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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CTPMV 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 CTPMV(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 * COMPLEX AP(*),X(*) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> CTPMV performs one of the matrix-vector operations 00028 *> 00029 *> x := A*x, or x := A**T*x, or x := A**H*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**H*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 COMPLEX 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 COMPLEX 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 complex_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 CTPMV(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 COMPLEX AP(*),X(*) 00156 * .. 00157 * 00158 * ===================================================================== 00159 * 00160 * .. Parameters .. 00161 COMPLEX ZERO 00162 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00163 * .. 00164 * .. Local Scalars .. 00165 COMPLEX TEMP 00166 INTEGER I,INFO,IX,J,JX,K,KK,KX 00167 LOGICAL NOCONJ,NOUNIT 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL XERBLA 00175 * .. 00176 * .. Intrinsic Functions .. 00177 INTRINSIC CONJG 00178 * .. 00179 * 00180 * Test the input parameters. 00181 * 00182 INFO = 0 00183 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00184 INFO = 1 00185 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00186 + .NOT.LSAME(TRANS,'C')) THEN 00187 INFO = 2 00188 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00189 INFO = 3 00190 ELSE IF (N.LT.0) THEN 00191 INFO = 4 00192 ELSE IF (INCX.EQ.0) THEN 00193 INFO = 7 00194 END IF 00195 IF (INFO.NE.0) THEN 00196 CALL XERBLA('CTPMV ',INFO) 00197 RETURN 00198 END IF 00199 * 00200 * Quick return if possible. 00201 * 00202 IF (N.EQ.0) RETURN 00203 * 00204 NOCONJ = LSAME(TRANS,'T') 00205 NOUNIT = LSAME(DIAG,'N') 00206 * 00207 * Set up the start point in X if the increment is not unity. This 00208 * will be ( N - 1 )*INCX too small for descending loops. 00209 * 00210 IF (INCX.LE.0) THEN 00211 KX = 1 - (N-1)*INCX 00212 ELSE IF (INCX.NE.1) THEN 00213 KX = 1 00214 END IF 00215 * 00216 * Start the operations. In this version the elements of AP are 00217 * accessed sequentially with one pass through AP. 00218 * 00219 IF (LSAME(TRANS,'N')) THEN 00220 * 00221 * Form x:= A*x. 00222 * 00223 IF (LSAME(UPLO,'U')) THEN 00224 KK = 1 00225 IF (INCX.EQ.1) THEN 00226 DO 20 J = 1,N 00227 IF (X(J).NE.ZERO) THEN 00228 TEMP = X(J) 00229 K = KK 00230 DO 10 I = 1,J - 1 00231 X(I) = X(I) + TEMP*AP(K) 00232 K = K + 1 00233 10 CONTINUE 00234 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 00235 END IF 00236 KK = KK + J 00237 20 CONTINUE 00238 ELSE 00239 JX = KX 00240 DO 40 J = 1,N 00241 IF (X(JX).NE.ZERO) THEN 00242 TEMP = X(JX) 00243 IX = KX 00244 DO 30 K = KK,KK + J - 2 00245 X(IX) = X(IX) + TEMP*AP(K) 00246 IX = IX + INCX 00247 30 CONTINUE 00248 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 00249 END IF 00250 JX = JX + INCX 00251 KK = KK + J 00252 40 