LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sptts2()

subroutine sptts2 ( integer  N,
integer  NRHS,
real, dimension( * )  D,
real, dimension( * )  E,
real, dimension( ldb, * )  B,
integer  LDB 
)

SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Download SPTTS2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SPTTS2 solves a tridiagonal system of the form
    A * X = B
 using the L*D*L**T 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.
Parameters
[in]N
          N is INTEGER
          The order of the tridiagonal matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          L*D*L**T factorization of A.
[in]E
          E is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor
          L from the L*D*L**T factorization of A.  E can also be regarded
          as the superdiagonal of the unit bidiagonal factor U from the
          factorization A = U**T*D*U.
[in,out]B
          B is 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.
[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 101 of file sptts2.f.

102 *
103 * -- LAPACK computational routine --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 *
107 * .. Scalar Arguments ..
108  INTEGER LDB, N, NRHS
109 * ..
110 * .. Array Arguments ..
111  REAL B( LDB, * ), D( * ), E( * )
112 * ..
113 *
114 * =====================================================================
115 *
116 * .. Local Scalars ..
117  INTEGER I, J
118 * ..
119 * .. External Subroutines ..
120  EXTERNAL sscal
121 * ..
122 * .. Executable Statements ..
123 *
124 * Quick return if possible
125 *
126  IF( n.LE.1 ) THEN
127  IF( n.EQ.1 )
128  $ CALL sscal( nrhs, 1. / d( 1 ), b, ldb )
129  RETURN
130  END IF
131 *
132 * Solve A * X = B using the factorization A = L*D*L**T,
133 * overwriting each right hand side vector with its solution.
134 *
135  DO 30 j = 1, nrhs
136 *
137 * Solve L * x = b.
138 *
139  DO 10 i = 2, n
140  b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
141  10 CONTINUE
142 *
143 * Solve D * L**T * x = b.
144 *
145  b( n, j ) = b( n, j ) / d( n )
146  DO 20 i = n - 1, 1, -1
147  b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
148  20 CONTINUE
149  30 CONTINUE
150 *
151  RETURN
152 *
153 * End of SPTTS2
154 *
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
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