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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,LDA,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 DOUBLE PRECISION A(LDA,*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * DTRMV performs one of the matrix-vector operations 00014 * 00015 * x := A*x, or x := A'*x, 00016 * 00017 * where x is an n element vector and A is an n by n unit, or non-unit, 00018 * upper or lower triangular matrix. 00019 * 00020 * Arguments 00021 * ========== 00022 * 00023 * UPLO - CHARACTER*1. 00024 * On entry, UPLO specifies whether the matrix is an upper or 00025 * lower triangular matrix as follows: 00026 * 00027 * UPLO = 'U' or 'u' A is an upper triangular matrix. 00028 * 00029 * UPLO = 'L' or 'l' A is a lower triangular matrix. 00030 * 00031 * Unchanged on exit. 00032 * 00033 * TRANS - CHARACTER*1. 00034 * On entry, TRANS specifies the operation to be performed as 00035 * follows: 00036 * 00037 * TRANS = 'N' or 'n' x := A*x. 00038 * 00039 * TRANS = 'T' or 't' x := A'*x. 00040 * 00041 * TRANS = 'C' or 'c' x := A'*x. 00042 * 00043 * Unchanged on exit. 00044 * 00045 * DIAG - CHARACTER*1. 00046 * On entry, DIAG specifies whether or not A is unit 00047 * triangular as follows: 00048 * 00049 * DIAG = 'U' or 'u' A is assumed to be unit triangular. 00050 * 00051 * DIAG = 'N' or 'n' A is not assumed to be unit 00052 * triangular. 00053 * 00054 * Unchanged on exit. 00055 * 00056 * N - INTEGER. 00057 * On entry, N specifies the order of the matrix A. 00058 * N must be at least zero. 00059 * Unchanged on exit. 00060 * 00061 * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). 00062 * Before entry with UPLO = 'U' or 'u', the leading n by n 00063 * upper triangular part of the array A must contain the upper 00064 * triangular matrix and the strictly lower triangular part of 00065 * A is not referenced. 00066 * Before entry with UPLO = 'L' or 'l', the leading n by n 00067 * lower triangular part of the array A must contain the lower 00068 * triangular matrix and the strictly upper triangular part of 00069 * A is not referenced. 00070 * Note that when DIAG = 'U' or 'u', the diagonal elements of 00071 * A are not referenced either, but are assumed to be unity. 00072 * Unchanged on exit. 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 * X - DOUBLE PRECISION array of dimension at least 00081 * ( 1 + ( n - 1 )*abs( INCX ) ). 00082 * Before entry, the incremented array X must contain the n 00083 * element vector x. On exit, X is overwritten with the 00084 * tranformed vector x. 00085 * 00086 * INCX - INTEGER. 00087 * On entry, INCX specifies the increment for the elements of 00088 * X. INCX must not be zero. 00089 * Unchanged on exit. 00090 * 00091 * Further Details 00092 * =============== 00093 * 00094 * Level 2 Blas routine. 00095 * 00096 * -- Written on 22-October-1986. 00097 * Jack Dongarra, Argonne National Lab. 00098 * Jeremy Du Croz, Nag Central Office. 00099 * Sven Hammarling, Nag Central Office. 00100 * Richard Hanson, Sandia National Labs. 00101 * 00102 * ===================================================================== 00103 * 00104 * .. Parameters .. 00105 DOUBLE PRECISION ZERO 00106 PARAMETER (ZERO=0.0D+0) 00107 * .. 00108 * .. Local Scalars .. 00109 DOUBLE PRECISION TEMP 00110 INTEGER I,INFO,IX,J,JX,KX 00111 LOGICAL NOUNIT 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 EXTERNAL LSAME 00116 * .. 00117 * .. External Subroutines .. 00118 EXTERNAL XERBLA 00119 * .. 00120 * .. Intrinsic Functions .. 00121 INTRINSIC MAX 00122 * .. 