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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DTPMV 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER INCX,N 00015 * CHARACTER DIAG,TRANS,UPLO 00016 * .. 00017 * .. Array Arguments .. 00018 * DOUBLE PRECISION AP(*),X(*) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> DTPMV performs one of the matrix-vector operations 00028 *> 00029 *> x := A*x, or x := A**T*x, 00030 *> 00031 *> where x is an n element vector and A is an n by n unit, or non-unit, 00032 *> upper or lower triangular matrix, supplied in packed form. 00033 *> \endverbatim 00034 * 00035 * Arguments: 00036 * ========== 00037 * 00038 *> \param[in] UPLO 00039 *> \verbatim 00040 *> UPLO is CHARACTER*1 00041 *> On entry, UPLO specifies whether the matrix is an upper or 00042 *> lower triangular matrix as follows: 00043 *> 00044 *> UPLO = 'U' or 'u' A is an upper triangular matrix. 00045 *> 00046 *> UPLO = 'L' or 'l' A is a lower triangular matrix. 00047 *> \endverbatim 00048 *> 00049 *> \param[in] TRANS 00050 *> \verbatim 00051 *> TRANS is CHARACTER*1 00052 *> On entry, TRANS specifies the operation to be performed as 00053 *> follows: 00054 *> 00055 *> TRANS = 'N' or 'n' x := A*x. 00056 *> 00057 *> TRANS = 'T' or 't' x := A**T*x. 00058 *> 00059 *> TRANS = 'C' or 'c' x := A**T*x. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] DIAG 00063 *> \verbatim 00064 *> DIAG is CHARACTER*1 00065 *> On entry, DIAG specifies whether or not A is unit 00066 *> triangular as follows: 00067 *> 00068 *> DIAG = 'U' or 'u' A is assumed to be unit triangular. 00069 *> 00070 *> DIAG = 'N' or 'n' A is not assumed to be unit 00071 *> triangular. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] N 00075 *> \verbatim 00076 *> N is INTEGER 00077 *> On entry, N specifies the order of the matrix A. 00078 *> N must be at least zero. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] AP 00082 *> \verbatim 00083 *> AP is DOUBLE PRECISION array of DIMENSION at least 00084 *> ( ( n*( n + 1 ) )/2 ). 00085 *> Before entry with UPLO = 'U' or 'u', the array AP must 00086 *> contain the upper triangular matrix packed sequentially, 00087 *> column by column, so that AP( 1 ) contains a( 1, 1 ), 00088 *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 00089 *> respectively, and so on. 00090 *> Before entry with UPLO = 'L' or 'l', the array AP must 00091 *> contain the lower triangular matrix packed sequentially, 00092 *> column by column, so that AP( 1 ) contains a( 1, 1 ), 00093 *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 00094 *> respectively, and so on. 00095 *> Note that when DIAG = 'U' or 'u', the diagonal elements of 00096 *> A are not referenced, but are assumed to be unity. 00097 *> \endverbatim 00098 *> 00099 *> \param[in,out] X 00100 *> \verbatim 00101 *> X is DOUBLE PRECISION array of dimension at least 00102 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00103 *> Before entry, the incremented array X must contain the n 00104 *> element vector x. On exit, X is overwritten with the 00105 *> tranformed vector x. 00106 *> \endverbatim 00107 *> 00108 *> \param[in] INCX 00109 *> \verbatim 00110 *> INCX is INTEGER 00111 *> On entry, INCX specifies the increment for the elements of 00112 *> X. INCX must not be zero. 00113 *> \endverbatim 00114 * 00115 * Authors: 00116 * ======== 00117 * 00118 *> \author Univ. of Tennessee 00119 *> \author Univ. of California Berkeley 00120 *> \author Univ. of Colorado Denver 00121 *> \author NAG Ltd. 00122 * 00123 *> \date November 2011 00124 * 00125 *> \ingroup double_blas_level2 00126 * 00127 *> \par Further Details: 00128 * ===================== 00129 *> 00130 *> \verbatim 00131 *> 00132 *> Level 2 Blas routine. 00133 *> The vector and matrix arguments are not referenced when N = 0, or M = 0 00134 *> 00135 *> -- Written on 22-October-1986. 00136 *> Jack Dongarra, Argonne National Lab. 00137 *> Jeremy Du Croz, Nag Central Office. 00138 *> Sven Hammarling, Nag Central Office. 00139 *> Richard Hanson, Sandia National Labs. 00140 *> \endverbatim 00141 *> 00142 * ===================================================================== 00143 SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00144 * 00145 * -- Reference BLAS level2 routine (version 3.4.0) -- 00146 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00148 * November 2011 00149 * 00150 * .. Scalar Arguments .. 00151 INTEGER INCX,N 00152 CHARACTER DIAG,TRANS,UPLO 00153 * .. 