REAL(X(JX)*TEMP) 00172 ELSE 00173 A(J,J) = REAL(A(J,J)) 00174 END IF 00175 JX = JX + INCX 00176 40 CONTINUE 00177 END IF 00178 ELSE 00179 * 00180 * Form A when A is stored in lower triangle. 00181 * 00182 IF (INCX.EQ.1) THEN 00183 DO 60 J = 1,N 00184 IF (X(J).NE.ZERO) THEN 00185 TEMP = ALPHA*CONJG(X(J)) 00186 A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(J)) 00187 DO 50 I = J + 1,N 00188 A(I,J) = A(I,J) + X(I)*TEMP 00189 50 CONTINUE 00190 ELSE 00191 A(J,J) = REAL(A(J,J)) 00192 END IF 00193 60 CONTINUE 00194 ELSE 00195 JX = KX 00196 DO 80 J = 1,N 00197 IF (X(JX).NE.ZERO) THEN 00198 TEMP = ALPHA*CONJG(X(JX)) 00199 A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(JX)) 00200 IX = JX 00201 DO 70 I = J + 1,N 00202 IX = IX + INCX 00203 A(I,J) = A(I,J) + X(IX)*TEMP 00204 70 CONTINUE 00205 ELSE 00206 A(J,J) = REAL(A(J,J)) 00207 END IF 00208 JX = JX + INCX 00209 80 CONTINUE 00210 END IF 00211 END IF 00212 * 00213 RETURN 00214 * 00215 * End of CHER . 00216 * 00217 END
1.7.2