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.

   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.

   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.

   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.

Author

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