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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 DOUBLE PRECISION AP(*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * DTPMV 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, supplied in packed form. 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 * AP - DOUBLE PRECISION array of DIMENSION at least 00062 * ( ( n*( n + 1 ) )/2 ). 00063 * Before entry with UPLO = 'U' or 'u', the array AP must 00064 * contain the upper triangular matrix packed sequentially, 00065 * column by column, so that AP( 1 ) contains a( 1, 1 ), 00066 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 00067 * respectively, and so on. 00068 * Before entry with UPLO = 'L' or 'l', the array AP must 00069 * contain the lower triangular matrix packed sequentially, 00070 * column by column, so that AP( 1 ) contains a( 1, 1 ), 00071 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 00072 * respectively, and so on. 00073 * Note that when DIAG = 'U' or 'u', the diagonal elements of 00074 * A are not referenced, but are assumed to be unity. 00075 * Unchanged on exit. 00076 * 00077 * X - DOUBLE PRECISION array of dimension at least 00078 * ( 1 + ( n - 1 )*abs( INCX ) ). 00079 * Before entry, the incremented array X must contain the n 00080 * element vector x. On exit, X is overwritten with the 00081 * tranformed vector x. 00082 * 00083 * INCX - INTEGER. 00084 * On entry, INCX specifies the increment for the elements of 00085 * X. INCX must not be zero. 00086 * Unchanged on exit. 00087 * 00088 * Further Details 00089 * =============== 00090 * 00091 * Level 2 Blas routine. 00092 * 00093 * -- Written on 22-October-1986. 00094 * Jack Dongarra, Argonne National Lab. 00095 * Jeremy Du Croz, Nag Central Office. 00096 * Sven Hammarling, Nag Central Office. 00097 * Richard Hanson, Sandia National Labs. 00098 * 00099 * ===================================================================== 00100 * 00101 * .. Parameters .. 00102 DOUBLE PRECISION ZERO 00103 PARAMETER (ZERO=0.0D+0) 00104 * .. 00105 * .. Local Scalars .. 00106 DOUBLE PRECISION TEMP 00107 INTEGER I,INFO,IX,J,JX,K,KK,KX 00108 LOGICAL NOUNIT 00109 * .. 00110 * .. External Functions .. 00111 LOGICAL LSAME 00112 EXTERNAL LSAME 00113 * .. 00114 * .. External Subroutines .. 00115 EXTERNAL XERBLA 00116 * .. 00117 * 00118 * Test the input parameters. 00119 * 00120 INFO = 0 00121 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00122 INFO = 1 00123 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00124 + .NOT.LSAME(TRANS,'C')) THEN 00125 INFO = 2 00126 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00127 INFO = 3 00128 ELSE IF (N.LT.0) THEN 00129 INFO = 4 00130 ELSE IF (INCX.EQ.0) THEN 00131 INFO = 7 00132 END IF 00133 IF (INFO.NE.0) THEN 00134 CALL XERBLA('DTPMV ',INFO) 00135 RETURN 00136 END IF 00137 * 00138 * Quick return if possible. 00139 * 00140 IF (N.EQ.0) RETURN 00141 * 00142 NOUNIT = LSAME(DIAG,'N') 00143 * 00144 * Set up the start point in X if the increment is not unity. This 00145 * will be ( N - 1 )*INCX too small for descending loops. 