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LAPACK 3.3.0
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LAPACK 3.3.0
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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'*x, or x := conjg( 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 := conjg( 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 - 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 * 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 COMPLEX ZERO 00103 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00104 * .. 00105 * .. Local Scalars .. 00106 COMPLEX TEMP 00107 INTEGER I,INFO,IX,J,JX,K,KK,KX 00108 LOGICAL NOCONJ,NOUNIT 00109 * .. 00110 * .. External Functions .. 00111 LOGICAL LSAME 00112 EXTERNAL LSAME 00113 * .. 00114 * .. External Subroutines .. 00115 EXTERNAL XERBLA 00116 * .. 00117 * .. Intrinsic Functions .. 00118 INTRINSIC CONJG 00119 * .. 00120 * 00121 * Test the input parameters. 00122 * 00123 INFO = 0 00124 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00125 INFO = 1 00126 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00127 + .NOT.LSAME(TRANS,'C')) THEN 00128 INFO = 2 00129 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00130 INFO = 3 00131 ELSE IF (N.LT.0) THEN 00132 INFO = 4 00133 ELSE IF (INCX.EQ.0) THEN 00134 INFO = 7 00135 END IF 00136 IF (INFO.NE.0) THEN 00137 CALL XERBLA('CTPMV ',INFO) 00138 RETURN 00139 END IF 00140 * 00141 * Quick return if possible. 00142 * 00143 IF (N.EQ.0) RETURN 00144 * 00145 NOCONJ = LSAME(TRANS,'T') 00146 NOUNIT = LSAME(DIAG,'N') 00147 * 00148 * Set up the start point in X if the increment is not unity. This 00149 * will be ( N - 1 )*INCX too small for descending loops. 00150 * 00151 IF (INCX.LE.0) THEN 00152 KX = 1 - (N-1)*INCX 00153 ELSE IF (INCX.NE.1) THEN 00154 KX = 1 00155 END IF 00156 * 00157 * Start the operations. In this version the elements of AP are 00158 * accessed sequentially with one pass through AP. 00159 * 00160 IF (LSAME(TRANS,'N')) THEN 00161 * 00162 * Form x:= A*x. 00163 * 00164 IF (LSAME(UPLO,'U')) THEN 00165 KK = 1 00166 IF (INCX.EQ.1) THEN 00167 DO 20 J = 1,N 00168 IF (X(J).NE.ZERO) THEN 00169 TEMP = X(J) 00170 K = KK 00171 DO 10 I = 1,J - 1 00172 X(I) = X(I) + TEMP*AP(K) 00173 K = K + 1 00174 10 CONTINUE 00175 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 00176 END IF 00177 KK = KK + J 00178 20 CONTINUE 00179 ELSE 00180 JX = KX 00181 DO 40 J = 1,N 00182 IF (X(JX).NE.ZERO) THEN 00183 TEMP = X(JX) 00184 IX = KX 00185 DO 30 K = KK,KK + J - 2 00186 X(IX) = X(IX) + TEMP*AP(K) 00187 IX = IX + INCX 00188 30 CONTINUE 00189 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 00190 END IF 00191 JX = JX + INCX 00192 KK = KK + J 00193 40 CONTINUE 00194 END IF 00195 ELSE 00196 KK = (N* (N+1))/2 00197 IF (INCX.EQ.1) THEN 00198 DO 60 J = N,1,-1 00199 IF (X(J).NE.ZERO) THEN 00200 TEMP = X(J) 00201 K = KK 00202 DO 50 I = N,J + 1,-1 00203 X(I) = X(I) + TEMP*AP(K) 00204 K = K - 1 00205 50 CONTINUE 00206 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 00207 END IF 00208 KK = KK - (N-J+1) 00209 60 CONTINUE 00210 ELSE 00211 KX = KX + (N-1)*INCX 00212 JX = KX 00213 DO 80 J = N,1,-1 00214 IF (X(JX).NE.ZERO) THEN 00215 TEMP = X(JX) 00216 IX = KX 00217 DO 70 K = KK,KK - (N- (J+1)),-1 00218 X(IX) = X(IX) + TEMP*AP(K) 00219 IX = IX - INCX 00220 70 CONTINUE 00221 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 00222 END IF 00223 JX = JX - INCX 00224 KK = KK - (N-J+1) 00225 80 CONTINUE 00226 END IF 00227 END IF 00228 ELSE 00229 * 00230 * Form x := A'*x or x := conjg( A' )*x. 00231 * 00232 IF (LSAME(UPLO,'U')) THEN 00233 KK = (N* (N+1))/2 00234 IF (INCX.EQ.1) THEN 00235 DO 110 J = N,1,-1 00236 TEMP = X(J) 00237 K = KK - 1 00238 IF (NOCONJ) THEN 00239 IF (NOUNIT) TEMP = TEMP*AP(KK) 00240 DO 90 I = J - 1,1,-1 00241 TEMP = TEMP + AP(K)*X(I) 00242 K = K - 1 00243 90 CONTINUE 00244 ELSE 00245 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00246 DO 100 I = J - 1,1,-1 00247 TEMP = TEMP + CONJG(AP(K))*X(I) 00248 K = K - 1 00249 100 CONTINUE 00250 END IF 00251 X(J) = TEMP 00252 KK = KK - J 00253 110 CONTINUE 00254 ELSE 00255 JX = KX + (N-1)*INCX 00256 DO 140 J = N,1,-1 00257 TEMP = X(JX) 00258 IX = JX 00259 IF (NOCONJ) THEN 00260 IF (NOUNIT) TEMP = TEMP*AP(KK) 00261 DO 120 K = KK - 1,KK - J + 1,-1 00262 IX = IX - INCX 00263 TEMP = TEMP + AP(K)*X(IX) 00264 120 CONTINUE 00265 ELSE 00266 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00267 DO 130 K = KK - 1,KK - J + 1,-1 00268 IX = IX - INCX 00269 TEMP = TEMP + CONJG(AP(K))*X(IX) 00270 130 CONTINUE 00271 END IF 00272 X(JX) = TEMP 00273 JX = JX - INCX 00274 KK = KK - J 00275 140 CONTINUE 00276 END IF 00277 ELSE 00278 KK = 1 00279 IF (INCX.EQ.1) THEN 00280 DO 170 J = 1,N 00281 TEMP = X(J) 00282 K = KK + 1 00283 IF (NOCONJ) THEN 00284 IF (NOUNIT) TEMP = TEMP*AP(KK) 00285 DO 150 I = J + 1,N 00286 TEMP = TEMP + AP(K)*X(I) 00287 K = K + 1 00288 150 CONTINUE 00289 ELSE 00290 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00291 DO 160 I = J + 1,N 00292 TEMP = TEMP + CONJG(AP(K))*X(I) 00293 K = K + 1 00294 160 CONTINUE 00295 END IF 00296 X(J) = TEMP 00297 KK = KK + (N-J+1) 00298 170 CONTINUE 00299 ELSE 00300 JX = KX 00301 DO 200 J = 1,N 00302 TEMP = X(JX) 00303 IX = JX 00304 IF (NOCONJ) THEN 00305 IF (NOUNIT) TEMP = TEMP*AP(KK) 00306 DO 180 K = KK + 1,KK + N - J 00307 IX = IX + INCX 00308 TEMP = TEMP + AP(K)*X(IX) 00309 180 CONTINUE 00310 ELSE 00311 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK)) 00312 DO 190 K = KK + 1,KK + N - J 00313 IX = IX + INCX 00314 TEMP = TEMP + CONJG(AP(K))*X(IX) 00315 190 CONTINUE 00316 END IF 00317 X(JX) = TEMP 00318 JX = JX + INCX 00319 KK = KK + (N-J+1) 00320 200 CONTINUE 00321 END IF 00322 END IF 00323 END IF 00324 * 00325 RETURN 00326 * 00327 * End of CTPMV . 00328 * 00329 END
1.7.3 
