*> \brief SGTSV computes the solution to system of linear equations A * X = B for GT matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SGTSV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. * REAL B( LDB, * ), D( * ), DL( * ), DU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGTSV solves the equation *> *> A*X = B, *> *> where A is an n by n tridiagonal matrix, by Gaussian elimination with *> partial pivoting. *> *> Note that the equation A**T*X = B may be solved by interchanging the *> order of the arguments DU and DL. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in,out] DL *> \verbatim *> DL is REAL array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. *> *> On exit, DL is overwritten by the (n-2) elements of the *> second super-diagonal of the upper triangular matrix U from *> the LU factorization of A, in DL(1), ..., DL(n-2). *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is REAL array, dimension (N) *> On entry, D must contain the diagonal elements of A. *> *> On exit, D is overwritten by the n diagonal elements of U. *> \endverbatim *> *> \param[in,out] DU *> \verbatim *> DU is REAL array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. *> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is REAL array, dimension (LDB,NRHS) *> On entry, the N by NRHS matrix of right hand side matrix B. *> On exit, if INFO = 0, the N by NRHS solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero, and the solution *> has not been computed. The factorization has not been *> completed unless i = N. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup realGTsolve * * ===================================================================== SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. REAL B( LDB, * ), D( * ), DL( * ), DU( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL FACT, TEMP * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( NRHS.LT.0 ) THEN INFO = -2 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGTSV ', -INFO ) RETURN END IF * IF( N.EQ.0 ) $ RETURN * IF( NRHS.EQ.1 ) THEN DO 10 I = 1, N - 2 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN * * No row interchange required * IF( D( I ).NE.ZERO ) THEN FACT = DL( I ) / D( I ) D( I+1 ) = D( I+1 ) - FACT*DU( I ) B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) ELSE INFO = I RETURN END IF DL( I ) = ZERO ELSE * * Interchange rows I and I+1 * FACT = D( I ) / DL( I ) D( I ) = DL( I ) TEMP = D( I+1 ) D( I+1 ) = DU( I ) - FACT*TEMP DL( I ) = DU( I+1 ) DU( I+1 ) = -FACT*DL( I ) DU( I ) = TEMP TEMP = B( I, 1 ) B( I, 1 ) = B( I+1, 1 ) B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) END IF 10 CONTINUE IF( N.GT.1 ) THEN I = N - 1 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN IF( D( I ).NE.ZERO ) THEN FACT = DL( I ) / D( I ) D( I+1 ) = D( I+1 ) - FACT*DU( I ) B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 ) ELSE INFO = I RETURN END IF ELSE FACT = D( I ) / DL( I ) D( I ) = DL( I ) TEMP = D( I+1 ) D( I+1 ) = DU( I ) - FACT*TEMP DU( I ) = TEMP TEMP = B( I, 1 ) B( I, 1 ) = B( I+1, 1 ) B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 ) END IF END IF IF( D( N ).EQ.ZERO ) THEN INFO = N RETURN END IF ELSE DO 40 I = 1, N - 2 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN * * No row interchange required * IF( D( I ).NE.ZERO ) THEN FACT = DL( I ) / D( I ) D( I+1 ) = D( I+1 ) - FACT*DU( I ) DO 20 J = 1, NRHS B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) 20 CONTINUE ELSE INFO = I RETURN END IF DL( I ) = ZERO ELSE * * Interchange rows I and I+1 * FACT = D( I ) / DL( I ) D( I ) = DL( I ) TEMP = D( I+1 ) D( I+1 ) = DU( I ) - FACT*TEMP DL( I ) = DU( I+1 ) DU( I+1 ) = -FACT*DL( I ) DU( I ) = TEMP DO 30 J = 1, NRHS TEMP = B( I, J ) B( I, J ) = B( I+1, J ) B( I+1, J ) = TEMP - FACT*B( I+1, J ) 30 CONTINUE END IF 40 CONTINUE IF( N.GT.1 ) THEN I = N - 1 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN IF( D( I ).NE.ZERO ) THEN FACT = DL( I ) / D( I ) D( I+1 ) = D( I+1 ) - FACT*DU( I ) DO 50 J = 1, NRHS B( I+1, J ) = B( I+1, J ) - FACT*B( I, J ) 50 CONTINUE ELSE INFO = I RETURN END IF ELSE FACT = D( I ) / DL( I ) D( I ) = DL( I ) TEMP = D( I+1 ) D( I+1 ) = DU( I ) - FACT*TEMP DU( I ) = TEMP DO 60 J = 1, NRHS TEMP = B( I, J ) B( I, J ) = B( I+1, J ) B( I+1, J ) = TEMP - FACT*B( I+1, J ) 60 CONTINUE END IF END IF IF( D( N ).EQ.ZERO ) THEN INFO = N RETURN END IF END IF * * Back solve with the matrix U from the factorization. * IF( NRHS.LE.2 ) THEN J = 1 70 CONTINUE B( N, J ) = B( N, J ) / D( N ) IF( N.GT.1 ) $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 ) DO 80 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* $ B( I+2, J ) ) / D( I ) 80 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 70 END IF ELSE DO 100 J = 1, NRHS B( N, J ) = B( N, J ) / D( N ) IF( N.GT.1 ) $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / $ D( N-1 ) DO 90 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )* $ B( I+2, J ) ) / D( I ) 90 CONTINUE 100 CONTINUE END IF * RETURN * * End of SGTSV * END