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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 DOUBLE PRECISION AP(*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * DTPSV solves one of the systems of equations 00014 * 00015 * A*x = b, or A'*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'*x = b. 00043 * 00044 * TRANS = 'C' or 'c' A'*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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 DOUBLE PRECISION ZERO 00106 PARAMETER (ZERO=0.0D+0) 00107 * .. 00108 * .. Local Scalars .. 00109 DOUBLE PRECISION TEMP 00110 INTEGER I,INFO,IX,J,JX,K,KK,KX 00111 LOGICAL NOUNIT 00112 * .. 00113 * .. External Functions .. 00114 LOGICAL LSAME 00115 EXTERNAL LSAME 00116 * .. 00117 * .. External Subroutines .. 00118 EXTERNAL XERBLA 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('DTPSV ',INFO) 00138 RETURN 00139 END IF 00140 * 00141 * Quick return if possible. 00142 * 00143 IF (N.EQ.0) RETURN 00144 * 00145 NOUNIT = LSAME(DIAG,'N') 00146 * 00147 * Set up the start point in X if the increment is not unity. This 00148 * will be ( N - 1 )*INCX too small for descending loops. 00149 * 00150 IF (INCX.LE.0) THEN 00151 KX = 1 - (N-1)*INCX 00152 ELSE IF (INCX.NE.1) THEN 00153 KX = 1 00154 END IF 00155 * 00156 * Start the operations. In this version the elements of AP are 00157 * accessed sequentially with one pass through AP. 00158 * 00159 IF (LSAME(TRANS,'N')) THEN 00160 * 00161 * Form x := inv( A )*x. 00162 * 00163 IF (LSAME(UPLO,'U')) THEN 00164 KK = (N* (N+1))/2 00165 IF (INCX.EQ.1) THEN 00166 DO 20 J = N,1,-1 00167 IF (X(J).NE.ZERO) THEN 00168 IF (NOUNIT) X(J) = X(J)/AP(KK) 00169 TEMP = X(J) 00170 K = KK - 1 00171 DO 10 I = J - 1,1,-1 00172 X(I) = X(I) - TEMP*AP(K) 00173 K = K - 1 00174 10 CONTINUE 00175 END IF 00176 KK = KK - J 00177 20 CONTINUE 00178 ELSE 00179 JX = KX + (N-1)*INCX 00180 DO 40 J = N,1,-1 00181 IF (X(JX).NE.ZERO) THEN 00182 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00183 TEMP = X(JX) 00184 IX = JX 00185 DO 30 K = KK - 1,KK - J + 1,-1 00186 IX = IX - INCX 00187 X(IX) = X(IX) - TEMP*AP(K) 00188 30 CONTINUE 00189 END IF 00190 JX = JX - INCX 00191 KK = KK - J 00192 40 CONTINUE 00193 END IF 00194 ELSE 00195 KK = 1 00196 IF (INCX.EQ.1) THEN 00197 DO 60 J = 1,N 00198 IF (X(J).NE.ZERO) THEN 00199 IF (NOUNIT) X(J) = X(J)/AP(KK) 00200 TEMP = X(J) 00201 K = KK + 1 00202 DO 50 I = J + 1,N 00203 X(I) = X(I) - TEMP*AP(K) 00204 K = K + 1 00205 50 CONTINUE 00206 END IF 00207 KK = KK + (N-J+1) 00208 60 CONTINUE 00209 ELSE 00210 JX = KX 00211 DO 80 J = 1,N 00212 IF (X(JX).NE.ZERO) THEN 00213 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 00214 TEMP = X(JX) 00215 IX = JX 00216 DO 70 K = KK + 1,KK + N - J 00217 IX = IX + INCX 00218 X(IX) = X(IX) - TEMP*AP(K) 00219 70 CONTINUE 00220 END IF 00221 JX = JX + INCX 00222 KK = KK + (N-J+1) 00223 80 CONTINUE 00224 END IF 00225 END IF 00226 ELSE 00227 * 00228 * Form x := inv( A' )*x. 00229 * 00230 IF (LSAME(UPLO,'U')) THEN 00231 KK = 1 00232 IF (INCX.EQ.1) THEN 00233 DO 100 J = 1,N 00234 TEMP = X(J) 00235 K = KK 00236 DO 90 I = 1,J - 1 00237 TEMP = TEMP - AP(K)*X(I) 00238 K = K + 1 00239 90 CONTINUE 00240 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00241 X(J) = TEMP 00242 KK = KK + J 00243 100 CONTINUE 00244 ELSE 00245 JX = KX 00246 DO 120 J = 1,N 00247 TEMP = X(JX) 00248 IX = KX 00249 DO 110 K = KK,KK + J - 2 00250 TEMP = TEMP - AP(K)*X(IX) 00251 IX = IX + INCX 00252 110 CONTINUE 00253 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 00254 X(JX) = TEMP 00255 JX = JX + INCX 00256 KK = KK + J 00257 120 CONTINUE 00258 END IF 00259 ELSE 00260 KK = (N* (N+1))/2 00261 IF (INCX.EQ.1) THEN 00262 DO 140 J = N,1,-1 00263 TEMP = X(J) 00264 K = KK 00265 DO 130 I = N,J + 1,-1 00266 TEMP = TEMP - AP(K)*X(I) 00267 K = K - 1 00268 130 CONTINUE 00269 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00270 X(J) = TEMP 00271 KK = KK - (N-J+1) 00272 140 CONTINUE 00273 ELSE 00274 KX = KX + (N-1)*INCX 00275 JX = KX 00276 DO 160 J = N,1,-1 00277 TEMP = X(JX) 00278 IX = KX 00279 DO 150 K = KK,KK - (N- (J+1)),-1 00280 TEMP = TEMP - AP(K)*X(IX) 00281 IX = IX - INCX 00282 150 CONTINUE 00283 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 00284 X(JX) = TEMP 00285 JX = JX - INCX 00286 KK = KK - (N-J+1) 00287 160 CONTINUE 00288 END IF 00289 END IF 00290 END IF 00291 * 00292 RETURN 00293 * 00294 * End of DTPSV . 00295 * 00296 END
1.7.3 