00123 * 00124 * Test the input parameters. 00125 * 00126 INFO = 0 00127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00128 INFO = 1 00129 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00130 + .NOT.LSAME(TRANS,'C')) THEN 00131 INFO = 2 00132 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00133 INFO = 3 00134 ELSE IF (N.LT.0) THEN 00135 INFO = 4 00136 ELSE IF (LDA.LT.MAX(1,N)) THEN 00137 INFO = 6 00138 ELSE IF (INCX.EQ.0) THEN 00139 INFO = 8 00140 END IF 00141 IF (INFO.NE.0) THEN 00142 CALL XERBLA('DTRMV ',INFO) 00143 RETURN 00144 END IF 00145 * 00146 * Quick return if possible. 00147 * 00148 IF (N.EQ.0) RETURN 00149 * 00150 NOUNIT = LSAME(DIAG,'N') 00151 * 00152 * Set up the start point in X if the increment is not unity. This 00153 * will be ( N - 1 )*INCX too small for descending loops. 00154 * 00155 IF (INCX.LE.0) THEN 00156 KX = 1 - (N-1)*INCX 00157 ELSE IF (INCX.NE.1) THEN 00158 KX = 1 00159 END IF 00160 * 00161 * Start the operations. In this version the elements of A are 00162 * accessed sequentially with one pass through A. 00163 * 00164 IF (LSAME(TRANS,'N')) THEN 00165 * 00166 * Form x := A*x. 00167 * 00168 IF (LSAME(UPLO,'U')) THEN 00169 IF (INCX.EQ.1) THEN 00170 DO 20 J = 1,N 00171 IF (X(J).NE.ZERO) THEN 00172 TEMP = X(J) 00173 DO 10 I = 1,J - 1 00174 X(I) = X(I) + TEMP*A(I,J) 00175 10 CONTINUE 00176 IF (NOUNIT) X(J) = X(J)*A(J,J) 00177 END IF 00178 20 CONTINUE 00179 ELSE 00180 JX = KX 00181 DO 40 J = 1,N 00182 IF (X(JX).NE.ZERO) THEN 00183 TEMP = X(JX) 00184 IX = KX 00185 DO 30 I = 1,J - 1 00186 X(IX) = X(IX) + TEMP*A(I,J) 00187 IX = IX + INCX 00188 30 CONTINUE 00189 IF (NOUNIT) X(JX) = X(JX)*A(J,J) 00190 END IF 00191 JX = JX + INCX 00192 40 CONTINUE 00193 END IF 00194 ELSE 00195 IF (INCX.EQ.1) THEN 00196 DO 60 J = N,1,-1 00197 IF (X(J).NE.ZERO) THEN 00198 TEMP = X(J) 00199 DO 50 I = N,J + 1,-1 00200 X(I) = X(I) + TEMP*A(I,J) 00201 50 CONTINUE 00202 IF (NOUNIT) X(J) = X(J)*A(J,J) 00203 END IF 00204 60 CONTINUE 00205 ELSE 00206 KX = KX + (N-1)*INCX 00207 JX = KX 00208 DO 80 J = N,1,-1 00209 IF (X(JX).NE.ZERO) THEN 00210 TEMP = X(JX) 00211 IX = KX 00212 DO 70 I = N,J + 1,-1 00213 X(IX) = X(IX) + TEMP*A(I,J) 00214 IX = IX - INCX 00215 70 CONTINUE 00216 IF (NOUNIT) X(JX) = X(JX)*A(J,J) 00217 END IF 00218 JX = JX - INCX 00219 80 CONTINUE 00220 END IF 00221 END IF 00222 ELSE 00223 * 00224 * Form x := A'*x. 00225 * 00226 IF (LSAME(UPLO,'U')) THEN 00227 IF (INCX.EQ.1) THEN 00228 DO 100 J = N,1,-1 00229 TEMP = X(J) 00230 IF (NOUNIT) TEMP = TEMP*A(J,J) 00231 DO 90 I = J - 1,1,-1 00232 TEMP = TEMP + A(I,J)*X(I) 00233 90 CONTINUE 00234 X(J) = TEMP 00235 100 CONTINUE 00236 ELSE 00237 JX = KX + (N-1)*INCX 00238 DO 120 J = N,1,-1 00239 TEMP = X(JX) 00240 IX = JX 00241 IF (NOUNIT) TEMP = TEMP*A(J,J) 00242 DO 110 I = J - 1,1,-1 00243 IX = IX - INCX 00244 TEMP = TEMP + A(I,J)*X(IX) 00245 110 CONTINUE 00246 X(JX) = TEMP 00247 JX = JX - INCX 00248 120 CONTINUE 00249 END IF 00250 ELSE 00251 IF (INCX.EQ.1) THEN 00252 DO 140 J = 1,N 00253 TEMP = X(J) 00254 IF (NOUNIT) TEMP = TEMP*A(J,J) 00255 DO 130 I = J + 1,N 00256 TEMP = TEMP + A(I,J)*X(I) 00257 130 CONTINUE 00258 X(J) = TEMP 00259 140 CONTINUE 00260 ELSE 00261 JX = KX 00262 DO 160 J = 1,N 00263 TEMP = X(JX) 00264 IX = JX 00265 IF (NOUNIT) TEMP = TEMP*A(J,J) 00266 DO 150 I = J + 1,N 00267 IX = IX + INCX 00268 TEMP = TEMP + A(I,J)*X(IX) 00269 150 CONTINUE 00270 X(JX) = TEMP 00271 JX = JX + INCX 00272 160 CONTINUE 00273 END IF 00274 END IF 00275 END IF 00276 * 00277 RETURN 00278 * 00279 * End of DTRMV . 00280 * 00281 END
1.7.3 
