ptsv(3)

NAME
ptsv - ptsv: factor and solve

SYNOPSIS

  Functions
subroutine cptsv (n, nrhs, d, e, b, ldb, info)
CPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine dptsv (n, nrhs, d, e, b, ldb, info)
DPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine sptsv (n, nrhs, d, e, b, ldb, info)
SPTSV computes the solution to system of linear equations A * X = B for PT matrices
subroutine zptsv (n, nrhs, d, e, b, ldb, info)
ZPTSV computes the solution to system of linear equations A * X = B for PT matrices

Detailed Description

Function Documentation

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

CPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     CPTSV computes the solution to a complex system of linear equations
     A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
     matrix, and X and B are N-by-NRHS matrices.
     A is factored as A = L*D*L**H, and the factored form of A is then
     used to solve the system of equations.

Parameters
    N

              N is INTEGER
              The order of the 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)
              On entry, the n diagonal elements of the tridiagonal matrix
              A.  On exit, the n diagonal elements of the diagonal matrix
              D from the factorization A = L*D*L**H.

    E

              E is COMPLEX array, dimension (N-1)
              On entry, the (n-1) subdiagonal elements of the tridiagonal
              matrix A.  On exit, the (n-1) subdiagonal elements of the
              unit bidiagonal factor L from the L*D*L**H factorization of
              A.  E can also be regarded as the superdiagonal of the unit
              bidiagonal factor U from the U**H*D*U factorization of A.

    B

              B is COMPLEX array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix 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 = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, the leading principal minor of order i
                    is not positive, and the solution has not been
                    computed.  The factorization has not been completed
                    unless i = N.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 114 of file cptsv.f.

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

DPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     DPTSV computes the solution to a real system of linear equations
     A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
     matrix, and X and B are N-by-NRHS matrices.
     A is factored as A = L*D*L**T, and the factored form of A is then
     used to solve the system of equations.

Parameters
    N

              N is INTEGER
              The order of the 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)
              On entry, the n diagonal elements of the tridiagonal matrix
              A.  On exit, the n diagonal elements of the diagonal matrix
              D from the factorization A = L*D*L**T.

    E

              E is DOUBLE PRECISION array, dimension (N-1)
              On entry, the (n-1) subdiagonal elements of the tridiagonal
              matrix A.  On exit, 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 U**T*D*U factorization of A.)

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix 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 = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, the leading principal minor of order i
                    is not positive, and the solution has not been
                    computed.  The factorization has not been completed
                    unless i = N.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 113 of file dptsv.f.

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

SPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     SPTSV computes the solution to a real system of linear equations
     A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
     matrix, and X and B are N-by-NRHS matrices.
     A is factored as A = L*D*L**T, and the factored form of A is then
     used to solve the system of equations.

Parameters
    N

              N is INTEGER
              The order of the 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)
              On entry, the n diagonal elements of the tridiagonal matrix
              A.  On exit, the n diagonal elements of the diagonal matrix
              D from the factorization A = L*D*L**T.

    E

              E is REAL array, dimension (N-1)
              On entry, the (n-1) subdiagonal elements of the tridiagonal
              matrix A.  On exit, 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 U**T*D*U factorization of A.)

    B

              B is REAL array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix 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 = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, the leading principal minor of order i
                    is not positive, and the solution has not been
                    computed.  The factorization has not been completed
                    unless i = N.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 113 of file sptsv.f.

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

ZPTSV computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

     ZPTSV computes the solution to a complex system of linear equations
     A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
     matrix, and X and B are N-by-NRHS matrices.
     A is factored as A = L*D*L**H, and the factored form of A is then
     used to solve the system of equations.

Parameters
    N

              N is INTEGER
              The order of the 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)
              On entry, the n diagonal elements of the tridiagonal matrix
              A.  On exit, the n diagonal elements of the diagonal matrix
              D from the factorization A = L*D*L**H.

    E

              E is COMPLEX*16 array, dimension (N-1)
              On entry, the (n-1) subdiagonal elements of the tridiagonal
              matrix A.  On exit, the (n-1) subdiagonal elements of the
              unit bidiagonal factor L from the L*D*L**H factorization of
              A.  E can also be regarded as the superdiagonal of the unit
              bidiagonal factor U from the U**H*D*U factorization of A.

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS solution matrix 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 = -i, the i-th argument had an illegal value
              > 0:  if INFO = i, the leading principal minor of order i
                    is not positive, and the solution has not been
                    computed.  The factorization has not been completed
                    unless i = N.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 114 of file zptsv.f.

Author

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