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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DGTTRF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DGTTRF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgttrf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgttrf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgttrf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * INTEGER INFO, N 00025 * .. 00026 * .. Array Arguments .. 00027 * INTEGER IPIV( * ) 00028 * DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DGTTRF computes an LU factorization of a real tridiagonal matrix A 00038 *> using elimination with partial pivoting and row interchanges. 00039 *> 00040 *> The factorization has the form 00041 *> A = L * U 00042 *> where L is a product of permutation and unit lower bidiagonal 00043 *> matrices and U is upper triangular with nonzeros in only the main 00044 *> diagonal and first two superdiagonals. 00045 *> \endverbatim 00046 * 00047 * Arguments: 00048 * ========== 00049 * 00050 *> \param[in] N 00051 *> \verbatim 00052 *> N is INTEGER 00053 *> The order of the matrix A. 00054 *> \endverbatim 00055 *> 00056 *> \param[in,out] DL 00057 *> \verbatim 00058 *> DL is DOUBLE PRECISION array, dimension (N-1) 00059 *> On entry, DL must contain the (n-1) sub-diagonal elements of 00060 *> A. 00061 *> 00062 *> On exit, DL is overwritten by the (n-1) multipliers that 00063 *> define the matrix L from the LU factorization of A. 00064 *> \endverbatim 00065 *> 00066 *> \param[in,out] D 00067 *> \verbatim 00068 *> D is DOUBLE PRECISION array, dimension (N) 00069 *> On entry, D must contain the diagonal elements of A. 00070 *> 00071 *> On exit, D is overwritten by the n diagonal elements of the 00072 *> upper triangular matrix U from the LU factorization of A. 00073 *> \endverbatim 00074 *> 00075 *> \param[in,out] DU 00076 *> \verbatim 00077 *> DU is DOUBLE PRECISION array, dimension (N-1) 00078 *> On entry, DU must contain the (n-1) super-diagonal elements 00079 *> of A. 00080 *> 00081 *> On exit, DU is overwritten by the (n-1) elements of the first 00082 *> super-diagonal of U. 00083 *> \endverbatim 00084 *> 00085 *> \param[out] DU2 00086 *> \verbatim 00087 *> DU2 is DOUBLE PRECISION array, dimension (N-2) 00088 *> On exit, DU2 is overwritten by the (n-2) elements of the 00089 *> second super-diagonal of U. 00090 *> \endverbatim 00091 *> 00092 *> \param[out] IPIV 00093 *> \verbatim 00094 *> IPIV is INTEGER array, dimension (N) 00095 *> The pivot indices; for 1 <= i <= n, row i of the matrix was 00096 *> interchanged with row IPIV(i). IPIV(i) will always be either 00097 *> i or i+1; IPIV(i) = i indicates a row interchange was not 00098 *> required. 00099 *> \endverbatim 00100 *> 00101 *> \param[out] INFO 00102 *> \verbatim 00103 *> INFO is INTEGER 00104 *> = 0: successful exit 00105 *> < 0: if INFO = -k, the k-th argument had an illegal value 00106 *> > 0: if INFO = k, U(k,k) is exactly zero. The factorization 00107 *> has been completed, but the factor U is exactly 00108 *> singular, and division by zero will occur if it is used 00109 *> to solve a system of equations. 00110 *> \endverbatim 00111 * 00112 * Authors: 00113 * ======== 00114 * 00115 *> \author Univ. of Tennessee 00116 *> \author Univ. of California Berkeley 00117 *> \author Univ. of Colorado Denver 00118 *> \author NAG Ltd. 00119 * 00120 *> \date November 2011 00121 * 00122 *> \ingroup doubleOTHERcomputational 00123 * 00124 * ===================================================================== 00125 SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) 00126 * 00127 * -- LAPACK computational routine (version 3.4.0) -- 00128 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00130 * November 2011 00131 * 00132 * .. Scalar Arguments .. 00133 INTEGER INFO, N 00134 * .. 00135 * .. Array Arguments .. 00136 INTEGER IPIV( * ) 00137 DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ) 00138 * .. 00139 * 00140 * ===================================================================== 00141 * 00142 * .. Parameters .. 00143 DOUBLE PRECISION ZERO 00144 PARAMETER ( ZERO = 0.0D+0 ) 00145 * .. 00146 * .. Local Scalars .. 00147 INTEGER I 00148 DOUBLE PRECISION FACT, TEMP 00149 * .. 00150 * .. Intrinsic Functions .. 00151 INTRINSIC ABS 00152 * .. 00153 * .. External Subroutines .. 00154 EXTERNAL XERBLA 00155 * .. 00156 * .. Executable Statements .. 00157 * 00158 INFO = 0 00159 IF( N.LT.0 ) THEN 00160 INFO = -1 00161 CALL XERBLA( 'DGTTRF', -INFO ) 00162 RETURN 00163 END IF 00164 * 00165 * Quick return if possible 00166 * 00167 IF( N.EQ.0 ) 00168 $ RETURN 00169 * 00170 * Initialize IPIV(i) = i and DU2(I) = 0 00171 * 00172 DO 10 I = 1, N 00173 IPIV( I ) = I 00174 10 CONTINUE 00175 DO 20 I = 1, N - 2 00176 DU2( I ) = ZERO 00177 20 CONTINUE 00178 * 00179 DO 30 I = 1, N - 2 00180 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00181 * 00182 * No row interchange required, eliminate DL(I) 00183 * 00184 IF( D( I ).NE.ZERO ) THEN 00185 FACT = DL( I ) / D( I ) 00186 DL( I ) = FACT 00187 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00188 END IF 00189 ELSE 00190 * 00191 * Interchange rows I and I+1, eliminate DL(I) 00192 * 00193 FACT = D( I ) / DL( I ) 00194 D( I ) = DL( I ) 00195 DL( I ) = FACT 00196 TEMP = DU( I ) 00197 DU( I ) = D( I+1 ) 00198 D( I+1 ) = TEMP - FACT*D( I+1 ) 00199 DU2( I ) = DU( I+1 ) 00200 DU( I+1 ) = -FACT*DU( I+1 ) 00201 IPIV( I ) = I + 1 00202 END IF 00203 30 CONTINUE 00204 IF( N.GT.1 ) THEN 00205 I = N - 1 00206 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00207 IF( D( I ).NE.ZERO ) THEN 00208 FACT = DL( I ) / D( I ) 00209 DL( I ) = FACT 00210 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00211 END IF 00212 ELSE 00213 FACT = D( I ) / DL( I ) 00214 D( I ) = DL( I ) 00215 DL( I ) = FACT 00216 TEMP = DU( I ) 00217 DU( I ) = D( I+1 ) 00218 D( I+1 ) = TEMP - FACT*D( I+1 ) 00219 IPIV( I ) = I + 1 00220 END IF 00221 END IF 00222 * 00223 * Check for a zero on the diagonal of U. 00224 * 00225 DO 40 I = 1, N 00226 IF( D( I ).EQ.ZERO ) THEN 00227 INFO = I 00228 GO TO 50 00229 END IF 00230 40 CONTINUE 00231 50 CONTINUE 00232 * 00233 RETURN 00234 * 00235 * End of DGTTRF 00236 * 00237 END