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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 COMPLEX AP(*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * CTPMV performs one of the matrix-vector operations 00014 * 00015 * x := A*x, or x := A**T*x, or x := A**H*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**T*x. 00040 * 00041 * TRANS = 'C' or 'c' x := A**H*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 - COMPLEX 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 - COMPLEX 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 * The vector and matrix arguments are not referenced when N = 0, or M = 0 00093 * 00094 * -- Written on 22-October-1986. 00095 * Jack Dongarra, Argonne National Lab. 00096 * Jeremy Du Croz, Nag Central Office. 00097 * Sven Hammarling, Nag Central Office. 00098 * Richard Hanson, Sandia National Labs. 00099 * 00100 * ===================================================================== 00101 * 00102 * .. Parameters .. 00103 COMPLEX ZERO 00104 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00105 * .. 00106 * .. Local Scalars .. 00107 COMPLEX TEMP 00108 INTEGER I,INFO,IX,J,JX,K,KK,KX 00109 LOGICAL NOCONJ,NOUNIT 00110 * .. 00111 * .. External Functions .. 00112 LOGICAL LSAME 00113 EXTERNAL LSAME 00114 * .. 00115 * .. External Subroutines .. 00116 EXTERNAL XERBLA 00117 * .. 00118 * .. Intrinsic Functions .. 00119 INTRINSIC CONJG 00120 * .. 00121 * 00122 * Test the input parameters. 00123 * 00124 INFO = 0 00125 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00126 INFO = 1 00127 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00128 + .NOT.LSAME(TRANS,'C')) THEN 00129 INFO = 2 00130 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00131 INFO = 3 00132 ELSE IF (N.LT.0) THEN 00133 INFO = 4 00134 ELSE IF (INCX.EQ.0) THEN 00135 INFO = 7 00136 END IF 00137 IF (INFO.NE.0) THEN 00138 CALL XERBLA('CTPMV ',INFO) 00139 RETURN 00140 END IF 00141 * 00142 * Quick return if possible. 00143 * 00144 IF (N.EQ.0) RETURN 00145 * 00146 NOCONJ = LSAME(TRANS,'T') 00147 NOUNIT = LSAME(DIAG,'N') 00148 * 00149 * Set up the start point in X if the increment is not unity. This 00150 * will be ( N - 1 )*INCX too small for descending loops. 00151 * 00152 IF (INCX.LE.0) THEN 00153 KX = 1 - (N-1)*INCX 00154 ELSE IF (INCX.NE.1) THEN 00155 KX = 1 00156 END IF 00157 * 00158 * Start the operations. In this version the elements of AP are 00159 * accessed sequentially with one pass through AP. 00160 * 00161 IF (LSAME(TRANS,'N')) THEN 00162 * 00163 * Form x:= A*x. 00164 * 00165 IF (LSAME(UPLO,'U')) THEN 00166 KK = 1 00167 IF (INCX.EQ.1) THEN 00168 DO 20 J = 1,N 00169 IF (X(J).NE.ZERO) THEN 00170 TEMP = X(J) 00171 K = KK 00172 DO 10 I = 1,J - 1 00173 X(I) = X(I) + TEMP*AP(K) 00174 K = K + 1 00175 10 CONTINUE 00176 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 00177 END IF 00178 KK = KK + J 00179 20 CONTINUE 00180 ELSE 00181 JX = KX 00182 DO 40 J = 1,N 00183 IF (X(JX).NE.ZERO) THEN 00184 TEMP = X(JX) 00185 IX = KX 00186 DO 30 K = KK,KK + J - 2 00187 X(IX) = X(IX) + TEMP*AP(K) 00188 IX = IX + INCX 00189 30 CONTINUE 00190 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 