LAPACK  3.8.0
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.
Date
December 2016

Definition at line 104 of file sptts2.f.

104 *
105 * -- LAPACK computational routine (version 3.7.0) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * December 2016
109 *
110 * .. Scalar Arguments ..
111  INTEGER ldb, n, nrhs
112 * ..
113 * .. Array Arguments ..
114  REAL b( ldb, * ), d( * ), e( * )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Local Scalars ..
120  INTEGER i, j
121 * ..
122 * .. External Subroutines ..
123  EXTERNAL sscal
124 * ..
125 * .. Executable Statements ..
126 *
127 * Quick return if possible
128 *
129  IF( n.LE.1 ) THEN
130  IF( n.EQ.1 )
131  $ CALL sscal( nrhs, 1. / d( 1 ), b, ldb )
132  RETURN
133  END IF
134 *
135 * Solve A * X = B using the factorization A = L*D*L**T,
136 * overwriting each right hand side vector with its solution.
137 *
138  DO 30 j = 1, nrhs
139 *
140 * Solve L * x = b.
141 *
142  DO 10 i = 2, n
143  b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
144  10 CONTINUE
145 *
146 * Solve D * L**T * x = b.
147 *
148  b( n, j ) = b( n, j ) / d( n )
149  DO 20 i = n - 1, 1, -1
150  b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
151  20 CONTINUE
152  30 CONTINUE
153 *
154  RETURN
155 *
156 * End of SPTTS2
157 *
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
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