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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY ) 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, INCY, LDA, N 00011 COMPLEX*16 ALPHA, BETA 00012 * .. 00013 * .. Array Arguments .. 00014 COMPLEX*16 A( LDA, * ), X( * ), Y( * ) 00015 * .. 00016 * 00017 * Purpose 00018 * ======= 00019 * 00020 * ZSYMV performs the matrix-vector operation 00021 * 00022 * y := alpha*A*x + beta*y, 00023 * 00024 * where alpha and beta are scalars, x and y are n element vectors and 00025 * A is an 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 * A (input) COMPLEX*16 array, dimension ( LDA, N ) 00053 * Before entry, with UPLO = 'U' or 'u', the leading n by n 00054 * upper triangular part of the array A must contain the upper 00055 * triangular part of the symmetric matrix and the strictly 00056 * lower triangular part of A is not referenced. 00057 * Before entry, with UPLO = 'L' or 'l', the leading n by n 00058 * lower triangular part of the array A must contain the lower 00059 * triangular part of the symmetric matrix and the strictly 00060 * upper triangular part of A is not referenced. 00061 * Unchanged on exit. 00062 * 00063 * LDA (input) INTEGER 00064 * On entry, LDA specifies the first dimension of A as declared 00065 * in the calling (sub) program. LDA must be at least 00066 * max( 1, N ). 00067 * Unchanged on exit. 00068 * 00069 * X (input) COMPLEX*16 array, dimension at least 00070 * ( 1 + ( N - 1 )*abs( INCX ) ). 00071 * Before entry, the incremented array X must contain the N- 00072 * element vector x. 00073 * Unchanged on exit. 00074 * 00075 * INCX (input) INTEGER 00076 * On entry, INCX specifies the increment for the elements of 00077 * X. INCX must not be zero. 00078 * Unchanged on exit. 00079 * 00080 * BETA (input) COMPLEX*16 00081 * On entry, BETA specifies the scalar beta. When BETA is 00082 * supplied as zero then Y need not be set on input. 00083 * Unchanged on exit. 00084 * 00085 * Y (input/output) COMPLEX*16 array, dimension at least 00086 * ( 1 + ( N - 1 )*abs( INCY ) ). 00087 * Before entry, the incremented array Y must contain the n 00088 * element vector y. On exit, Y is overwritten by the updated 00089 * vector y. 00090 * 00091 * INCY (input) INTEGER 00092 * On entry, INCY specifies the increment for the elements of 00093 * Y. INCY must not be zero. 00094 * Unchanged on exit. 00095 * 00096 * ===================================================================== 00097 * 00098 * .. Parameters .. 00099 COMPLEX*16 ONE 00100 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 00101 COMPLEX*16 ZERO 00102 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) 00103 * .. 00104 * .. Local Scalars .. 00105 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY 00106 COMPLEX*16 TEMP1, TEMP2 00107 * .. 00108 * .. External Functions .. 00109 LOGICAL LSAME 00110 EXTERNAL LSAME 00111 * .. 00112 * .. External Subroutines .. 00113 EXTERNAL XERBLA 00114 * .. 00115 * .. Intrinsic Functions .. 00116 INTRINSIC MAX 00117 * .. 00118 * .. Executable Statements .. 