00146 * 00147 IF (INCX.LE.0) THEN 00148 KX = 1 - (N-1)*INCX 00149 ELSE IF (INCX.NE.1) THEN 00150 KX = 1 00151 END IF 00152 * 00153 * Start the operations. In this version the elements of AP are 00154 * accessed sequentially with one pass through AP. 00155 * 00156 IF (LSAME(TRANS,'N')) THEN 00157 * 00158 * Form x:= A*x. 00159 * 00160 IF (LSAME(UPLO,'U')) THEN 00161 KK = 1 00162 IF (INCX.EQ.1) THEN 00163 DO 20 J = 1,N 00164 IF (X(J).NE.ZERO) THEN 00165 TEMP = X(J) 00166 K = KK 00167 DO 10 I = 1,J - 1 00168 X(I) = X(I) + TEMP*AP(K) 00169 K = K + 1 00170 10 CONTINUE 00171 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 00172 END IF 00173 KK = KK + J 00174 20 CONTINUE 00175 ELSE 00176 JX = KX 00177 DO 40 J = 1,N 00178 IF (X(JX).NE.ZERO) THEN 00179 TEMP = X(JX) 00180 IX = KX 00181 DO 30 K = KK,KK + J - 2 00182 X(IX) = X(IX) + TEMP*AP(K) 00183 IX = IX + INCX 00184 30 CONTINUE 00185 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 00186 END IF 00187 JX = JX + INCX 00188 KK = KK + J 00189 40 CONTINUE 00190 END IF 00191 ELSE 00192 KK = (N* (N+1))/2 00193 IF (INCX.EQ.1) THEN 00194 DO 60 J = N,1,-1 00195 IF (X(J).NE.ZERO) THEN 00196 TEMP = X(J) 00197 K = KK 00198 DO 50 I = N,J + 1,-1 00199 X(I) = X(I) + TEMP*AP(K) 00200 K = K - 1 00201 50 CONTINUE 00202 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 00203 END IF 00204 KK = KK - (N-J+1) 00205 60 CONTINUE 00206 ELSE 00207 KX = KX + (N-1)*INCX 00208 JX = KX 00209 DO 80 J = N,1,-1 00210 IF (X(JX).NE.ZERO) THEN 00211 TEMP = X(JX) 00212 IX = KX 00213 DO 70 K = KK,KK - (N- (J+1)),-1 00214 X(IX) = X(IX) + TEMP*AP(K) 00215 IX = IX - INCX 00216 70 CONTINUE 00217 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 00218 END IF 00219 JX = JX - INCX 00220 KK = KK - (N-J+1) 00221 80 CONTINUE 00222 END IF 00223 END IF 00224 ELSE 00225 * 00226 * Form x := A'*x. 00227 * 00228 IF (LSAME(UPLO,'U')) THEN 00229 KK = (N* (N+1))/2 00230 IF (INCX.EQ.1) THEN 00231 DO 100 J = N,1,-1 00232 TEMP = X(J) 00233 IF (NOUNIT) TEMP = TEMP*AP(KK) 00234 K = KK - 1 00235 DO 90 I = J - 1,1,-1 00236 TEMP = TEMP + AP(K)*X(I) 00237 K = K - 1 00238 90 CONTINUE 00239 X(J) = TEMP 00240 KK = KK - J 00241 100 CONTINUE 00242 ELSE 00243 JX = KX + (N-1)*INCX 00244 DO 120 J = N,1,-1 00245 TEMP = X(JX) 00246 IX = JX 00247 IF (NOUNIT) TEMP = TEMP*AP(KK) 00248 DO 110 K = KK - 1,KK - J + 1,-1 00249 IX = IX - INCX 00250 TEMP = TEMP + AP(K)*X(IX) 00251 110 CONTINUE 00252 X(JX) = TEMP 00253 JX = JX - INCX 00254 KK = KK - J 00255 120 CONTINUE 00256 END IF 00257 ELSE 00258 KK = 1 00259 IF (INCX.EQ.1) THEN 00260 DO 140 J = 1,N 00261 TEMP = X(J) 00262 IF (NOUNIT) TEMP = TEMP*AP(KK) 00263 K = KK + 1 00264 DO 130 I = J + 1,N 00265 TEMP = TEMP + AP(K)*X(I) 00266 K = K + 1 00267 130 CONTINUE 00268 X(J) = TEMP 00269 KK = KK + (N-J+1) 00270 140 CONTINUE 00271 ELSE 00272 JX = KX 00273 DO 160 J = 1,N 00274 TEMP = X(JX) 00275 IX = JX 00276 IF (NOUNIT) TEMP = TEMP*AP(KK) 00277 DO 150 K = KK + 1,KK + N - J 00278 IX = IX + INCX 00279 TEMP = TEMP + AP(K)*X(IX) 00280 150 CONTINUE 00281 X(JX) = TEMP 00282 JX = JX + INCX 00283 KK = KK + (N-J+1) 00284 160 CONTINUE 00285 END IF 00286 END IF 00287 END IF 00288 * 00289 RETURN 00290 * 00291 * End of DTPMV . 00292 * 00293 END
1.7.3 
