NAME

ptts2 - ptts2: triangular solve using factor, unblocked

SYNOPSIS

Functions

subroutine cptts2 (iuplo, n, nrhs, d, e, b, ldb)
CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf. subroutine dptts2 (n, nrhs, d, e, b, ldb)
DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf. subroutine sptts2 (n, nrhs, d, e, b, ldb)
SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf. subroutine zptts2 (iuplo, n, nrhs, d, e, b, ldb)
ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Detailed Description

Function Documentation

subroutine cptts2 (integer iuplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb)

CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Purpose:



 CPTTS2 solves a tridiagonal system of the form


    A * X = B


 using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.


 D is a diagonal matrix specified in the vector D, U (or L) is a unit


 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in


 the vector E, and X and B are N by NRHS matrices.

Parameters

IUPLO



          IUPLO is INTEGER


          Specifies the form of the factorization and whether the


          vector E is the superdiagonal of the upper bidiagonal factor


          U or the subdiagonal of the lower bidiagonal factor L.


          = 1:  A = U**H *D*U, E is the superdiagonal of U


          = 0:  A = L*D*L**H, E is the subdiagonal of L



          N is INTEGER


          The order of the tridiagonal matrix A.  N >= 0.

NRHS



          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.



          D is REAL array, dimension (N)


          The n diagonal elements of the diagonal matrix D from the


          factorization A = U**H *D*U or A = L*D*L**H.



          E is COMPLEX array, dimension (N-1)


          If IUPLO = 1, the (n-1) superdiagonal elements of the unit


          bidiagonal factor U from the factorization A = U**H*D*U.


          If IUPLO = 0, the (n-1) subdiagonal elements of the unit


          bidiagonal factor L from the factorization A = L*D*L**H.



          B is COMPLEX array, dimension (LDB,NRHS)


          On entry, the right hand side vectors B for the system of


          linear equations.


          On exit, the solution vectors, X.

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 112 of file cptts2.f.

subroutine dptts2 (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb)

DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Purpose:



 DPTTS2 solves a tridiagonal system of the form


    A * X = B


 using the L*D*L**T factorization of A computed by DPTTRF.  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



          N is INTEGER


          The order of the tridiagonal matrix A.  N >= 0.

NRHS



          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.



          D is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the diagonal matrix D from the


          L*D*L**T factorization of A.



          E is DOUBLE PRECISION 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.



          B is DOUBLE PRECISION array, dimension (LDB,NRHS)


          On entry, the right hand side vectors B for the system of


          linear equations.


          On exit, the solution vectors, X.

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 dptts2.f.

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.

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



          N is INTEGER


          The order of the tridiagonal matrix A.  N >= 0.

NRHS



          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.



          D is REAL array, dimension (N)


          The n diagonal elements of the diagonal matrix D from the


          L*D*L**T factorization of A.



          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.



          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.

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.

subroutine zptts2 (integer iuplo, integer n, integer nrhs, double precision, dimension( * ) d, complex16, dimension( ) e, complex16, dimension( ldb, ) b, integer ldb)

ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.

Purpose:



 ZPTTS2 solves a tridiagonal system of the form


    A * X = B


 using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.


 D is a diagonal matrix specified in the vector D, U (or L) is a unit


 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in


 the vector E, and X and B are N by NRHS matrices.

Parameters

IUPLO



          IUPLO is INTEGER


          Specifies the form of the factorization and whether the


          vector E is the superdiagonal of the upper bidiagonal factor


          U or the subdiagonal of the lower bidiagonal factor L.


          = 1:  A = U**H *D*U, E is the superdiagonal of U


          = 0:  A = L*D*L**H, E is the subdiagonal of L



          N is INTEGER


          The order of the tridiagonal matrix A.  N >= 0.

NRHS



          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.



          D is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the diagonal matrix D from the


          factorization A = U**H *D*U or A = L*D*L**H.



          E is COMPLEX*16 array, dimension (N-1)


          If IUPLO = 1, the (n-1) superdiagonal elements of the unit


          bidiagonal factor U from the factorization A = U**H*D*U.


          If IUPLO = 0, the (n-1) subdiagonal elements of the unit


          bidiagonal factor L from the factorization A = L*D*L**H.



          B is COMPLEX*16 array, dimension (LDB,NRHS)


          On entry, the right hand side vectors B for the system of


          linear equations.


          On exit, the solution vectors, X.

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 112 of file zptts2.f.

Author

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