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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 CTPSV(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 * CTPSV solves one of the systems of equations 00014 * 00015 * A*x = b, or A**T*x = b, or A**H*x = b, 00016 * 00017 * where b and x are n element vectors and A is an n by n unit, or 00018 * non-unit, upper or lower triangular matrix, supplied in packed form. 00019 * 00020 * No test for singularity or near-singularity is included in this 00021 * routine. Such tests must be performed before calling this routine. 00022 * 00023 * Arguments 00024 * ========== 00025 * 00026 * UPLO - CHARACTER*1. 00027 * On entry, UPLO specifies whether the matrix is an upper or 00028 * lower triangular matrix as follows: 00029 * 00030 * UPLO = 'U' or 'u' A is an upper triangular matrix. 00031 * 00032 * UPLO = 'L' or 'l' A is a lower triangular matrix. 00033 * 00034 * Unchanged on exit. 00035 * 00036 * TRANS - CHARACTER*1. 00037 * On entry, TRANS specifies the equations to be solved as 00038 * follows: 00039 * 00040 * TRANS = 'N' or 'n' A*x = b. 00041 * 00042 * TRANS = 'T' or 't' A**T*x = b. 00043 * 00044 * TRANS = 'C' or 'c' A**H*x = b. 00045 * 00046 * Unchanged on exit. 00047 * 00048 * DIAG - CHARACTER*1. 00049 * On entry, DIAG specifies whether or not A is unit 00050 * triangular as follows: 00051 * 00052 * DIAG = 'U' or 'u' A is assumed to be unit triangular. 00053 * 00054 * DIAG = 'N' or 'n' A is not assumed to be unit 00055 * triangular. 00056 * 00057 * Unchanged on exit. 00058 * 00059 * N - INTEGER. 00060 * On entry, N specifies the order of the matrix A. 00061 * N must be at least zero. 00062 * Unchanged on exit. 00063 * 00064 * AP - COMPLEX array of DIMENSION at least 00065 * ( ( n*( n + 1 ) )/2 ). 00066 * Before entry with UPLO = 'U' or 'u', the array AP must 00067 * contain the upper triangular matrix packed sequentially, 00068 * column by column, so that AP( 1 ) contains a( 1, 1 ), 00069 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 00070 * respectively, and so on. 00071 * Before entry with UPLO = 'L' or 'l', the array AP must 00072 * contain the lower triangular matrix packed sequentially, 00073 * column by column, so that AP( 1 ) contains a( 1, 1 ), 00074 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 00075 * respectively, and so on. 00076 * Note that when DIAG = 'U' or 'u', the diagonal elements of 00077 * A are not referenced, but are assumed to be unity. 00078 * Unchanged on exit. 00079 * 00080 * X - COMPLEX array of dimension at least 00081 * ( 1 + ( n - 1 )*abs( INCX ) ). 00082 * Before entry, the incremented array X must contain the n 00083 * element right-hand side vector b. On exit, X is overwritten 00084 * with the solution vector x. 00085 * 00086 * INCX - INTEGER. 00087 * On entry, INCX specifies the increment for the elements of 00088 * X. INCX must not be zero. 00089 * Unchanged on exit. 00090 * 00091 * Further Details 00092 * =============== 00093 * 00094 * Level 2 Blas routine. 00095 * 00096 * -- Written on 22-October-1986. 00097 * Jack Dongarra, Argonne National Lab. 00098 * Jeremy Du Croz, Nag Central Office. 00099 * Sven Hammarling, Nag Central Office. 00100 * Richard Hanson, Sandia National Labs. 00101 * 00102 * ===================================================================== 00103 * 00104 * .. Parameters .. 00105 COMPLEX ZERO 00106 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00107 * .. 00108 * .. Local Scalars .. 00109 COMPLEX TEMP 00110 INTEGER I,INFO,IX,J,JX,K,KK,KX 00111 LOGICAL NOCONJ,NOUNIT 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 EXTERNAL LSAME 00116 * .. 00117 * .. External Subroutines .. 00118 EXTERNAL XERBLA 00119 * .. 00120 * .. Intrinsic Functions .. 00121 INTRINSIC CONJG 00122 * .. 00123 * 00124 * Test the input parameters. 00125 * 00126 INFO = 0 00127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00128 INFO = 1 00129 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00130 + .NOT.LSAME(TRANS,'C')) THEN 00131 INFO = 2 00132 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00133 INFO = 3 00134 ELSE IF (N.LT.0) THEN 00135 INFO = 4 00136 ELSE IF (INCX.EQ.0) THEN 00137 INFO = 7 00138 END IF 00139 IF (INFO.NE.0) THEN 00140 CALL XERBLA('CTPSV ',INFO) 00141 RETURN 00142 END IF 00143 * 00144 * Quick return if possible. 