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ptsv(3) LAPACK 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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