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( LDA.LT.MAX( 1, N ) ) THEN 00128 INFO = 5 00129 ELSE IF( INCX.EQ.0 ) THEN 00130 INFO = 7 00131 ELSE IF( INCY.EQ.0 ) THEN 00132 INFO = 10 00133 END IF 00134 IF( INFO.NE.0 ) THEN 00135 CALL XERBLA( 'ZSYMV ', INFO ) 00136 RETURN 00137 END IF 00138 * 00139 * Quick return if possible. 00140 * 00141 IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) ) 00142 $ RETURN 00143 * 00144 * Set up the start points in X and Y. 00145 * 00146 IF( INCX.GT.0 ) THEN 00147 KX = 1 00148 ELSE 00149 KX = 1 - ( N-1 )*INCX 00150 END IF 00151 IF( INCY.GT.0 ) THEN 00152 KY = 1 00153 ELSE 00154 KY = 1 - ( N-1 )*INCY 00155 END IF 00156 * 00157 * Start the operations. In this version the elements of A are 00158 * accessed sequentially with one pass through the triangular part 00159 * of A. 00160 * 00161 * First form y := beta*y. 00162 * 00163 IF( BETA.NE.ONE ) THEN 00164 IF( INCY.EQ.1 ) THEN 00165 IF( BETA.EQ.ZERO ) THEN 00166 DO 10 I = 1, N 00167 Y( I ) = ZERO 00168 10 CONTINUE 00169 ELSE 00170 DO 20 I = 1, N 00171 Y( I ) = BETA*Y( I ) 00172 20 CONTINUE 00173 END IF 00174 ELSE 00175 IY = KY 00176 IF( BETA.EQ.ZERO ) THEN 00177 DO 30 I = 1, N 00178 Y( IY ) = ZERO 00179 IY = IY + INCY 00180 30 CONTINUE 00181 ELSE 00182 DO 40 I = 1, N 00183 Y( IY ) = BETA*Y( IY ) 00184 IY = IY + INCY 00185 40 CONTINUE 00186 END IF 00187 END IF 00188 END IF 00189 IF( ALPHA.EQ.ZERO ) 00190 $ RETURN 00191 IF( LSAME( UPLO, 'U' ) ) THEN 00192 * 00193 * Form y when A is stored in upper triangle. 00194 * 00195 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN 00196 DO 60 J = 1, N 00197 TEMP1 = ALPHA*X( J ) 00198 TEMP2 = ZERO 00199 DO 50 I = 1, J - 1 00200 Y( I ) = Y( I ) + TEMP1*A( I, J ) 00201 TEMP2 = TEMP2 + A( I, J )*X( I ) 00202 50 CONTINUE 00203 Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2 00204 60 CONTINUE 00205 ELSE 00206 JX = KX 00207 JY = KY 00208 DO 80 J = 1, N 00209 TEMP1 = ALPHA*X( JX ) 00210 TEMP2 = ZERO 00211 IX = KX 00212 IY = KY 00213 DO 70 I = 1, J - 1 00214 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) 00215 TEMP2 = TEMP2 + A( I, J )*X( IX ) 00216 IX = IX + INCX 00217 IY = IY + INCY 00218 70 CONTINUE 00219 Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2 00220 JX = JX + INCX 00221 JY = JY + INCY 00222 80 CONTINUE 00223 END IF 00224 ELSE 00225 * 00226 * Form y when A is stored in lower triangle. 00227 * 00228 IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN 00229 DO 100 J = 1, N 00230 TEMP1 = ALPHA*X( J ) 00231 TEMP2 = ZERO 00232 Y( J ) = Y( J ) + TEMP1*A( J, J ) 00233 DO 90 I = J + 1, N 00234 Y( I ) = Y( I ) + TEMP1*A( I, J ) 00235 TEMP2 = TEMP2 + A( I, J )*X( I ) 00236 90 CONTINUE 00237 Y( J ) = Y( J ) + ALPHA*TEMP2 00238 100 CONTINUE 00239 ELSE 00240 JX = KX 00241 JY = KY 00242 DO 120 J = 1, N 00243 TEMP1 = ALPHA*X( JX ) 00244 TEMP2 = ZERO 00245 Y( JY ) = Y( JY ) + TEMP1*A( J, J ) 00246 IX = JX 00247 IY = JY 00248 DO 110 I = J + 1, N 00249 IX = IX + INCX 00250 IY = IY + INCY 00251 Y( IY ) = Y( IY ) + TEMP1*A( I, J ) 00252 TEMP2 = TEMP2 + A( I, J )*X( IX ) 00253 110 CONTINUE 00254 Y( JY ) = Y( JY ) + ALPHA*TEMP2 00255 JX = JX + INCX 00256 JY = JY + INCY 00257 120 CONTINUE 00258 END IF 00259 END IF 00260 * 00261 RETURN 00262 * 00263 * End of ZSYMV 00264 * 00265 END
1.7.3 
