Man page - gesvx(3)

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Manual

gesvx

NAME

gesvx - gesvx: factor and solve, expert

SYNOPSIS

Functions

subroutine cgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
CGESVX computes the solution to system of linear equations A * X = B for GE matrices
subroutine dgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info)
DGESVX computes the solution to system of linear equations A * X = B for GE matrices
subroutine sgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info)
SGESVX computes the solution to system of linear equations A * X = B for GE matrices
subroutine zgesvx (fact, trans, n, nrhs, a, lda, af, ldaf, ipiv, equed, r, c, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
ZGESVX computes the solution to system of linear equations A * X = B for GE matrices

Detailed Description

Function Documentation

subroutine cgesvx (character fact, character trans, integer n, integernrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension(ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, characterequed, real, dimension( * ) r, real, dimension( * ) c, 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)

CGESVX computes the solution to system of linear equations A * X = B for GE matrices

Purpose:

CGESVX uses the LU factorization to compute the solution to a complex
system of linear equations
A * X = B,
where A is an N-by-N 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 = ’E’, real scaling factors are computed to equilibrate
the system:
TRANS = ’N’: diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = ’T’: (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = ’C’: (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS=’N’)
or diag(C)*B (if TRANS = ’T’ or ’C’).

2. If FACT = ’N’ or ’E’, the LU decomposition is used to factor the
matrix A (after equilibration if FACT = ’E’) as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.

3. If some U(i,i)=0, so that U is exactly singular, 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.

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

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

6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = ’N’) or diag(R) (if TRANS = ’T’ or ’C’) so
that it solves the original system before equilibration.

Parameters

FACT

FACT is CHARACTER*1
Specifies whether or not the factored form of the matrix A is
supplied on entry, and if not, whether the matrix A should be
equilibrated before it is factored.
= ’F’: On entry, AF and IPIV contain the factored form of A.
If EQUED is not ’N’, the matrix A has been
equilibrated with scaling factors given by R and C.
A, AF, and IPIV are not modified.
= ’N’: The matrix A will be copied to AF and factored.
= ’E’: The matrix A will be equilibrated if necessary, then
copied to AF and factored.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

N is INTEGER
The number of linear equations, i.e., 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.

A is COMPLEX array, dimension (LDA,N)
On entry, the N-by-N matrix A. If FACT = ’F’ and EQUED is
not ’N’, then A must have been equilibrated by the scaling
factors in R and/or C. A is not modified if FACT = ’F’ or
’N’, or if FACT = ’E’ and EQUED = ’N’ on exit.

On exit, if EQUED .ne. ’N’, A is scaled as follows:
EQUED = ’R’: A := diag(R) * A
EQUED = ’C’: A := A * diag(C)
EQUED = ’B’: A := diag(R) * A * diag(C).

LDA

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

AF is COMPLEX array, dimension (LDAF,N)
If FACT = ’F’, then AF is an input argument and on entry
contains the factors L and U from the factorization
A = P*L*U as computed by CGETRF. If EQUED .ne. ’N’, then
AF is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AF is an output argument and on exit
returns the factors L and U from the factorization A = P*L*U
of the original matrix A.

If FACT = ’E’, then AF is an output argument and on exit
returns the factors L and U from the factorization A = P*L*U
of the equilibrated matrix A (see the description of A for
the form of the equilibrated matrix).

LDAF

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

IPIV

IPIV is INTEGER array, dimension (N)
If FACT = ’F’, then IPIV is an input argument and on entry
contains the pivot indices from the factorization A = P*L*U
as computed by CGETRF; row i of the matrix was interchanged
with row IPIV(i).

If FACT = ’N’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the original matrix A.

If FACT = ’E’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the equilibrated matrix A.

EQUED

EQUED is CHARACTER*1
Specifies the form of equilibration that was done.
= ’N’: No equilibration (always true if FACT = ’N’).
= ’R’: Row equilibration, i.e., A has been premultiplied by
diag(R).
= ’C’: Column equilibration, i.e., A has been postmultiplied
by diag(C).
= ’B’: Both row and column equilibration, i.e., A has been
replaced by diag(R) * A * diag(C).
EQUED is an input argument if FACT = ’F’; otherwise, it is an
output argument.

R is REAL array, dimension (N)
The row scale factors for A. If EQUED = ’R’ or ’B’, A is
multiplied on the left by diag(R); if EQUED = ’N’ or ’C’, R
is not accessed. R is an input argument if FACT = ’F’;
otherwise, R is an output argument. If FACT = ’F’ and
EQUED = ’R’ or ’B’, each element of R must be positive.

C is REAL array, dimension (N)
The column scale factors for A. If EQUED = ’C’ or ’B’, A is
multiplied on the right by diag(C); if EQUED = ’N’ or ’R’, C
is not accessed. C is an input argument if FACT = ’F’;
otherwise, C is an output argument. If FACT = ’F’ and
EQUED = ’C’ or ’B’, each element of C must be positive.

