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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 SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.3.1) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * -- April 2011 -- 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, LDB, N, NRHS 00010 * .. 00011 * .. Array Arguments .. 00012 REAL B( LDB, * ), D( * ), DL( * ), DU( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * SGTSV solves the equation 00019 * 00020 * A*X = B, 00021 * 00022 * where A is an n by n tridiagonal matrix, by Gaussian elimination with 00023 * partial pivoting. 00024 * 00025 * Note that the equation A**T*X = B may be solved by interchanging the 00026 * order of the arguments DU and DL. 00027 * 00028 * Arguments 00029 * ========= 00030 * 00031 * N (input) INTEGER 00032 * The order of the matrix A. N >= 0. 00033 * 00034 * NRHS (input) INTEGER 00035 * The number of right hand sides, i.e., the number of columns 00036 * of the matrix B. NRHS >= 0. 00037 * 00038 * DL (input/output) REAL array, dimension (N-1) 00039 * On entry, DL must contain the (n-1) sub-diagonal elements of 00040 * A. 00041 * 00042 * On exit, DL is overwritten by the (n-2) elements of the 00043 * second super-diagonal of the upper triangular matrix U from 00044 * the LU factorization of A, in DL(1), ..., DL(n-2). 00045 * 00046 * D (input/output) REAL array, dimension (N) 00047 * On entry, D must contain the diagonal elements of A. 00048 * 00049 * On exit, D is overwritten by the n diagonal elements of U. 00050 * 00051 * DU (input/output) REAL array, dimension (N-1) 00052 * On entry, DU must contain the (n-1) super-diagonal elements 00053 * of A. 00054 * 00055 * On exit, DU is overwritten by the (n-1) elements of the first 00056 * super-diagonal of U. 00057 * 00058 * B (input/output) REAL array, dimension (LDB,NRHS) 00059 * On entry, the N by NRHS matrix of right hand side matrix B. 00060 * On exit, if INFO = 0, the N by NRHS solution matrix X. 00061 * 00062 * LDB (input) INTEGER 00063 * The leading dimension of the array B. LDB >= max(1,N). 00064 * 00065 * INFO (output) INTEGER 00066 * = 0: successful exit 00067 * < 0: if INFO = -i, the i-th argument had an illegal value 00068 * > 0: if INFO = i, U(i,i) is exactly zero, and the solution 00069 * has not been computed. The factorization has not been 00070 * completed unless i = N. 00071 * 00072 * ===================================================================== 00073 * 00074 * .. Parameters .. 00075 REAL ZERO 00076 PARAMETER ( ZERO = 0.0E+0 ) 00077 * .. 00078 * .. Local Scalars .. 00079 INTEGER I, J 00080 REAL FACT, TEMP 00081 * .. 00082 * .. Intrinsic Functions .. 00083 INTRINSIC ABS, MAX 00084 * .. 00085 * .. External Subroutines .. 00086 EXTERNAL XERBLA 00087 * .. 00088 * .. Executable Statements .. 00089 * 00090 INFO = 0 00091 IF( N.LT.0 ) THEN 00092 INFO = -1 00093 ELSE IF( NRHS.LT.0 ) THEN 00094 INFO = -2 00095 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00096 INFO = -7 00097 END IF 00098 IF( INFO.NE.0 ) THEN 00099 CALL XERBLA( 'SGTSV ', -INFO ) 00100 RETURN 00101 END IF 00102 * 00103 IF( N.EQ.0 ) 00104 $ RETURN 00105 * 00106 IF( NRHS.EQ.1 ) THEN 00107 DO 10 I = 1, N - 2 00108 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00109 * 00110 * No row interchange required 00111 * 00112 IF( D( I ).NE.ZERO ) THEN 00113 FACT = DL( I ) / D( I ) 00114 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00115 B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) 00116 ELSE 00117 INFO = I 00118 RETURN 00119 END IF 00120 DL( I ) = ZERO 00121 ELSE 