pttrs(3)

NAME
pttrs - pttrs: triangular solve using factor

SYNOPSIS

  Functions
subroutine cpttrs (uplo, n, nrhs, d, e, b, ldb, info)
CPTTRS
subroutine dpttrs (n, nrhs, d, e, b, ldb, info)
DPTTRS
subroutine spttrs (n, nrhs, d, e, b, ldb, info)
SPTTRS
subroutine zpttrs (uplo, n, nrhs, d, e, b, ldb, info)
ZPTTRS

Detailed Description

Function Documentation

  subroutine cpttrs (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPTTRS

Purpose:

     CPTTRS 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
    UPLO

              UPLO is CHARACTER*1
              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.
              = 'U':  A = U**H*D*U, E is the superdiagonal of U
              = 'L':  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 UPLO = 'U', the (n-1) superdiagonal elements of the unit
              bidiagonal factor U from the factorization A = U**H*D*U.
              If UPLO = 'L', 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).

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 120 of file cpttrs.f.

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

DPTTRS

Purpose:

     DPTTRS 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).

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 108 of file dpttrs.f.

  subroutine spttrs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)

SPTTRS

Purpose:

     SPTTRS 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).

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 108 of file spttrs.f.

  subroutine zpttrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPTTRS

Purpose:

     ZPTTRS 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
    UPLO

              UPLO is CHARACTER*1
              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.
              = 'U':  A = U**H *D*U, E is the superdiagonal of U
              = 'L':  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 UPLO = 'U', the (n-1) superdiagonal elements of the unit
              bidiagonal factor U from the factorization A = U**H*D*U.
              If UPLO = 'L', 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).

    INFO

              INFO is INTEGER
              = 0: successful exit
              < 0: if INFO = -k, the k-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 120 of file zpttrs.f.

Author

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