|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 SUBROUTINE SSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00002 * .. Scalar Arguments .. 00003 REAL ALPHA,BETA 00004 INTEGER INCX,INCY,LDA,N 00005 CHARACTER UPLO 00006 * .. 00007 * .. Array Arguments .. 00008 REAL A(LDA,*),X(*),Y(*) 00009 * .. 00010 * 00011 * Purpose 00012 * ======= 00013 * 00014 * SSYMV performs the matrix-vector operation 00015 * 00016 * y := alpha*A*x + beta*y, 00017 * 00018 * where alpha and beta are scalars, x and y are n element vectors and 00019 * A is an n by n symmetric 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 * A - REAL array of DIMENSION ( LDA, n ). 00047 * Before entry with UPLO = 'U' or 'u', the leading n by n 00048 * upper triangular part of the array A must contain the upper 00049 * triangular part of the symmetric matrix and the strictly 00050 * lower triangular part of A is not referenced. 00051 * Before entry with UPLO = 'L' or 'l', the leading n by n 00052 * lower triangular part of the array A must contain the lower 00053 * triangular part of the symmetric matrix and the strictly 00054 * upper triangular part of A is not referenced. 00055 * Unchanged on exit. 00056 * 00057 * LDA - INTEGER. 00058 * On entry, LDA specifies the first dimension of A as declared 00059 * in the calling (sub) program. LDA must be at least 00060 * max( 1, n ). 00061 * Unchanged on exit. 00062 * 00063 * X - REAL array of dimension at least 00064 * ( 1 + ( n - 1 )*abs( INCX ) ). 00065 * Before entry, the incremented array X must contain the n 00066 * element vector x. 00067 * Unchanged on exit. 00068 * 00069 * INCX - INTEGER. 00070 * On entry, INCX specifies the increment for the elements of 00071 * X. INCX must not be zero. 00072 * Unchanged on exit. 00073 * 00074 * BETA - REAL . 00075 * On entry, BETA specifies the scalar beta. When BETA is 00076 * supplied as zero then Y need not be set on input. 00077 * Unchanged on exit. 00078 * 00079 * Y - REAL array of dimension at least 00080 * ( 1 + ( n - 1 )*abs( INCY ) ). 00081 * Before entry, the incremented array Y must contain the n 00082 * element vector y. On exit, Y is overwritten by the updated 00083 * vector y. 00084 * 00085 * INCY - INTEGER. 00086 * On entry, INCY specifies the increment for the elements of 00087 * Y. INCY must not be zero. 00088 * Unchanged on exit. 00089 * 00090 * Further Details 00091 * =============== 00092 * 00093 * Level 2 Blas routine. 00094 * 00095 * -- Written on 22-October-1986. 00096 * Jack Dongarra, Argonne National Lab. 00097 * Jeremy Du Croz, Nag Central Office. 00098 * Sven Hammarling, Nag Central Office. 00099 * Richard Hanson, Sandia National Labs. 00100 * 00101 * ===================================================================== 00102 * 00103 * .. Parameters .. 00104 REAL ONE,ZERO 00105 PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) 00106 * .. 00107 * .. Local Scalars .. 00108 REAL TEMP1,TEMP2 00109 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY 00110 * .. 00111 * .. External Functions .. 00112 LOGICAL LSAME 00113 EXTERNAL LSAME 00114 * .. 00115 * .. External Subroutines .. 00116 EXTERNAL XERBLA 00117 * .. 00118 * .. Intrinsic Functions .. 00119 INTRINSIC MAX 00120 * .. 00121 * 00122 * Test the input parameters. 00123 * 00124 INFO = 0 00125 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00126 INFO = 1 00127 ELSE IF (N.LT.0) THEN 00128 INFO = 2 00129 ELSE IF (LDA.LT.MAX(1,N)) THEN 00130 INFO = 5 00131 ELSE IF (INCX.EQ.0) THEN 00132 INFO = 7 00133 ELSE IF (INCY.EQ.0) THEN 00134 INFO = 10 00135 END IF 00136 IF (INFO.NE.0) THEN 00137 CALL XERBLA('SSYMV ',INFO) 00138 RETURN 00139 END IF 00140 * 00141 * Quick return if possible. 00142 * 00143 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00144 * 00145 * Set up the start points in X and Y. 00146 * 00147 IF (INCX.GT.0) THEN 00148 KX = 1 00149 ELSE 00150 KX = 1 - (N-1)*INCX 00151 END IF 00152 IF (INCY.GT.0) THEN 00153 KY = 1 00154 ELSE 00155 KY = 1 - (N-1)*INCY 00156 END IF 00157 * 00158 * Start the operations. In this version the elements of A are 00159 * accessed sequentially with one pass through the triangular part 00160 * of A. 00161 * 00162 * First form y := beta*y. 00163 * 00164 IF (BETA.NE.ONE) THEN 00165 IF (INCY.EQ.1) THEN 00166 IF (BETA.EQ.ZERO) THEN 00167 DO 10 I = 1,N 00168 Y(I) = ZERO 00169 10 CONTINUE 00170 ELSE 00171 DO 20 I = 1,N 00172 Y(I) = BETA*Y(I) 00173 20 CONTINUE 00174 END IF 00175 ELSE 00176 IY = KY 00177 IF (BETA.EQ.ZERO) THEN 00178 DO 30 I = 1,N 00179 Y(IY) = ZERO 00180 IY = IY + INCY 00181 30 CONTINUE 00182 ELSE 00183 DO 40 I = 1,N 00184 Y(IY) = BETA*Y(IY) 00185 IY = IY + INCY 00186 40 CONTINUE 00187 END IF 00188 END IF 00189 END IF 00190 IF (ALPHA.EQ.ZERO) 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 SSYMV . 00264 * 00265 END
1.7.3 
