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SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
* * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. INTEGER IUPLO, LDB, N, NRHS * .. * .. Array Arguments .. DOUBLE PRECISION D( * ) COMPLEX*16 B( LDB, * ), E( * ) * .. * * Purpose * ======= * * ZPTTS2 solves a tridiagonal system of the form * A * X = B * using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF. * D is a diagonal matrix specified in the vector D, U (or L) is a unit * bidiagonal matrix whose superdiagonal (subdiagonal) is specified in * the vector E, and X and B are N by NRHS matrices. * * Arguments * ========= * * IUPLO (input) INTEGER * Specifies the form of the factorization and whether the * vector E is the superdiagonal of the upper bidiagonal factor * U or the subdiagonal of the lower bidiagonal factor L. * = 1: A = U**H *D*U, E is the superdiagonal of U * = 0: A = L*D*L**H, E is the subdiagonal of L * * 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) DOUBLE PRECISION array, dimension (N) * The n diagonal elements of the diagonal matrix D from the * factorization A = U**H *D*U or A = L*D*L**H. * * E (input) COMPLEX*16 array, dimension (N-1) * If IUPLO = 1, the (n-1) superdiagonal elements of the unit * bidiagonal factor U from the factorization A = U**H*D*U. * If IUPLO = 0, the (n-1) subdiagonal elements of the unit * bidiagonal factor L from the factorization A = L*D*L**H. * * B (input/output) DOUBLE PRECISION 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 ZDSCAL * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.1 ) THEN IF( N.EQ.1 ) $ CALL ZDSCAL( NRHS, 1.D0 / D( 1 ), B, LDB ) RETURN END IF * IF( IUPLO.EQ.1 ) THEN * * Solve A * X = B using the factorization A = U**H *D*U, * overwriting each right hand side vector with its solution. * IF( NRHS.LE.2 ) THEN J = 1 10 CONTINUE * * Solve U**H * x = b. * DO 20 I = 2, N B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) ) 20 CONTINUE * * Solve D * U * x = b. * DO 30 I = 1, N B( I, J ) = B( I, J ) / D( I ) 30 CONTINUE DO 40 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - B( I+1, J )*E( I ) 40 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 10 END IF ELSE DO 70 J = 1, NRHS * * Solve U**H * x = b. * DO 50 I = 2, N B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) ) 50 CONTINUE * * Solve D * U * x = b. * B( N, J ) = B( N, J ) / D( N ) DO 60 I = N - 1, 1, -1 B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I ) 60 CONTINUE 70 CONTINUE END IF ELSE * * Solve A * X = B using the factorization A = L*D*L**H, * overwriting each right hand side vector with its solution. * IF( NRHS.LE.2 ) THEN J = 1 80 CONTINUE * * Solve L * x = b. * DO 90 I = 2, N B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) 90 CONTINUE * * Solve D * L**H * x = b. * DO 100 I = 1, N B( I, J ) = B( I, J ) / D( I ) 100 CONTINUE DO 110 I = N - 1, 1, -1 B( I, J ) = B( I, J ) - B( I+1, J )*DCONJG( E( I ) ) 110 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 80 END IF ELSE DO 140 J = 1, NRHS * * Solve L * x = b. * DO 120 I = 2, N B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) 120 CONTINUE * * Solve D * L**H * x = b. * B( N, J ) = B( N, J ) / D( N ) DO 130 I = N - 1, 1, -1 B( I, J ) = B( I, J ) / D( I ) - $ B( I+1, J )*DCONJG( E( I ) ) 130 CONTINUE 140 CONTINUE END IF END IF * RETURN * * End of ZPTTS2 * END |