00122 * 00123 * Interchange rows I and I+1 00124 * 00125 FACT = D( I ) / DL( I ) 00126 D( I ) = DL( I ) 00127 TEMP = D( I+1 ) 00128 D( I+1 ) = DU( I ) - FACT*TEMP 00129 DL( I ) = DU( I+1 ) 00130 DU( I+1 ) = -FACT*DL( I ) 00131 DU( I ) = TEMP 00132 TEMP = B( I, 1 ) 00133 B( I, 1 ) = B( I+1, 1 ) 00134 B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) 00135 END IF 00136 10 CONTINUE 00137 IF( N.GT.1 ) THEN 00138 I = N - 1 00139 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00140 IF( D( I ).NE.ZERO ) THEN 00141 FACT = DL( I ) / D( I ) 00142 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00143 B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) 00144 ELSE 00145 INFO = I 00146 RETURN 00147 END IF 00148 ELSE 00149 FACT = D( I ) / DL( I ) 00150 D( I ) = DL( I ) 00151 TEMP = D( I+1 ) 00152 D( I+1 ) = DU( I ) - FACT*TEMP 00153 DU( I ) = TEMP 00154 TEMP = B( I, 1 ) 00155 B( I, 1 ) = B( I+1, 1 ) 00156 B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) 00157 END IF 00158 END IF 00159 IF( D( N ).EQ.ZERO ) THEN 00160 INFO = N 00161 RETURN 00162 END IF 00163 ELSE 00164 DO 40 I = 1, N - 2 00165 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00166 * 00167 * No row interchange required 00168 * 00169 IF( D( I ).NE.ZERO ) THEN 00170 FACT = DL( I ) / D( I ) 00171 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00172 DO 20 J = 1, NRHS 00173 B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) 00174 20 CONTINUE 00175 ELSE 00176 INFO = I 00177 RETURN 00178 END IF 00179 DL( I ) = ZERO 00180 ELSE 00181 * 00182 * Interchange rows I and I+1 00183 * 00184 FACT = D( I ) / DL( I ) 00185 D( I ) = DL( I ) 00186 TEMP = D( I+1 ) 00187 D( I+1 ) = DU( I ) - FACT*TEMP 00188 DL( I ) = DU( I+1 ) 00189 DU( I+1 ) = -FACT*DL( I ) 00190 DU( I ) = TEMP 00191 DO 30 J = 1, NRHS 00192 TEMP = B( I, J ) 00193 B( I, J ) = B( I+1, J ) 00194 B( I+1, J ) = TEMP - FACT*B( I+1, J ) 00195 30 CONTINUE 00196 END IF 00197 40 CONTINUE 00198 IF( N.GT.1 ) THEN 00199 I = N - 1 00200 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN 00201 IF( D( I ).NE.ZERO ) THEN 00202 FACT = DL( I ) / D( I ) 00203 D( I+1 ) = D( I+1 ) - FACT*DU( I ) 00204 DO 50 J = 1, NRHS 00205 B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) 00206 50 CONTINUE 00207 ELSE 00208 INFO = I 00209 RETURN 00210 END IF 00211 ELSE 00212 FACT = D( I ) / DL( I ) 00213 D( I ) = DL( I ) 00214 TEMP = D( I+1 ) 00215 D( I+1 ) = DU( I ) - FACT*TEMP 00216 DU( I ) = TEMP 00217 DO 60 J = 1, NRHS 00218 TEMP = B( I, J ) 00219 B( I, J ) = B( I+1, J ) 00220 B( I+1, J ) = TEMP - FACT*B( I+1, J ) 00221 60 CONTINUE 00222 END IF 00223 END IF 00224 IF( D( N ).EQ.ZERO ) THEN 00225 INFO = N 00226 RETURN 00227 END IF 00228 END IF 00229 * 00230 * Back solve with the matrix U from the factorization. 00231 * 00232 IF( NRHS.LE.2 ) THEN 00233 J = 1 00234 70 CONTINUE 00235 B( N, J ) = B( N, J ) / D( N ) 00236 IF( N.GT.1 ) 00237 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 ) 00238 DO 80 I = N - 2, 1, -1 00239 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* 00240 $ B( I+2, J ) ) / D( I ) 00241 80 CONTINUE 00242 IF( J.LT.NRHS ) THEN 00243 J = J + 1 00244 GO TO 70 00245 END IF 00246 ELSE 00247 DO 100 J = 1, NRHS 00248 B( N, J ) = B( N, J ) / D( N ) 00249 IF( N.GT.1 ) 00250 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / 00251 $ D( N-1 ) 00252 DO 90 I = N - 2, 1, -1 00253 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* 00254 $ B( I+2, J ) ) / D( I ) 00255 90 CONTINUE 00256 100 CONTINUE 00257 END IF 00258 * 00259 RETURN 00260 * 00261 * End of SGTSV 00262 * 00263 END
1.7.3 
