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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 SPTTS2( N, NRHS, D, E, B, LDB ) 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 LDB, N, NRHS 00010 * .. 00011 * .. Array Arguments .. 00012 REAL B( LDB, * ), D( * ), E( * ) 00013 * .. 00014 * 00015 * Purpose 00016 * ======= 00017 * 00018 * SPTTS2 solves a tridiagonal system of the form 00019 * A * X = B 00020 * using the L*D*L**T factorization of A computed by SPTTRF. D is a 00021 * diagonal matrix specified in the vector D, L is a unit bidiagonal 00022 * matrix whose subdiagonal is specified in the vector E, and X and B 00023 * are N by NRHS matrices. 00024 * 00025 * Arguments 00026 * ========= 00027 * 00028 * N (input) INTEGER 00029 * The order of the tridiagonal matrix A. N >= 0. 00030 * 00031 * NRHS (input) INTEGER 00032 * The number of right hand sides, i.e., the number of columns 00033 * of the matrix B. NRHS >= 0. 00034 * 00035 * D (input) REAL array, dimension (N) 00036 * The n diagonal elements of the diagonal matrix D from the 00037 * L*D*L**T factorization of A. 00038 * 00039 * E (input) REAL array, dimension (N-1) 00040 * The (n-1) subdiagonal elements of the unit bidiagonal factor 00041 * L from the L*D*L**T factorization of A. E can also be regarded 00042 * as the superdiagonal of the unit bidiagonal factor U from the 00043 * factorization A = U**T*D*U. 00044 * 00045 * B (input/output) REAL array, dimension (LDB,NRHS) 00046 * On entry, the right hand side vectors B for the system of 00047 * linear equations. 00048 * On exit, the solution vectors, X. 00049 * 00050 * LDB (input) INTEGER 00051 * The leading dimension of the array B. LDB >= max(1,N). 00052 * 00053 * ===================================================================== 00054 * 00055 * .. Local Scalars .. 00056 INTEGER I, J 00057 * .. 00058 * .. External Subroutines .. 00059 EXTERNAL SSCAL 00060 * .. 00061 * .. Executable Statements .. 00062 * 00063 * Quick return if possible 00064 * 00065 IF( N.LE.1 ) THEN 00066 IF( N.EQ.1 ) 00067 $ CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB ) 00068 RETURN 00069 END IF 00070 * 00071 * Solve A * X = B using the factorization A = L*D*L**T, 00072 * overwriting each right hand side vector with its solution. 00073 * 00074 DO 30 J = 1, NRHS 00075 * 00076 * Solve L * x = b. 00077 * 00078 DO 10 I = 2, N 00079 B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) 00080 10 CONTINUE 00081 * 00082 * Solve D * L**T * x = b. 00083 * 00084 B( N, J ) = B( N, J ) / D( N ) 00085 DO 20 I = N - 1, 1, -1 00086 B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I ) 00087 20 CONTINUE 00088 30 CONTINUE 00089 * 00090 RETURN 00091 * 00092 * End of SPTTS2 00093 * 00094 END
1.7.3 
