00001 SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER UPLO 00010 INTEGER INCX, LDA, N 00011 COMPLEX*16 ALPHA 00012 * .. 00013 * .. Array Arguments .. 00014 COMPLEX*16 A( LDA, * ), X( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZSYR performs the symmetric rank 1 operation 00021 * 00022 * A := alpha*x*( x' ) + A, 00023 * 00024 * where alpha is a complex scalar, x is an n element vector and A is an 00025 * n by n symmetric matrix. 00026 * 00027 * Arguments 00028 * ========== 00029 * 00030 * UPLO (input) CHARACTER*1 00031 * On entry, UPLO specifies whether the upper or lower 00032 * triangular part of the array A is to be referenced as 00033 * follows: 00034 * 00035 * UPLO = 'U' or 'u' Only the upper triangular part of A 00036 * is to be referenced. 00037 * 00038 * UPLO = 'L' or 'l' Only the lower triangular part of A 00039 * is to be referenced. 00040 * 00041 * Unchanged on exit. 00042 * 00043 * N (input) INTEGER 00044 * On entry, N specifies the order of the matrix A. 00045 * N must be at least zero. 00046 * Unchanged on exit. 00047 * 00048 * ALPHA (input) COMPLEX*16 00049 * On entry, ALPHA specifies the scalar alpha. 00050 * Unchanged on exit. 00051 * 00052 * X (input) COMPLEX*16 array, dimension at least 00053 * ( 1 + ( N - 1 )*abs( INCX ) ). 00054 * Before entry, the incremented array X must contain the N- 00055 * element vector x. 00056 * Unchanged on exit. 00057 * 00058 * INCX (input) INTEGER 00059 * On entry, INCX specifies the increment for the elements of 00060 * X. INCX must not be zero. 00061 * Unchanged on exit. 00062 * 00063 * A (input/output) COMPLEX*16 array, dimension ( LDA, N ) 00064 * Before entry, with UPLO = 'U' or 'u', the leading n by n 00065 * upper triangular part of the array A must contain the upper 00066 * triangular part of the symmetric matrix and the strictly 00067 * lower triangular part of A is not referenced. On exit, the 00068 * upper triangular part of the array A is overwritten by the 00069 * upper triangular part of the updated matrix. 00070 * Before entry, with UPLO = 'L' or 'l', the leading n by n 00071 * lower triangular part of the array A must contain the lower 00072 * triangular part of the symmetric matrix and the strictly 00073 * upper triangular part of A is not referenced. On exit, the 00074 * lower triangular part of the array A is overwritten by the 00075 * lower triangular part of the updated matrix. 00076 * 00077 * LDA (input) INTEGER 00078 * On entry, LDA specifies the first dimension of A as declared 00079 * in the calling (sub) program. LDA must be at least 00080 * max( 1, N ). 00081 * Unchanged on exit. 00082 * 00083 * ===================================================================== 00084 * 00085 * .. Parameters .. 00086 COMPLEX*16 ZERO 00087 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 00088 * .. 00089 * .. Local Scalars .. 00090 INTEGER I, INFO, IX, J, JX, KX 00091 COMPLEX*16 TEMP 00092 * .. 00093 * .. External Functions .. 00094 LOGICAL LSAME 00095 EXTERNAL LSAME 00096 * .. 00097 * .. External Subroutines .. 00098 EXTERNAL XERBLA 00099 * .. 00100 * .. Intrinsic Functions .. 00101 INTRINSIC MAX 00102 * .. 00103 * .. Executable Statements .. 00104 * 00105 * Test the input parameters. 00106 * 00107 INFO = 0 00108 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00109 INFO = 1 00110 ELSE IF( N.LT.0 ) THEN 00111 INFO = 2 00112 ELSE IF( INCX.EQ.0 ) THEN 00113 INFO = 5 00114 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00115 INFO = 7 00116 END IF 00117 IF( INFO.NE.0 ) THEN 00118 CALL XERBLA( 'ZSYR ', INFO ) 00119 RETURN 00120 END IF 00121 * 00122 * Quick return if possible. 00123 * 00124 IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) ) 00125 $ RETURN 00126 * 00127 * Set the start point in X if the increment is not unity. 00128 * 00129 IF( INCX.LE.0 ) THEN 00130 KX = 1 - ( N-1 )*INCX 00131 ELSE IF( INCX.NE.1 ) THEN 00132 KX = 1 00133 END IF 00134 * 00135 * Start the operations. In this version the elements of A are 00136 * accessed sequentially with one pass through the triangular part 00137 * of A. 00138 * 00139 IF( LSAME( UPLO, 'U' ) ) THEN 00140 * 00141 * Form A when A is stored in upper triangle. 00142 * 00143 IF( INCX.EQ.1 ) THEN 00144 DO 20 J = 1, N 00145 IF( X( J ).NE.ZERO ) THEN 00146 TEMP = ALPHA*X( J ) 00147 DO 10 I = 1, J 00148 A( I, J ) = A( I, J ) + X( I )*TEMP 00149 10 CONTINUE 00150 END IF 00151 20 CONTINUE 00152 ELSE 00153 JX = KX 00154 DO 40 J = 1, N 00155 IF( X( JX ).NE.ZERO ) THEN 00156 TEMP = ALPHA*X( JX ) 00157 IX = KX 00158 DO 30 I = 1, J 00159 A( I, J ) = A( I, J ) + X( IX )*TEMP 00160 IX = IX + INCX 00161 30 CONTINUE 00162 END IF 00163 JX = JX + INCX 00164 40 CONTINUE 00165 END IF 00166 ELSE 00167 * 00168 * Form A when A is stored in lower triangle. 00169 * 00170 IF( INCX.EQ.1 ) THEN 00171 DO 60 J = 1, N 00172 IF( X( J ).NE.ZERO ) THEN 00173 TEMP = ALPHA*X( J ) 00174 DO 50 I = J, N 00175 A( I, J ) = A( I, J ) + X( I )*TEMP 00176 50 CONTINUE 00177 END IF 00178 60 CONTINUE 00179 ELSE 00180 JX = KX 00181 DO 80 J = 1, N 00182 IF( X( JX ).NE.ZERO ) THEN 00183 TEMP = ALPHA*X( JX ) 00184 IX = JX 00185 DO 70 I = J, N 00186 A( I, J ) = A( I, J ) + X( IX )*TEMP 00187 IX = IX + INCX 00188 70 CONTINUE 00189 END IF 00190 JX = JX + INCX 00191 80 CONTINUE 00192 END IF 00193 END IF 00194 * 00195 RETURN 00196 * 00197 * End of ZSYR 00198 * 00199 END
1.7.2