00145 * 00146 IF (N.EQ.0) RETURN 00147 * 00148 NOCONJ = LSAME(TRANS,'T') 00149 NOUNIT = LSAME(DIAG,'N') 00150 * 00151 * Set up the start point in X if the increment is not unity. This 00152 * will be ( N - 1 )*INCX too small for descending loops. 00153 * 00154 IF (INCX.LE.0) THEN 00155 KX = 1 - (N-1)*INCX 00156 ELSE IF (INCX.NE.1) THEN 00157 KX = 1 00158 END IF 00159 * 00160 * Start the operations. In this version the elements of AP are 00161 * accessed sequentially with one pass through AP. 00162 * 00163 IF (LSAME(TRANS,'N')) THEN 00164 * 00165 * Form x := inv( A )*x. 00166 * 00167 IF (LSAME(UPLO,'U')) THEN 00168 KK = (N* (N+1))/2 00169 IF (INCX.EQ.1) THEN 00170 DO 20 J = N,1,-1 00171 IF (X(J).NE.ZERO) THEN 00172 IF (NOUNIT) X(J) = X(J)/AP(KK) 00173 TEMP = X(J) 00174 K = KK - 1 00175 DO 10 I = J - 1,1,-1 00176 X(I) = X(I) - TEMP*AP(K) 00177 K = K - 1 00178 10 CONTINUE 00179 END IF 00180 KK = KK - J 00181 20 CONTINUE 00182 ELSE 00183 JX = KX + (N-1)*INCX 00184 DO 40 J = N,1,-1 00185 IF (X(JX).NE.ZERO) THEN 00186 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00187 TEMP = X(JX) 00188 IX = JX 00189 DO 30 K = KK - 1,KK - J + 1,-1 00190 IX = IX - INCX 00191 X(IX) = X(IX) - TEMP*AP(K) 00192 30 CONTINUE 00193 END IF 00194 JX = JX - INCX 00195 KK = KK - J 00196 40 CONTINUE 00197 END IF 00198 ELSE 00199 KK = 1 00200 IF (INCX.EQ.1) THEN 00201 DO 60 J = 1,N 00202 IF (X(J).NE.ZERO) THEN 00203 IF (NOUNIT) X(J) = X(J)/AP(KK) 00204 TEMP = X(J) 00205 K = KK + 1 00206 DO 50 I = J + 1,N 00207 X(I) = X(I) - TEMP*AP(K) 00208 K = K + 1 00209 50 CONTINUE 00210 END IF 00211 KK = KK + (N-J+1) 00212 60 CONTINUE 00213 ELSE 00214 JX = KX 00215 DO 80 J = 1,N 00216 IF (X(JX).NE.ZERO) THEN 00217 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00218 TEMP = X(JX) 00219 IX = JX 00220 DO 70 K = KK + 1,KK + N - J 00221 IX = IX + INCX 00222 X(IX) = X(IX) - TEMP*AP(K) 00223 70 CONTINUE 00224 END IF 00225 JX = JX + INCX 00226 KK = KK + (N-J+1) 00227 80 CONTINUE 00228 END IF 00229 END IF 00230 ELSE 00231 * 00232 * Form x := inv( A**T )*x or x := inv( A**H )*x. 00233 * 00234 IF (LSAME(UPLO,'U')) THEN 00235 KK = 1 00236 IF (INCX.EQ.1) THEN 00237 DO 110 J = 1,N 00238 TEMP = X(J) 00239 K = KK 00240 IF (NOCONJ) THEN 00241 DO 90 I = 1,J - 1 00242 TEMP = TEMP - AP(K)*X(I) 00243 K = K + 1 00244 90 CONTINUE 00245 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00246 ELSE 00247 DO 100 I = 1,J - 1 00248 TEMP = TEMP - CONJG(AP(K))*X(I) 00249 K = K + 1 00250 100 CONTINUE 00251 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) 00252 END IF 00253 X(J) = TEMP 00254 KK = KK + J 00255 110 CONTINUE 00256 ELSE 00257 JX = KX 00258 DO 140 J = 1,N 00259 TEMP = X(JX) 00260 IX = KX 00261 IF (NOCONJ) THEN 00262 DO 120 K = KK,KK + J - 2 00263 TEMP = TEMP - AP(K)*X(IX) 00264 IX = IX + INCX 00265 120 CONTINUE 00266 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00267 ELSE 00268 DO 130 K = KK,KK + J - 2 00269 TEMP = TEMP - CONJG(AP(K))*X(IX) 00270 IX = IX + INCX 00271 130 CONTINUE 00272 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) 00273 END IF 00274 X(JX) = TEMP 00275 JX = JX + INCX 00276 KK = KK + J 00277 140 CONTINUE 00278 END IF 00279 ELSE 00280 KK = (N* (N+1))/2 00281 IF (INCX.EQ.1) THEN 00282 DO 170 J = N,1,-1 00283 TEMP = X(J) 00284 K = KK 00285 IF (NOCONJ) THEN 00286 DO 150 I = N,J + 1,-1 00287 TEMP = TEMP - AP(K)*X(I) 00288 K = K - 1 00289 150 CONTINUE 00290 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00291 ELSE 00292 DO 160 I = N,J + 1,-1 00293 TEMP = TEMP - CONJG(AP(K))*X(I) 00294 K = K - 1 00295 160 CONTINUE 00296 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) 00297 END IF 00298 X(J) = TEMP 00299 KK = KK - (N-J+1) 00300 170 CONTINUE 00301 ELSE 00302 KX = KX + (N-1)*INCX 00303 JX = KX 00304 DO 200 J = N,1,-1 00305 TEMP = X(JX) 00306 IX = KX 00307 IF (NOCONJ) THEN 00308 DO 180 K = KK,KK - (N- (J+1)),-1 00309 TEMP = TEMP - AP(K)*X(IX) 00310 IX = IX - INCX 00311 180 CONTINUE 00312 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00313 ELSE 00314 DO 190 K = KK,KK - (N- (J+1)),-1 00315 TEMP = TEMP - CONJG(AP(K))*X(IX) 00316 IX = IX - INCX 00317 190 CONTINUE 00318 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) 00319 END IF 00320 X(JX) = TEMP 00321 JX = JX - INCX 00322 KK = KK - (N-J+1) 00323 200 CONTINUE 00324 END IF 00325 END IF 00326 END IF 00327 * 00328 RETURN 00329 * 00330 * End of CTPSV . 00331 * 00332 END
1.7.3 