00191 END IF 00192 JX = JX + INCX 00193 KK = KK + J 00194 40 CONTINUE 00195 END IF 00196 ELSE 00197 KK = (N* (N+1))/2 00198 IF (INCX.EQ.1) THEN 00199 DO 60 J = N,1,-1 00200 IF (X(J).NE.ZERO) THEN 00201 TEMP = X(J) 00202 K = KK 00203 DO 50 I = N,J + 1,-1 00204 X(I) = X(I) + TEMP*AP(K) 00205 K = K - 1 00206 50 CONTINUE 00207 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 00208 END IF 00209 KK = KK - (N-J+1) 00210 60 CONTINUE 00211 ELSE 00212 KX = KX + (N-1)*INCX 00213 JX = KX 00214 DO 80 J = N,1,-1 00215 IF (X(JX).NE.ZERO) THEN 00216 TEMP = X(JX) 00217 IX = KX 00218 DO 70 K = KK,KK - (N- (J+1)),-1 00219 X(IX) = X(IX) + TEMP*AP(K) 00220 IX = IX - INCX 00221 70 CONTINUE 00222 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 00223 END IF 00224 JX = JX - INCX 00225 KK = KK - (N-J+1) 00226 80 CONTINUE 00227 END IF 00228 END IF 00229 ELSE 00230 * 00231 * Form x := A**T*x or x := A**H*x. 00232 * 00233 IF (LSAME(UPLO,'U')) THEN 00234 KK = (N* (N+1))/2 00235 IF (INCX.EQ.1) THEN 00236 DO 110 J = N,1,-1 00237 TEMP = X(J) 00238 K = KK - 1 00239 IF (NOCONJ) THEN 00240 IF (NOUNIT) TEMP = TEMP*AP(KK) 00241 DO 90 I = J - 1,1,-1 00242 TEMP = TEMP + AP(K)*X(I) 00243 K = K - 1 00244 90 CONTINUE 00245 ELSE 00246 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00247 DO 100 I = J - 1,1,-1 00248 TEMP = TEMP + CONJG(AP(K))*X(I) 00249 K = K - 1 00250 100 CONTINUE 00251 END IF 00252 X(J) = TEMP 00253 KK = KK - J 00254 110 CONTINUE 00255 ELSE 00256 JX = KX + (N-1)*INCX 00257 DO 140 J = N,1,-1 00258 TEMP = X(JX) 00259 IX = JX 00260 IF (NOCONJ) THEN 00261 IF (NOUNIT) TEMP = TEMP*AP(KK) 00262 DO 120 K = KK - 1,KK - J + 1,-1 00263 IX = IX - INCX 00264 TEMP = TEMP + AP(K)*X(IX) 00265 120 CONTINUE 00266 ELSE 00267 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00268 DO 130 K = KK - 1,KK - J + 1,-1 00269 IX = IX - INCX 00270 TEMP = TEMP + CONJG(AP(K))*X(IX) 00271 130 CONTINUE 00272 END IF 00273 X(JX) = TEMP 00274 JX = JX - INCX 00275 KK = KK - J 00276 140 CONTINUE 00277 END IF 00278 ELSE 00279 KK = 1 00280 IF (INCX.EQ.1) THEN 00281 DO 170 J = 1,N 00282 TEMP = X(J) 00283 K = KK + 1 00284 IF (NOCONJ) THEN 00285 IF (NOUNIT) TEMP = TEMP*AP(KK) 00286 DO 150 I = J + 1,N 00287 TEMP = TEMP + AP(K)*X(I) 00288 K = K + 1 00289 150 CONTINUE 00290 ELSE 00291 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00292 DO 160 I = J + 1,N 00293 TEMP = TEMP + CONJG(AP(K))*X(I) 00294 K = K + 1 00295 160 CONTINUE 00296 END IF 00297 X(J) = TEMP 00298 KK = KK + (N-J+1) 00299 170 CONTINUE 00300 ELSE 00301 JX = KX 00302 DO 200 J = 1,N 00303 TEMP = X(JX) 00304 IX = JX 00305 IF (NOCONJ) THEN 00306 IF (NOUNIT) TEMP = TEMP*AP(KK) 00307 DO 180 K = KK + 1,KK + N - J 00308 IX = IX + INCX 00309 TEMP = TEMP + AP(K)*X(IX) 00310 180 CONTINUE 00311 ELSE 00312 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00313 DO 190 K = KK + 1,KK + N - J 00314 IX = IX + INCX 00315 TEMP = TEMP + CONJG(AP(K))*X(IX) 00316 190 CONTINUE 00317 END IF 00318 X(JX) = TEMP 00319 JX = JX + INCX 00320 KK = KK + (N-J+1) 00321 200 CONTINUE 00322 END IF 00323 END IF 00324 END IF 00325 * 00326 RETURN 00327 * 00328 * End of CTPMV . 00329 * 00330 END
1.7.3 
