SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDB, N, NRHS * .. * .. Array Arguments .. REAL B( LDB, * ), D( * ), E( * ) * .. * * Purpose * ======= * * SPTTS2 solves a tridiagonal system of the form * A * X = B * using the L*D*L' factorization of A computed by SPTTRF. D is a * diagonal matrix specified in the vector D, L is a unit bidiagonal * matrix whose subdiagonal is specified in the vector E, and X and B * are N by NRHS matrices. * * Arguments * ========= * * N (input) INTEGER * The order of the tridiagonal matrix A. N >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrix B. NRHS >= 0. * * D (input) REAL array, dimension (N) * The n diagonal elements of the diagonal matrix D from the * L*D*L' factorization of A. * * E (input) REAL array, dimension (N-1) * The (n-1) subdiagonal elements of the unit bidiagonal factor * L from the L*D*L' factorization of A. E can also be regarded * as the superdiagonal of the unit bidiagonal factor U from the * factorization A = U'*D*U. * * B (input/output) REAL array, dimension (LDB,NRHS) * On entry, the right hand side vectors B for the system of * linear equations. * On exit, the solution vectors, X. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Subroutines .. EXTERNAL SSCAL * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.1 ) THEN IF( N.EQ.1 ) $ CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB ) RETURN END IF * * Solve A * X = B using the factorization A = L*D*L', * overwriting each right hand side vector with its solution. * DO 30 J = 1, NRHS * * Solve L * x = b. * DO 10 I = 2, N B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) 10 CONTINUE * * Solve D * L' * x = b. * B( N, J ) = B( N, J ) / D( N ) DO 20 I = N - 1, 1, -1 B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I ) 20 CONTINUE 30 CONTINUE * RETURN * * End of SPTTS2 * END