00154 * .. Array Arguments .. 00155 DOUBLE PRECISION AP(*),X(*) 00156 * .. 00157 * 00158 * ===================================================================== 00159 * 00160 * .. Parameters .. 00161 DOUBLE PRECISION ZERO 00162 PARAMETER (ZERO=0.0D+0) 00163 * .. 00164 * .. Local Scalars .. 00165 DOUBLE PRECISION TEMP 00166 INTEGER I,INFO,IX,J,JX,K,KK,KX 00167 LOGICAL NOUNIT 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL XERBLA 00175 * .. 00176 * 00177 * Test the input parameters. 00178 * 00179 INFO = 0 00180 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00181 INFO = 1 00182 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00183 + .NOT.LSAME(TRANS,'C')) THEN 00184 INFO = 2 00185 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00186 INFO = 3 00187 ELSE IF (N.LT.0) THEN 00188 INFO = 4 00189 ELSE IF (INCX.EQ.0) THEN 00190 INFO = 7 00191 END IF 00192 IF (INFO.NE.0) THEN 00193 CALL XERBLA('DTPMV ',INFO) 00194 RETURN 00195 END IF 00196 * 00197 * Quick return if possible. 00198 * 00199 IF (N.EQ.0) RETURN 00200 * 00201 NOUNIT = LSAME(DIAG,'N') 00202 * 00203 * Set up the start point in X if the increment is not unity. This 00204 * will be ( N - 1 )*INCX too small for descending loops. 00205 * 00206 IF (INCX.LE.0) THEN 00207 KX = 1 - (N-1)*INCX 00208 ELSE IF (INCX.NE.1) THEN 00209 KX = 1 00210 END IF 00211 * 00212 * Start the operations. In this version the elements of AP are 00213 * accessed sequentially with one pass through AP. 00214 * 00215 IF (LSAME(TRANS,'N')) THEN 00216 * 00217 * Form x:= A*x. 00218 * 00219 IF (LSAME(UPLO,'U')) THEN 00220 KK = 1 00221 IF (INCX.EQ.1) THEN 00222 DO 20 J = 1,N 00223 IF (X(J).NE.ZERO) THEN 00224 TEMP = X(J) 00225 K = KK 00226 DO 10 I = 1,J - 1 00227 X(I) = X(I) + TEMP*AP(K) 00228 K = K + 1 00229 10 CONTINUE 00230 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 00231 END IF 00232 KK = KK + J 00233 20 CONTINUE 00234 ELSE 00235 JX = KX 00236 DO 40 J = 1,N 00237 IF (X(JX).NE.ZERO) THEN 00238 TEMP = X(JX) 00239 IX = KX 00240 DO 30 K = KK,KK + J - 2 00241 X(IX) = X(IX) + TEMP*AP(K) 00242 IX = IX + INCX 00243 30 CONTINUE 00244 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 00245 END IF 00246 JX = JX + INCX 00247 KK = KK + J 00248 40 CONTINUE 00249 END IF 00250 ELSE 00251 KK = (N* (N+1))/2 00252 IF (INCX.EQ.1) THEN 00253 DO 60 J = N,1,-1 00254 IF (X(J).NE.ZERO) THEN 00255 TEMP = X(J) 00256 K = KK 00257 DO 50 I = N,J + 1,-1 00258 X(I) = X(I) + TEMP*AP(K) 00259 K = K - 1 00260 50 CONTINUE 00261 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 00262 END IF 00263 KK = KK - (N-J+1) 00264 60 CONTINUE 00265 ELSE 00266 KX = KX + (N-1)*INCX 00267 JX = KX 00268 DO 80 J = N,1,-1 00269 IF (X(JX).NE.ZERO) THEN 00270 TEMP = X(JX) 00271 IX = KX 00272 DO 70 K = KK,KK - (N- (J+1)),-1 00273 X(IX) = X(IX) + TEMP*AP(K) 00274 IX = IX - INCX 00275 70 CONTINUE 00276 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 00277 END IF 00278 JX = JX - INCX 00279 KK = KK - (N-J+1) 00280 80 CONTINUE 00281 END IF 00282 END IF 00283 ELSE 00284 * 00285 * Form x := A**T*x. 00286 * 00287 IF (LSAME(UPLO,'U')) THEN 00288 KK = (N* (N+1))/2 00289 IF (INCX.EQ.1) THEN 00290 DO 100 J = N,1,-1 00291 TEMP = X(J) 00292 IF (NOUNIT) TEMP = TEMP*AP(KK) 00293 K = KK - 1 00294 DO 90 I = J - 1,1,-1 00295 TEMP = TEMP + AP(K)*X(I) 00296 K = K - 1 00297 90 CONTINUE 00298 X(J) = TEMP 00299 KK = KK - J 00300 100 CONTINUE 00301 ELSE 00302 JX = KX + (N-1)*INCX 00303 DO 120 J = N,1,-1 00304 TEMP = X(JX) 00305 IX = JX 00306 IF (NOUNIT) TEMP = TEMP*AP(KK) 00307 DO 110 K = KK - 1,KK - J + 1,-1 00308 IX = IX - INCX 00309 TEMP = TEMP + AP(K)*X(IX) 00310 110 CONTINUE 00311 X(JX) = TEMP 00312 JX = JX - INCX 00313 KK = KK - J 00314 120 CONTINUE 00315 END IF 00316 ELSE 00317 KK = 1 00318 IF (INCX.EQ.1) THEN 00319 DO 140 J = 1,N 00320 TEMP = X(J) 00321 IF (NOUNIT) TEMP = TEMP*AP(KK) 00322 K = KK + 1 00323 DO 130 I = J + 1,N 00324 TEMP = TEMP + AP(K)*X(I) 00325 K = K + 1 00326 130 CONTINUE 00327 X(J) = TEMP 00328 KK = KK + (N-J+1) 00329 140 CONTINUE 00330 ELSE 00331 JX = KX 00332 DO 160 J = 1,N 00333 TEMP = X(JX) 00334 IX = JX 00335 IF (NOUNIT) TEMP = TEMP*AP(KK) 00336 DO 150 K = KK + 1,KK + N - J 00337 IX = IX + INCX 00338 TEMP = TEMP + AP(K)*X(IX) 00339 150 CONTINUE 00340 X(JX) = TEMP 00341 JX = JX + INCX 00342 KK = KK + (N-J+1) 00343 160 CONTINUE 00344 END IF 00345 END IF 00346 END IF 00347 * 00348 RETURN 00349 * 00350 * End of DTPMV . 00351 * 00352 END