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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DTPSV 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 DTPSV(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 *> DTPSV solves one of the systems of equations 00028 *> 00029 *> A*x = b, or A**T*x = b, 00030 *> 00031 *> where b and x are n element vectors and A is an n by n unit, or 00032 *> non-unit, upper or lower triangular matrix, supplied in packed form. 00033 *> 00034 *> No test for singularity or near-singularity is included in this 00035 *> routine. Such tests must be performed before calling this routine. 00036 *> \endverbatim 00037 * 00038 * Arguments: 00039 * ========== 00040 * 00041 *> \param[in] UPLO 00042 *> \verbatim 00043 *> UPLO is CHARACTER*1 00044 *> On entry, UPLO specifies whether the matrix is an upper or 00045 *> lower triangular matrix as follows: 00046 *> 00047 *> UPLO = 'U' or 'u' A is an upper triangular matrix. 00048 *> 00049 *> UPLO = 'L' or 'l' A is a lower triangular matrix. 00050 *> \endverbatim 00051 *> 00052 *> \param[in] TRANS 00053 *> \verbatim 00054 *> TRANS is CHARACTER*1 00055 *> On entry, TRANS specifies the equations to be solved as 00056 *> follows: 00057 *> 00058 *> TRANS = 'N' or 'n' A*x = b. 00059 *> 00060 *> TRANS = 'T' or 't' A**T*x = b. 00061 *> 00062 *> TRANS = 'C' or 'c' A**T*x = b. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] DIAG 00066 *> \verbatim 00067 *> DIAG is CHARACTER*1 00068 *> On entry, DIAG specifies whether or not A is unit 00069 *> triangular as follows: 00070 *> 00071 *> DIAG = 'U' or 'u' A is assumed to be unit triangular. 00072 *> 00073 *> DIAG = 'N' or 'n' A is not assumed to be unit 00074 *> triangular. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] N 00078 *> \verbatim 00079 *> N is INTEGER 00080 *> On entry, N specifies the order of the matrix A. 00081 *> N must be at least zero. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] AP 00085 *> \verbatim 00086 *> AP is DOUBLE PRECISION array of DIMENSION at least 00087 *> ( ( n*( n + 1 ) )/2 ). 00088 *> Before entry with UPLO = 'U' or 'u', the array AP must 00089 *> contain the upper triangular matrix packed sequentially, 00090 *> column by column, so that AP( 1 ) contains a( 1, 1 ), 00091 *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 00092 *> respectively, and so on. 00093 *> Before entry with UPLO = 'L' or 'l', the array AP must 00094 *> contain the lower triangular matrix packed sequentially, 00095 *> column by column, so that AP( 1 ) contains a( 1, 1 ), 00096 *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 00097 *> respectively, and so on. 00098 *> Note that when DIAG = 'U' or 'u', the diagonal elements of 00099 *> A are not referenced, but are assumed to be unity. 00100 *> \endverbatim 00101 *> 00102 *> \param[in,out] X 00103 *> \verbatim 00104 *> X is DOUBLE PRECISION array of dimension at least 00105 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00106 *> Before entry, the incremented array X must contain the n 00107 *> element right-hand side vector b. On exit, X is overwritten 00108 *> with the solution vector x. 00109 *> \endverbatim 00110 *> 00111 *> \param[in] INCX 00112 *> \verbatim 00113 *> INCX is INTEGER 00114 *> On entry, INCX specifies the increment for the elements of 00115 *> X. INCX must not be zero. 00116 *> \endverbatim 00117 * 00118 * Authors: 00119 * ======== 00120 * 00121 *> \author Univ. of Tennessee 00122 *> \author Univ. of California Berkeley 00123 *> \author Univ. of Colorado Denver 00124 *> \author NAG Ltd. 00125 * 00126 *> \date November 2011 00127 * 00128 *> \ingroup double_blas_level2 00129 * 00130 *> \par Further Details: 00131 * ===================== 00132 *> 00133 *> \verbatim 00134 *> 00135 *> Level 2 Blas routine. 00136 *> 00137 *> -- Written on 22-October-1986. 00138 *> Jack Dongarra, Argonne National Lab. 00139 *> Jeremy Du Croz, Nag Central Office. 00140 *> Sven Hammarling, Nag Central Office. 00141 *> Richard Hanson, Sandia National Labs. 00142 *> \endverbatim 00143 *> 00144 * ===================================================================== 00145 SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00146 * 00147 * -- Reference BLAS level2 routine (version 3.4.0) -- 00148 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00150 * November 2011 00151 * 00152 * .. Scalar Arguments .. 00153 INTEGER INCX,N 00154 CHARACTER DIAG,TRANS,UPLO 00155 * .. 00156 * .. Array Arguments .. 00157 DOUBLE PRECISION AP(*),X(*) 00158 * .. 