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.

  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.

  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.

  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.

Author

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