sgtts2()

subroutine sgtts2	(	integer	itrans,
		integer	n,
		integer	nrhs,
		real, dimension( * )	dl,
		real, dimension( * )	d,
		real, dimension( * )	du,
		real, dimension( * )	du2,
		integer, dimension( * )	ipiv,
		real, dimension( ldb, * )	b,
		integer	ldb )

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Download SGTTS2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SGTTS2 solves one of the systems of equations
!>    A*X = B  or  A**T*X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by SGTTRF.
!> 

Parameters

[in]	ITRANS	!> ITRANS is INTEGER !> Specifies the form of the system of equations. !> = 0: A * X = B (No transpose) !> = 1: A**T* X = B (Transpose) !> = 2: A**T* X = B (Conjugate transpose = Transpose) !>
[in]	N	!> N is INTEGER !> The order of the matrix A. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>
[in]	DL	!> DL is REAL array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A. !>
[in]	D	!> D is REAL array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
[in]	DU	!> DU is REAL array, dimension (N-1) !> The (n-1) elements of the first super-diagonal of U. !>
[in]	DU2	!> DU2 is REAL array, dimension (N-2) !> The (n-2) elements of the second super-diagonal of U. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, row i of the matrix was !> interchanged with row IPIV(i). IPIV(i) will always be either !> i or i+1; IPIV(i) = i indicates a row interchange was not !> required. !>
[in,out]	B	!> B is REAL array, dimension (LDB,NRHS) !> On entry, the matrix of right hand side vectors B. !> On exit, B is overwritten by the solution vectors X. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 125 of file sgtts2.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            ITRANS, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      REAL               B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      INTEGER            I, IP, J
      REAL               TEMP
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.EQ.0 .OR. nrhs.EQ.0 )
     $   RETURN
*
      IF( itrans.EQ.0 ) THEN
*
*        Solve A*X = B using the LU factorization of A,
*        overwriting each right hand side vector with its solution.
*
         IF( nrhs.LE.1 ) THEN
            j = 1
   10       CONTINUE
*
*           Solve L*x = b.
*
            DO 20 i = 1, n - 1
               ip = ipiv( i )
               temp = b( i+1-ip+i, j ) - dl( i )*b( ip, j )
               b( i, j ) = b( ip, j )
               b( i+1, j ) = temp
   20       CONTINUE
*
*           Solve U*x = b.
*
            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 30 i = n - 2, 1, -1
               b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
     $                     b( i+2, j ) ) / d( i )
   30       CONTINUE
            IF( j.LT.nrhs ) THEN
               j = j + 1
               GO TO 10
            END IF
         ELSE
            DO 60 j = 1, nrhs
*
*              Solve L*x = b.
*
               DO 40 i = 1, n - 1
                  IF( ipiv( i ).EQ.i ) THEN
                     b( i+1, j ) = b( i+1, j ) - dl( i )*b( i, j )
                  ELSE
                     temp = b( i, j )
                     b( i, j ) = b( i+1, j )
                     b( i+1, j ) = temp - dl( i )*b( i, j )
                  END IF
   40          CONTINUE
*
*              Solve U*x = b.
*
               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 50 i = n - 2, 1, -1
                  b( i, j ) = ( b( i, j )-du( i )*b( i+1, j )-du2( i )*
     $                        b( i+2, j ) ) / d( i )
   50          CONTINUE
   60       CONTINUE
         END IF
      ELSE
*
*        Solve A**T * X = B.
*
         IF( nrhs.LE.1 ) THEN
*
*           Solve U**T*x = b.
*
            j = 1
   70       CONTINUE
            b( 1, j ) = b( 1, j ) / d( 1 )
            IF( n.GT.1 )
     $         b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
            DO 80 i = 3, n
               b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-du2( i-2 )*
     $                     b( i-2, j ) ) / d( i )
   80       CONTINUE
*
*           Solve L**T*x = b.
*
            DO 90 i = n - 1, 1, -1
               ip = ipiv( i )
               temp = b( i, j ) - dl( i )*b( i+1, j )
               b( i, j ) = b( ip, j )
               b( ip, j ) = temp
   90       CONTINUE
            IF( j.LT.nrhs ) THEN
               j = j + 1
               GO TO 70
            END IF
*
         ELSE
            DO 120 j = 1, nrhs
*
*              Solve U**T*x = b.
*
               b( 1, j ) = b( 1, j ) / d( 1 )
               IF( n.GT.1 )
     $            b( 2, j ) = ( b( 2, j )-du( 1 )*b( 1, j ) ) / d( 2 )
               DO 100 i = 3, n
                  b( i, j ) = ( b( i, j )-du( i-1 )*b( i-1, j )-
     $                        du2( i-2 )*b( i-2, j ) ) / d( i )
  100          CONTINUE
               DO 110 i = n - 1, 1, -1
                  IF( ipiv( i ).EQ.i ) THEN
                     b( i, j ) = b( i, j ) - dl( i )*b( i+1, j )
                  ELSE
                     temp = b( i+1, j )
                     b( i+1, j ) = b( i, j ) - dl( i )*temp
                     b( i, j ) = temp
                  END IF
  110          CONTINUE
  120       CONTINUE
         END IF
      END IF
*
*     End of SGTTS2
*

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