00159 * 00160 * ===================================================================== 00161 * 00162 * .. Parameters .. 00163 DOUBLE PRECISION ZERO 00164 PARAMETER (ZERO=0.0D+0) 00165 * .. 00166 * .. Local Scalars .. 00167 DOUBLE PRECISION TEMP 00168 INTEGER I,INFO,IX,J,JX,K,KK,KX 00169 LOGICAL NOUNIT 00170 * .. 00171 * .. External Functions .. 00172 LOGICAL LSAME 00173 EXTERNAL LSAME 00174 * .. 00175 * .. External Subroutines .. 00176 EXTERNAL XERBLA 00177 * .. 00178 * 00179 * Test the input parameters. 00180 * 00181 INFO = 0 00182 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00183 INFO = 1 00184 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00185 + .NOT.LSAME(TRANS,'C')) THEN 00186 INFO = 2 00187 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00188 INFO = 3 00189 ELSE IF (N.LT.0) THEN 00190 INFO = 4 00191 ELSE IF (INCX.EQ.0) THEN 00192 INFO = 7 00193 END IF 00194 IF (INFO.NE.0) THEN 00195 CALL XERBLA('DTPSV ',INFO) 00196 RETURN 00197 END IF 00198 * 00199 * Quick return if possible. 00200 * 00201 IF (N.EQ.0) RETURN 00202 * 00203 NOUNIT = LSAME(DIAG,'N') 00204 * 00205 * Set up the start point in X if the increment is not unity. This 00206 * will be ( N - 1 )*INCX too small for descending loops. 00207 * 00208 IF (INCX.LE.0) THEN 00209 KX = 1 - (N-1)*INCX 00210 ELSE IF (INCX.NE.1) THEN 00211 KX = 1 00212 END IF 00213 * 00214 * Start the operations. In this version the elements of AP are 00215 * accessed sequentially with one pass through AP. 00216 * 00217 IF (LSAME(TRANS,'N')) THEN 00218 * 00219 * Form x := inv( A )*x. 00220 * 00221 IF (LSAME(UPLO,'U')) THEN 00222 KK = (N* (N+1))/2 00223 IF (INCX.EQ.1) THEN 00224 DO 20 J = N,1,-1 00225 IF (X(J).NE.ZERO) THEN 00226 IF (NOUNIT) X(J) = X(J)/AP(KK) 00227 TEMP = X(J) 00228 K = KK - 1 00229 DO 10 I = J - 1,1,-1 00230 X(I) = X(I) - TEMP*AP(K) 00231 K = K - 1 00232 10 CONTINUE 00233 END IF 00234 KK = KK - J 00235 20 CONTINUE 00236 ELSE 00237 JX = KX + (N-1)*INCX 00238 DO 40 J = N,1,-1 00239 IF (X(JX).NE.ZERO) THEN 00240 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00241 TEMP = X(JX) 00242 IX = JX 00243 DO 30 K = KK - 1,KK - J + 1,-1 00244 IX = IX - INCX 00245 X(IX) = X(IX) - TEMP*AP(K) 00246 30 CONTINUE 00247 END IF 00248 JX = JX - INCX 00249 KK = KK - J 00250 40 CONTINUE 00251 END IF 00252 ELSE 00253 KK = 1 00254 IF (INCX.EQ.1) THEN 00255 DO 60 J = 1,N 00256 IF (X(J).NE.ZERO) THEN 00257 IF (NOUNIT) X(J) = X(J)/AP(KK) 00258 TEMP = X(J) 00259 K = KK + 1 00260 DO 50 I = J + 1,N 00261 X(I) = X(I) - TEMP*AP(K) 00262 K = K + 1 00263 50 CONTINUE 00264 END IF 00265 KK = KK + (N-J+1) 00266 60 CONTINUE 00267 ELSE 00268 JX = KX 00269 DO 80 J = 1,N 00270 IF (X(JX).NE.ZERO) THEN 00271 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00272 TEMP = X(JX) 00273 IX = JX 00274 DO 70 K = KK + 1,KK + N - J 00275 IX = IX + INCX 00276 X(IX) = X(IX) - TEMP*AP(K) 00277 70 CONTINUE 00278 END IF 00279 JX = JX + INCX 00280 KK = KK + (N-J+1) 00281 80 CONTINUE 00282 END IF 00283 END IF 00284 ELSE 00285 * 00286 * Form x := inv( A**T )*x. 00287 * 00288 IF (LSAME(UPLO,'U')) THEN 00289 KK = 1 00290 IF (INCX.EQ.1) THEN 00291 DO 100 J = 1,N 00292 TEMP = X(J) 00293 K = KK 00294 DO 90 I = 1,J - 1 00295 TEMP = TEMP - AP(K)*X(I) 00296 K = K + 1 00297 90 CONTINUE 00298 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00299 X(J) = TEMP 00300 KK = KK + J 00301 100 CONTINUE 00302 ELSE 00303 JX = KX 00304 DO 120 J = 1,N 00305 TEMP = X(JX) 00306 IX = KX 00307 DO 110 K = KK,KK + J - 2 00308 TEMP = TEMP - AP(K)*X(IX) 00309 IX = IX + INCX 00310 110 CONTINUE 00311 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00312 X(JX) = TEMP 00313 JX = JX + INCX 00314 KK = KK + J 00315 120 CONTINUE 00316 END IF 00317 ELSE 00318 KK = (N* (N+1))/2 00319 IF (INCX.EQ.1) THEN 00320 DO 140 J = N,1,-1 00321 TEMP = X(J) 00322 K = KK 00323 DO 130 I = N,J + 1,-1 00324 TEMP = TEMP - AP(K)*X(I) 00325 K = K - 1 00326 130 CONTINUE 00327 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00328 X(J) = TEMP 00329 KK = KK - (N-J+1) 00330 140 CONTINUE 00331 ELSE 00332 KX = KX + (N-1)*INCX 00333 JX = KX 00334 DO 160 J = N,1,-1 00335 TEMP = X(JX) 00336 IX = KX 00337 DO 150 K = KK,KK - (N- (J+1)),-1 00338 TEMP = TEMP - AP(K)*X(IX) 00339 IX = IX - INCX 00340 150 CONTINUE 00341 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00342 X(JX) = TEMP 00343 JX = JX - INCX 00344 KK = KK - (N-J+1) 00345 160 CONTINUE 00346 END IF 00347 END IF 00348 END IF 00349 * 00350 RETURN 00351 * 00352 * End of DTPSV . 00353 * 00354 END