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit,
if EQUED = ’N’, B is not modified;
if TRANS = ’N’ and EQUED = ’R’ or ’B’, B is overwritten by
diag(R)*B;
if TRANS = ’T’ or ’C’ and EQUED = ’C’ or ’B’, B is
overwritten by diag(C)*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
to the original system of equations. Note that A and B are
modified on exit if EQUED .ne. ’N’, and the solution to the
equilibrated system is inv(diag(C))*X if TRANS = ’N’ and
EQUED = ’C’ or ’B’, or inv(diag(R))*X if TRANS = ’T’ or ’C’
and EQUED = ’R’ or ’B’.

LDX

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

RCOND

RCOND is REAL
The estimate of the reciprocal condition number of the matrix
A after equilibration (if done). 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 estimated 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). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.

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 (2*N)

RWORK

RWORK is REAL array, dimension (MAX(1,2*N))
On exit, RWORK(1) contains the reciprocal pivot growth
factor norm(A)/norm(U). The ’max absolute element’ norm is
used. If RWORK(1) is much less than 1, then the stability
of the LU factorization of the (equilibrated) matrix A
could be poor. This also means that the solution X, condition
estimator RCOND, and forward error bound FERR could be
unreliable. If factorization fails with 0<INFO<=N, then
RWORK(1) contains the reciprocal pivot growth factor for the
leading INFO columns of A.

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: U(i,i) is exactly zero. The factorization has
been completed, but the factor U is exactly
singular, so the solution and error bounds
could not be 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 dgesvx (character fact, character trans, integer n, integernrhs, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( ldaf, * ) af, integer ldaf, integer, dimension( ) ipiv, character equed, double precision, dimension( ) r, doubleprecision, dimension( * ) c, double precision, dimension( ldb, * ) b,integer ldb, double precision, dimension( ldx, * ) x, integer ldx,double precision rcond, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)

DGESVX computes the solution to system of linear equations A * X = B for GE matrices

Purpose:

DGESVX uses the LU factorization to compute the solution to a real
system of linear equations
A * X = B,
where A is an N-by-N 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:

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

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

6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = ’N’) or diag(R) (if TRANS = ’T’ or ’C’) so
that it solves the original system before equilibration.

Parameters

FACT

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Transpose)

N is INTEGER
The number of linear equations, i.e., 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.

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the N-by-N matrix A. If FACT = ’F’ and EQUED is
not ’N’, then A must have been equilibrated by the scaling
factors in R and/or C. A is not modified if FACT = ’F’ or
’N’, or if FACT = ’E’ and EQUED = ’N’ on exit.

On exit, if EQUED .ne. ’N’, A is scaled as follows:
EQUED = ’R’: A := diag(R) * A
EQUED = ’C’: A := A * diag(C)
EQUED = ’B’: A := diag(R) * A * diag(C).

LDA

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

AF is DOUBLE PRECISION array, dimension (LDAF,N)
If FACT = ’F’, then AF is an input argument and on entry
contains the factors L and U from the factorization
A = P*L*U as computed by DGETRF. If EQUED .ne. ’N’, then
AF is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AF is an output argument and on exit
returns the factors L and U from the factorization A = P*L*U
of the original matrix A.

LDAF

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

IPIV

IPIV is INTEGER array, dimension (N)
If FACT = ’F’, then IPIV is an input argument and on entry
contains the pivot indices from the factorization A = P*L*U
as computed by DGETRF; row i of the matrix was interchanged
with row IPIV(i).

If FACT = ’N’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the original matrix A.

If FACT = ’E’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the equilibrated matrix A.

EQUED

R is DOUBLE PRECISION array, dimension (N)
The row scale factors for A. If EQUED = ’R’ or ’B’, A is
multiplied on the left by diag(R); if EQUED = ’N’ or ’C’, R
is not accessed. R is an input argument if FACT = ’F’;
otherwise, R is an output argument. If FACT = ’F’ and
EQUED = ’R’ or ’B’, each element of R must be positive.

C is DOUBLE PRECISION array, dimension (N)
The column scale factors for A. If EQUED = ’C’ or ’B’, A is
multiplied on the right by diag(C); if EQUED = ’N’ or ’R’, C
is not accessed. C is an input argument if FACT = ’F’;
otherwise, C is an output argument. If FACT = ’F’ and
EQUED = ’C’ or ’B’, each element of C must be positive.

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit,
if EQUED = ’N’, B is not modified;
if TRANS = ’N’ and EQUED = ’R’ or ’B’, B is overwritten by
diag(R)*B;
if TRANS = ’T’ or ’C’ and EQUED = ’C’ or ’B’, B is
overwritten by diag(C)*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 or INFO = N+1, the N-by-NRHS solution matrix X
to the original system of equations. Note that A and B are
modified on exit if EQUED .ne. ’N’, and the solution to the
equilibrated system is inv(diag(C))*X if TRANS = ’N’ and
EQUED = ’C’ or ’B’, or inv(diag(R))*X if TRANS = ’T’ or ’C’
and EQUED = ’R’ or ’B’.

LDX

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

RCOND

RCOND is DOUBLE PRECISION
The estimate of the reciprocal condition number of the matrix
A after equilibration (if done). 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 estimated 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). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.