CONTINUE 00253 END IF 00254 ELSE 00255 KK = (N* (N+1))/2 00256 IF (INCX.EQ.1) THEN 00257 DO 60 J = N,1,-1 00258 IF (X(J).NE.ZERO) THEN 00259 TEMP = X(J) 00260 K = KK 00261 DO 50 I = N,J + 1,-1 00262 X(I) = X(I) + TEMP*AP(K) 00263 K = K - 1 00264 50 CONTINUE 00265 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 00266 END IF 00267 KK = KK - (N-J+1) 00268 60 CONTINUE 00269 ELSE 00270 KX = KX + (N-1)*INCX 00271 JX = KX 00272 DO 80 J = N,1,-1 00273 IF (X(JX).NE.ZERO) THEN 00274 TEMP = X(JX) 00275 IX = KX 00276 DO 70 K = KK,KK - (N- (J+1)),-1 00277 X(IX) = X(IX) + TEMP*AP(K) 00278 IX = IX - INCX 00279 70 CONTINUE 00280 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 00281 END IF 00282 JX = JX - INCX 00283 KK = KK - (N-J+1) 00284 80 CONTINUE 00285 END IF 00286 END IF 00287 ELSE 00288 * 00289 * Form x := A**T*x or x := A**H*x. 00290 * 00291 IF (LSAME(UPLO,'U')) THEN 00292 KK = (N* (N+1))/2 00293 IF (INCX.EQ.1) THEN 00294 DO 110 J = N,1,-1 00295 TEMP = X(J) 00296 K = KK - 1 00297 IF (NOCONJ) THEN 00298 IF (NOUNIT) TEMP = TEMP*AP(KK) 00299 DO 90 I = J - 1,1,-1 00300 TEMP = TEMP + AP(K)*X(I) 00301 K = K - 1 00302 90 CONTINUE 00303 ELSE 00304 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00305 DO 100 I = J - 1,1,-1 00306 TEMP = TEMP + CONJG(AP(K))*X(I) 00307 K = K - 1 00308 100 CONTINUE 00309 END IF 00310 X(J) = TEMP 00311 KK = KK - J 00312 110 CONTINUE 00313 ELSE 00314 JX = KX + (N-1)*INCX 00315 DO 140 J = N,1,-1 00316 TEMP = X(JX) 00317 IX = JX 00318 IF (NOCONJ) THEN 00319 IF (NOUNIT) TEMP = TEMP*AP(KK) 00320 DO 120 K = KK - 1,KK - J + 1,-1 00321 IX = IX - INCX 00322 TEMP = TEMP + AP(K)*X(IX) 00323 120 CONTINUE 00324 ELSE 00325 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00326 DO 130 K = KK - 1,KK - J + 1,-1 00327 IX = IX - INCX 00328 TEMP = TEMP + CONJG(AP(K))*X(IX) 00329 130 CONTINUE 00330 END IF 00331 X(JX) = TEMP 00332 JX = JX - INCX 00333 KK = KK - J 00334 140 CONTINUE 00335 END IF 00336 ELSE 00337 KK = 1 00338 IF (INCX.EQ.1) THEN 00339 DO 170 J = 1,N 00340 TEMP = X(J) 00341 K = KK + 1 00342 IF (NOCONJ) THEN 00343 IF (NOUNIT) TEMP = TEMP*AP(KK) 00344 DO 150 I = J + 1,N 00345 TEMP = TEMP + AP(K)*X(I) 00346 K = K + 1 00347 150 CONTINUE 00348 ELSE 00349 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00350 DO 160 I = J + 1,N 00351 TEMP = TEMP + CONJG(AP(K))*X(I) 00352 K = K + 1 00353 160 CONTINUE 00354 END IF 00355 X(J) = TEMP 00356 KK = KK + (N-J+1) 00357 170 CONTINUE 00358 ELSE 00359 JX = KX 00360 DO 200 J = 1,N 00361 TEMP = X(JX) 00362 IX = JX 00363 IF (NOCONJ) THEN 00364 IF (NOUNIT) TEMP = TEMP*AP(KK) 00365 DO 180 K = KK + 1,KK + N - J 00366 IX = IX + INCX 00367 TEMP = TEMP + AP(K)*X(IX) 00368 180 CONTINUE 00369 ELSE 00370 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00371 DO 190 K = KK + 1,KK + N - J 00372 IX = IX + INCX 00373 TEMP = TEMP + CONJG(AP(K))*X(IX) 00374 190 CONTINUE 00375 END IF 00376 X(JX) = TEMP 00377 JX = JX + INCX 00378 KK = KK + (N-J+1) 00379 200 CONTINUE 00380 END IF 00381 END IF 00382 END IF 00383 * 00384 RETURN 00385 * 00386 * End of CTPMV . 00387 * 00388 END