Annotation of rpl/lapack/lapack/dptts2.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DPTTS2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DPTTS2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptts2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dptts2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dptts2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER LDB, N, NRHS
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DPTTS2 solves a tridiagonal system of the form
! 37: *> A * X = B
! 38: *> using the L*D*L**T factorization of A computed by DPTTRF. D is a
! 39: *> diagonal matrix specified in the vector D, L is a unit bidiagonal
! 40: *> matrix whose subdiagonal is specified in the vector E, and X and B
! 41: *> are N by NRHS matrices.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] N
! 48: *> \verbatim
! 49: *> N is INTEGER
! 50: *> The order of the tridiagonal matrix A. N >= 0.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] NRHS
! 54: *> \verbatim
! 55: *> NRHS is INTEGER
! 56: *> The number of right hand sides, i.e., the number of columns
! 57: *> of the matrix B. NRHS >= 0.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] D
! 61: *> \verbatim
! 62: *> D is DOUBLE PRECISION array, dimension (N)
! 63: *> The n diagonal elements of the diagonal matrix D from the
! 64: *> L*D*L**T factorization of A.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] E
! 68: *> \verbatim
! 69: *> E is DOUBLE PRECISION array, dimension (N-1)
! 70: *> The (n-1) subdiagonal elements of the unit bidiagonal factor
! 71: *> L from the L*D*L**T factorization of A. E can also be regarded
! 72: *> as the superdiagonal of the unit bidiagonal factor U from the
! 73: *> factorization A = U**T*D*U.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in,out] B
! 77: *> \verbatim
! 78: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 79: *> On entry, the right hand side vectors B for the system of
! 80: *> linear equations.
! 81: *> On exit, the solution vectors, X.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] LDB
! 85: *> \verbatim
! 86: *> LDB is INTEGER
! 87: *> The leading dimension of the array B. LDB >= max(1,N).
! 88: *> \endverbatim
! 89: *
! 90: * Authors:
! 91: * ========
! 92: *
! 93: *> \author Univ. of Tennessee
! 94: *> \author Univ. of California Berkeley
! 95: *> \author Univ. of Colorado Denver
! 96: *> \author NAG Ltd.
! 97: *
! 98: *> \date November 2011
! 99: *
! 100: *> \ingroup doubleOTHERcomputational
! 101: *
! 102: * =====================================================================
1.1 bertrand 103: SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
104: *
1.9 ! bertrand 105: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 106: * -- LAPACK is a software package provided by Univ. of Tennessee, --
107: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 108: * November 2011
1.1 bertrand 109: *
110: * .. Scalar Arguments ..
111: INTEGER LDB, N, NRHS
112: * ..
113: * .. Array Arguments ..
114: DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
115: * ..
116: *
117: * =====================================================================
118: *
119: * .. Local Scalars ..
120: INTEGER I, J
121: * ..
122: * .. External Subroutines ..
123: EXTERNAL DSCAL
124: * ..
125: * .. Executable Statements ..
126: *
127: * Quick return if possible
128: *
129: IF( N.LE.1 ) THEN
130: IF( N.EQ.1 )
131: $ CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
132: RETURN
133: END IF
134: *
1.8 bertrand 135: * Solve A * X = B using the factorization A = L*D*L**T,
1.1 bertrand 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: *
1.8 bertrand 146: * Solve D * L**T * x = b.
1.1 bertrand 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 DPTTS2
157: *
158: END
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