ptts2(3)

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

              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

              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

              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

              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

              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

              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

              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

              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

              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

              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

              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

              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, complex*16, dimension( * ) e, complex*16, 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

              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

              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

              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

              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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