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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 00002 * .. Scalar Arguments .. 00003 INTEGER INCX,LDA,N 00004 CHARACTER DIAG,TRANS,UPLO 00005 * .. 00006 * .. Array Arguments .. 00007 COMPLEX A(LDA,*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * CTRSV solves one of the systems of equations 00014 * 00015 * A*x = b, or A'*x = b, or conjg( 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. 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' conjg( 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 * A - COMPLEX array of DIMENSION ( LDA, n ). 00065 * Before entry with UPLO = 'U' or 'u', the leading n by n 00066 * upper triangular part of the array A must contain the upper 00067 * triangular matrix and the strictly lower triangular part of 00068 * A is not referenced. 00069 * Before entry with UPLO = 'L' or 'l', the leading n by n 00070 * lower triangular part of the array A must contain the lower 00071 * triangular matrix and the strictly upper triangular part of 00072 * A is not referenced. 00073 * Note that when DIAG = 'U' or 'u', the diagonal elements of 00074 * A are not referenced either, but are assumed to be unity. 00075 * Unchanged on exit. 00076 * 00077 * LDA - INTEGER. 00078 * On entry, LDA specifies the first dimension of A as declared 00079 * in the calling (sub) program. LDA must be at least 00080 * max( 1, n ). 00081 * Unchanged on exit. 00082 * 00083 * X - COMPLEX array of dimension at least 00084 * ( 1 + ( n - 1 )*abs( INCX ) ). 00085 * Before entry, the incremented array X must contain the n 00086 * element right-hand side vector b. On exit, X is overwritten 00087 * with the solution vector x. 00088 * 00089 * INCX - INTEGER. 00090 * On entry, INCX specifies the increment for the elements of 00091 * X. INCX must not be zero. 00092 * Unchanged on exit. 00093 * 00094 * Further Details 00095 * =============== 00096 * 00097 * Level 2 Blas routine. 00098 * 00099 * -- Written on 22-October-1986. 00100 * Jack Dongarra, Argonne National Lab. 00101 * Jeremy Du Croz, Nag Central Office. 00102 * Sven Hammarling, Nag Central Office. 00103 * Richard Hanson, Sandia National Labs. 00104 * 00105 * ===================================================================== 00106 * 00107 * .. Parameters .. 00108 COMPLEX ZERO 00109 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 00110 * .. 00111 * .. Local Scalars .. 00112 COMPLEX TEMP 00113 INTEGER I,INFO,IX,J,JX,KX 00114 LOGICAL NOCONJ,NOUNIT 00115 * .. 00116 * .. External Functions .. 00117 LOGICAL LSAME 00118 EXTERNAL LSAME 00119 * .. 00120 * .. External Subroutines .. 00121 EXTERNAL XERBLA 00122 * .. 00123 * .. Intrinsic Functions .. 00124 INTRINSIC CONJG,MAX 00125 * .. 00126 * 00127 * Test the input parameters. 00128 * 00129 INFO = 0 00130 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00131 INFO = 1 00132 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00133 + .NOT.LSAME(TRANS,'C')) THEN 00134 INFO = 2 00135 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00136 INFO = 3 00137 ELSE IF (N.LT.0) THEN 00138 INFO = 4 00139 ELSE IF (LDA.LT.MAX(1,N)) THEN 00140 INFO = 6 00141 ELSE IF (INCX.EQ.0) THEN 00142 INFO = 8 00143 END IF 00144 IF (INFO.NE.0) THEN 00145 CALL XERBLA('CTRSV ',INFO) 00146 RETURN 00147 END IF 00148 * 00149 * Quick return if possible. 00150 * 00151 IF (N.EQ.0) RETURN 00152 * 00153 NOCONJ = LSAME(TRANS,'T') 00154 NOUNIT = LSAME(DIAG,'N') 00155 * 00156 * Set up the start point in X if the increment is not unity. This 00157 * will be ( N - 1 )*INCX too small for descending loops. 