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 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 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 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 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 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 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 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 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 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 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 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 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, complex16, dimension( ) e, complex16, 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 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 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 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 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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