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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DTRSV(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 DOUBLE PRECISION A(LDA,*),X(*) 00008 * .. 00009 * 00010 * Purpose 00011 * ======= 00012 * 00013 * DTRSV 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. 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 * A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 * 00095 * Level 2 Blas routine. 00096 * 00097 * -- Written on 22-October-1986. 00098 * Jack Dongarra, Argonne National Lab. 00099 * Jeremy Du Croz, Nag Central Office. 00100 * Sven Hammarling, Nag Central Office. 00101 * Richard Hanson, Sandia National Labs. 00102 * 00103 * ===================================================================== 00104 * 00105 * .. Parameters .. 00106 DOUBLE PRECISION ZERO 00107 PARAMETER (ZERO=0.0D+0) 00108 * .. 00109 * .. Local Scalars .. 00110 DOUBLE PRECISION TEMP 00111 INTEGER I,INFO,IX,J,JX,KX 00112 LOGICAL NOUNIT 00113 * .. 00114 * .. External Functions .. 00115 LOGICAL LSAME 00116 EXTERNAL LSAME 00117 * .. 00118 * .. External Subroutines .. 00119 EXTERNAL XERBLA 00120 * .. 00121 * .. Intrinsic Functions .. 00122 INTRINSIC MAX 00123 * .. 00124 * 00125 * Test the input parameters. 00126 * 00127 INFO = 0 00128 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00129 INFO = 1 00130 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00131 + .NOT.LSAME(TRANS,'C')) THEN 00132 INFO = 2 00133 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00134 INFO = 3 00135 ELSE IF (N.LT.0) THEN 00136 INFO = 4 00137 ELSE IF (LDA.LT.MAX(1,N)) THEN 00138 INFO = 6 00139 ELSE IF (INCX.EQ.0) THEN 00140 INFO = 8 00141 END IF 00142 IF (INFO.NE.0) THEN 00143 CALL XERBLA('DTRSV ',INFO) 00144 RETURN 00145 END IF 00146 * 00147 * Quick return if possible. 00148 * 00149 IF (N.EQ.0) RETURN 00150 * 00151 NOUNIT = LSAME(DIAG,'N') 00152 * 00153 * Set up the start point in X if the increment is not unity. This 00154 * will be ( N - 1 )*INCX too small for descending loops. 00155 * 00156 IF (INCX.LE.0) THEN 00157 KX = 1 - (N-1)*INCX 00158 ELSE IF (INCX.NE.1) THEN 00159 KX = 1 00160 END IF 00161 * 00162 * Start the operations. In this version the elements of A are 00163 * accessed sequentially with one pass through A. 00164 * 00165 IF (LSAME(TRANS,'N')) THEN 00166 * 00167 * Form x := inv( A )*x. 00168 * 00169 IF (LSAME(UPLO,'U')) THEN 00170 IF (INCX.EQ.1) THEN 00171 DO 20 J = N,1,-1 00172 IF (X(J).NE.ZERO) THEN 00173 IF (NOUNIT) X(J) = X(J)/A(J,J) 00174 TEMP = X(J) 00175 DO 10 I = J - 1,1,-1 00176 X(I) = X(I) - TEMP*A(I,J) 00177 10 CONTINUE 00178 END IF 00179 20 CONTINUE 00180 ELSE 00181 JX = KX + (N-1)*INCX 00182 DO 40 J = N,1,-1 00183 IF (X(JX).NE.ZERO) THEN 00184 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00185 TEMP = X(JX) 00186 IX = JX 00187 DO 30 I = J - 1,1,-1 00188 IX = IX - INCX 00189 X(IX) = X(IX) - TEMP*A(I,J) 00190 30 CONTINUE 00191 END IF 00192 JX = JX - INCX 00193 40 CONTINUE 00194 END IF 00195 ELSE 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)/A(J,J) 00200 TEMP = X(J) 00201 DO 50 I = J + 1,N 00202 X(I) = X(I) - TEMP*A(I,J) 00203 50 CONTINUE 00204 END IF 00205 60 CONTINUE 00206 ELSE 00207 JX = KX 00208 DO 80 J = 1,N 00209 IF (X(JX).NE.ZERO) THEN 00210 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00211 TEMP = X(JX) 00212 IX = JX 00213 DO 70 I = J + 1,N 00214 IX = IX + INCX 00215 X(IX) = X(IX) - TEMP*A(I,J) 00216 70 CONTINUE 00217 END IF 00218 JX = JX + INCX 00219 80 CONTINUE 00220 END IF 00221 END IF 00222 ELSE 00223 * 00224 * Form x := inv( A' )*x. 00225 * 00226 IF (LSAME(UPLO,'U')) THEN 00227 IF (INCX.EQ.1) THEN 00228 DO 100 J = 1,N 00229 TEMP = X(J) 00230 DO 90 I = 1,J - 1 00231 TEMP = TEMP - A(I,J)*X(I) 00232 90 CONTINUE 00233 IF (NOUNIT) TEMP = TEMP/A(J,J) 00234 X(J) = TEMP 00235 100 CONTINUE 00236 ELSE 00237 JX = KX 00238 DO 120 J = 1,N 00239 TEMP = X(JX) 00240 IX = KX 00241 DO 110 I = 1,J - 1 00242 TEMP = TEMP - A(I,J)*X(IX) 00243 IX = IX + INCX 00244 110 CONTINUE 00245 IF (NOUNIT) TEMP = TEMP/A(J,J) 00246 X(JX) = TEMP 00247 JX = JX + INCX 00248 120 CONTINUE 00249 END IF 00250 ELSE 00251 IF (INCX.EQ.1) THEN 00252 DO 140 J = N,1,-1 00253 TEMP = X(J) 00254 DO 130 I = N,J + 1,-1 00255 TEMP = TEMP - A(I,J)*X(I) 00256 130 CONTINUE 00257 IF (NOUNIT) TEMP = TEMP/A(J,J) 00258 X(J) = TEMP 00259 140 CONTINUE 00260 ELSE 00261 KX = KX + (N-1)*INCX 00262 JX = KX 00263 DO 160 J = N,1,-1 00264 TEMP = X(JX) 00265 IX = KX 00266 DO 150 I = N,J + 1,-1 00267 TEMP = TEMP - A(I,J)*X(IX) 00268 IX = IX - INCX 00269 150 CONTINUE 00270 IF (NOUNIT) TEMP = TEMP/A(J,J) 00271 X(JX) = TEMP 00272 JX = JX - INCX 00273 160 CONTINUE 00274 END IF 00275 END IF 00276 END IF 00277 * 00278 RETURN 00279 * 00280 * End of DTRSV . 00281 * 00282 END
1.7.3 