00158 * 00159 IF (INCX.LE.0) THEN 00160 KX = 1 - (N-1)*INCX 00161 ELSE IF (INCX.NE.1) THEN 00162 KX = 1 00163 END IF 00164 * 00165 * Start the operations. In this version the elements of A are 00166 * accessed sequentially with one pass through A. 00167 * 00168 IF (LSAME(TRANS,'N')) THEN 00169 * 00170 * Form x := inv( A )*x. 00171 * 00172 IF (LSAME(UPLO,'U')) THEN 00173 IF (INCX.EQ.1) THEN 00174 DO 20 J = N,1,-1 00175 IF (X(J).NE.ZERO) THEN 00176 IF (NOUNIT) X(J) = X(J)/A(J,J) 00177 TEMP = X(J) 00178 DO 10 I = J - 1,1,-1 00179 X(I) = X(I) - TEMP*A(I,J) 00180 10 CONTINUE 00181 END IF 00182 20 CONTINUE 00183 ELSE 00184 JX = KX + (N-1)*INCX 00185 DO 40 J = N,1,-1 00186 IF (X(JX).NE.ZERO) THEN 00187 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00188 TEMP = X(JX) 00189 IX = JX 00190 DO 30 I = J - 1,1,-1 00191 IX = IX - INCX 00192 X(IX) = X(IX) - TEMP*A(I,J) 00193 30 CONTINUE 00194 END IF 00195 JX = JX - INCX 00196 40 CONTINUE 00197 END IF 00198 ELSE 00199 IF (INCX.EQ.1) THEN 00200 DO 60 J = 1,N 00201 IF (X(J).NE.ZERO) THEN 00202 IF (NOUNIT) X(J) = X(J)/A(J,J) 00203 TEMP = X(J) 00204 DO 50 I = J + 1,N 00205 X(I) = X(I) - TEMP*A(I,J) 00206 50 CONTINUE 00207 END IF 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)/A(J,J) 00214 TEMP = X(JX) 00215 IX = JX 00216 DO 70 I = J + 1,N 00217 IX = IX + INCX 00218 X(IX) = X(IX) - TEMP*A(I,J) 00219 70 CONTINUE 00220 END IF 00221 JX = JX + INCX 00222 80 CONTINUE 00223 END IF 00224 END IF 00225 ELSE 00226 * 00227 * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. 00228 * 00229 IF (LSAME(UPLO,'U')) THEN 00230 IF (INCX.EQ.1) THEN 00231 DO 110 J = 1,N 00232 TEMP = X(J) 00233 IF (NOCONJ) THEN 00234 DO 90 I = 1,J - 1 00235 TEMP = TEMP - A(I,J)*X(I) 00236 90 CONTINUE 00237 IF (NOUNIT) TEMP = TEMP/A(J,J) 00238 ELSE 00239 DO 100 I = 1,J - 1 00240 TEMP = TEMP - CONJG(A(I,J))*X(I) 00241 100 CONTINUE 00242 IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) 00243 END IF 00244 X(J) = TEMP 00245 110 CONTINUE 00246 ELSE 00247 JX = KX 00248 DO 140 J = 1,N 00249 IX = KX 00250 TEMP = X(JX) 00251 IF (NOCONJ) THEN 00252 DO 120 I = 1,J - 1 00253 TEMP = TEMP - A(I,J)*X(IX) 00254 IX = IX + INCX 00255 120 CONTINUE 00256 IF (NOUNIT) TEMP = TEMP/A(J,J) 00257 ELSE 00258 DO 130 I = 1,J - 1 00259 TEMP = TEMP - CONJG(A(I,J))*X(IX) 00260 IX = IX + INCX 00261 130 CONTINUE 00262 IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) 00263 END IF 00264 X(JX) = TEMP 00265 JX = JX + INCX 00266 140 CONTINUE 00267 END IF 00268 ELSE 00269 IF (INCX.EQ.1) THEN 00270 DO 170 J = N,1,-1 00271 TEMP = X(J) 00272 IF (NOCONJ) THEN 00273 DO 150 I = N,J + 1,-1 00274 TEMP = TEMP - A(I,J)*X(I) 00275 150 CONTINUE 00276 IF (NOUNIT) TEMP = TEMP/A(J,J) 00277 ELSE 00278 DO 160 I = N,J + 1,-1 00279 TEMP = TEMP - CONJG(A(I,J))*X(I) 00280 160 CONTINUE 00281 IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) 00282 END IF 00283 X(J) = TEMP 00284 170 CONTINUE 00285 ELSE 00286 KX = KX + (N-1)*INCX 00287 JX = KX 00288 DO 200 J = N,1,-1 00289 IX = KX 00290 TEMP = X(JX) 00291 IF (NOCONJ) THEN 00292 DO 180 I = N,J + 1,-1 00293 TEMP = TEMP - A(I,J)*X(IX) 00294 IX = IX - INCX 00295 180 CONTINUE 00296 IF (NOUNIT) TEMP = TEMP/A(J,J) 00297 ELSE 00298 DO 190 I = N,J + 1,-1 00299 TEMP = TEMP - CONJG(A(I,J))*X(IX) 00300 IX = IX - INCX 00301 190 CONTINUE 00302 IF (NOUNIT) TEMP = TEMP/CONJG(A(J,J)) 00303 END IF 00304 X(JX) = TEMP 00305 JX = JX - INCX 00306 200 CONTINUE 00307 END IF 00308 END IF 00309 END IF 00310 * 00311 RETURN 00312 * 00313 * End of CTRSV . 00314 * 00315 END
1.7.3 
