Ubuntu Manpage: ptsvx - ptsvx: factor and solve, expert

Provided by: liblapack-doc_3.12.0-3build1.1_all

NAME

       ptsvx - ptsvx: factor and solve, expert

SYNOPSIS

   Functions
       subroutine cptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work,
           rwork, info)
            CPTSVX computes the solution to system of linear equations A * X = B for PT matrices
       subroutine dptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work,
           info)
            DPTSVX computes the solution to system of linear equations A * X = B for PT matrices
       subroutine sptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work,
           info)
            SPTSVX computes the solution to system of linear equations A * X = B for PT matrices
       subroutine zptsvx (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond, ferr, berr, work,
           rwork, info)
            ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Detailed Description

Function Documentation

subroutine cptsvx (character fact, integer n, integer nrhs, real, dimension( * ) d, complex,
dimension( * ) e, real, dimension( * ) df, complex, dimension( * ) ef, complex, dimension(
ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real rcond, real,
dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real,
dimension( * ) rwork, integer info)
CPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

CPTSVX uses the factorization A = L*D*L**H to compute 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.

Error bounds on the solution and a condition estimate are also
provided.

Description:

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**H*D*U.

2. If the leading principal minor of order i is not positive,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.

3. The system of equations is solved for X using the factored form
of A.

4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.

Parameters
FACT

FACT is CHARACTER*1
Specifies whether or not the factored form of the matrix
A is supplied on entry.
= 'F': On entry, DF and EF contain the factored form of A.
D, E, DF, and EF will not be modified.
= 'N': The matrix A will be copied to DF and EF and
factored.

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 matrices B and X. NRHS >= 0.

D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.

E is COMPLEX array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

DF is REAL array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.

EF is COMPLEX array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.

B is COMPLEX array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X is COMPLEX array, dimension (LDX,NRHS)
If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

RCOND

RCOND is REAL
The reciprocal condition number of the matrix A. If RCOND
is less than the machine precision (in particular, if
RCOND = 0), the matrix is singular to working precision.
This condition is indicated by a return code of INFO > 0.

FERR

FERR is REAL array, dimension (NRHS)
The forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).

BERR

BERR is REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any
element of A or B that makes X(j) an exact solution).

WORK

WORK is COMPLEX array, dimension (N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= N: the leading principal minor of order i of A
is not positive, so the factorization could not
be completed, and the solution has not been
computed. RCOND = 0 is returned.
= N+1: U is nonsingular, but RCOND is less than machine
precision, meaning that the matrix is singular
to working precision. Nevertheless, the
solution and error bounds are computed because
there are a number of situations where the
computed solution can be more accurate than the
value of RCOND would suggest.

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dptsvx (character fact, integer n, integer nrhs, double precision, dimension( * )
d, double precision, dimension( * ) e, double precision, dimension( * ) df, double
precision, dimension( * ) ef, double precision, dimension( ldb, * ) b, integer ldb, double
precision, dimension( ldx, * ) x, integer ldx, double precision rcond, double precision,
dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( *
) work, integer info)
DPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

DPTSVX uses the factorization A = L*D*L**T to compute 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.

Error bounds on the solution and a condition estimate are also
provided.

Description:

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**T*D*U.

3. The system of equations is solved for X using the factored form
of A.

4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.

Parameters
FACT

FACT is CHARACTER*1
Specifies whether or not the factored form of A has been
supplied on entry.
= 'F': On entry, DF and EF contain the factored form of A.
D, E, DF, and EF will not be modified.
= 'N': The matrix A will be copied to DF and EF and
factored.

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 matrices B and X. NRHS >= 0.

D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.

E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

DF is DOUBLE PRECISION array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.

EF is DOUBLE PRECISION array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X is DOUBLE PRECISION array, dimension (LDX,NRHS)
If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

RCOND

RCOND is DOUBLE PRECISION
The reciprocal condition number of the matrix A. If RCOND
is less than the machine precision (in particular, if
RCOND = 0), the matrix is singular to working precision.
This condition is indicated by a return code of INFO > 0.

FERR

FERR is DOUBLE PRECISION array, dimension (NRHS)
The forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j).

BERR

BERR is DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in any
element of A or B that makes X(j) an exact solution).

WORK

WORK is DOUBLE PRECISION array, dimension (2*N)

INFO

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sptsvx (character fact, integer n, integer nrhs, real, dimension( * ) d, real,
dimension( * ) e, real, dimension( * ) df, real, dimension( * ) ef, real, dimension( ldb,
* ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real rcond, real, dimension(
* ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer info)
SPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

SPTSVX uses the factorization A = L*D*L**T to compute 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.

Error bounds on the solution and a condition estimate are also
provided.

Description:

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**T*D*U.

3. The system of equations is solved for X using the factored form
of A.

4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.

Parameters
FACT

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 matrices B and X. NRHS >= 0.

D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.

E is REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

DF is REAL array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**T factorization of A.

EF is REAL array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**T factorization of A.

B is REAL array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X is REAL array, dimension (LDX,NRHS)
If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

RCOND

FERR

BERR

WORK

WORK is REAL array, dimension (2*N)

INFO

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zptsvx (character fact, integer n, integer nrhs, double precision, dimension( * )
d, complex*16, dimension( * ) e, double precision, dimension( * ) df, complex*16,
dimension( * ) ef, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
ldx, * ) x, integer ldx, double precision rcond, double precision, dimension( * ) ferr,
double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision,
dimension( * ) rwork, integer info)
ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Purpose:

ZPTSVX uses the factorization A = L*D*L**H to compute 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.

Error bounds on the solution and a condition estimate are also
provided.

Description:

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L
is a unit lower bidiagonal matrix and D is diagonal. The
factorization can also be regarded as having the form
A = U**H*D*U.

3. The system of equations is solved for X using the factored form
of A.

4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.

Parameters
FACT

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 matrices B and X. NRHS >= 0.

D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.

E is COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

DF is DOUBLE PRECISION array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the diagonal matrix D
from the L*D*L**H factorization of A.

EF is COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then EF is an input argument and on entry
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.
If FACT = 'N', then EF is an output argument and on exit
contains the (n-1) subdiagonal elements of the unit
bidiagonal factor L from the L*D*L**H factorization of A.

B is COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X is COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

RCOND

FERR

BERR

WORK

WORK is COMPLEX*16 array, dimension (N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

Author
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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