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 (MAX(1,4*N))
On exit, WORK(1) contains the reciprocal pivot growth
factor norm(A)/norm(U). The ’max absolute element’ norm is
used. If WORK(1) is much less than 1, then the stability
of the LU factorization of the (equilibrated) matrix A
could be poor. This also means that the solution X, condition
estimator RCOND, and forward error bound FERR could be
unreliable. If factorization fails with 0<INFO<=N, then
WORK(1) contains the reciprocal pivot growth factor for the
leading INFO columns of A.

IWORK

IWORK is INTEGER array, dimension (N)

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgesvx (character fact, character trans, integer n, integernrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf,* ) af, integer ldaf, integer, dimension( * ) ipiv, character equed,real, dimension( * ) r, real, dimension( * ) c, real, dimension( ldb, ) b, integer ldb, real, dimension( ldx, ) x, integer ldx, real rcond,real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension(* ) work, integer, dimension( * ) iwork, integer info)

SGESVX computes the solution to system of linear equations A * X = B for GE matrices

Purpose:

SGESVX uses the LU factorization to compute the solution to a real
system of linear equations
A * X = B,
where A is an N-by-N 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:

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

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

6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = ’N’) or diag(R) (if TRANS = ’T’ or ’C’) so
that it solves the original system before equilibration.

Parameters

FACT

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Transpose)

N is INTEGER
The number of linear equations, i.e., 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.

A is REAL array, dimension (LDA,N)
On entry, the N-by-N matrix A. If FACT = ’F’ and EQUED is
not ’N’, then A must have been equilibrated by the scaling
factors in R and/or C. A is not modified if FACT = ’F’ or
’N’, or if FACT = ’E’ and EQUED = ’N’ on exit.

On exit, if EQUED .ne. ’N’, A is scaled as follows:
EQUED = ’R’: A := diag(R) * A
EQUED = ’C’: A := A * diag(C)
EQUED = ’B’: A := diag(R) * A * diag(C).

LDA

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

AF is REAL array, dimension (LDAF,N)
If FACT = ’F’, then AF is an input argument and on entry
contains the factors L and U from the factorization
A = P*L*U as computed by SGETRF. If EQUED .ne. ’N’, then
AF is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AF is an output argument and on exit
returns the factors L and U from the factorization A = P*L*U
of the original matrix A.

LDAF

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

IPIV

IPIV is INTEGER array, dimension (N)
If FACT = ’F’, then IPIV is an input argument and on entry
contains the pivot indices from the factorization A = P*L*U
as computed by SGETRF; row i of the matrix was interchanged
with row IPIV(i).

If FACT = ’N’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the original matrix A.

If FACT = ’E’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the equilibrated matrix A.

EQUED

B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit,
if EQUED = ’N’, B is not modified;
if TRANS = ’N’ and EQUED = ’R’ or ’B’, B is overwritten by
diag(R)*B;
if TRANS = ’T’ or ’C’ and EQUED = ’C’ or ’B’, B is
overwritten by diag(C)*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 or INFO = N+1, the N-by-NRHS solution matrix X
to the original system of equations. Note that A and B are
modified on exit if EQUED .ne. ’N’, and the solution to the
equilibrated system is inv(diag(C))*X if TRANS = ’N’ and
EQUED = ’C’ or ’B’, or inv(diag(R))*X if TRANS = ’T’ or ’C’
and EQUED = ’R’ or ’B’.

LDX

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

RCOND

FERR

BERR

WORK

WORK is REAL array, dimension (MAX(1,4*N))
On exit, WORK(1) contains the reciprocal pivot growth
factor norm(A)/norm(U). The ’max absolute element’ norm is
used. If WORK(1) is much less than 1, then the stability
of the LU factorization of the (equilibrated) matrix A
could be poor. This also means that the solution X, condition
estimator RCOND, and forward error bound FERR could be
unreliable. If factorization fails with 0<INFO<=N, then
WORK(1) contains the reciprocal pivot growth factor for the
leading INFO columns of A.

IWORK

IWORK is INTEGER array, dimension (N)

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgesvx (character fact, character trans, integer n, integernrhs, complex16, dimension( lda, ) a, integer lda, complex16,dimension( ldaf, ) af, integer ldaf, integer, dimension( * ) ipiv,character equed, double precision, dimension( * ) r, double precision,dimension( * ) c, complex16, dimension( ldb, ) b, integer ldb,complex16, dimension( ldx, ) x, integer ldx, double precision rcond,double precision, dimension( * ) ferr, double precision, dimension( * )berr, complex16, dimension( ) work, double precision, dimension( * )rwork, integer info)

ZGESVX computes the solution to system of linear equations A * X = B for GE matrices

Purpose:

ZGESVX uses the LU factorization to compute the solution to a complex
system of linear equations
A * X = B,
where A is an N-by-N 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:

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

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

6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = ’N’) or diag(R) (if TRANS = ’T’ or ’C’) so
that it solves the original system before equilibration.

Parameters

FACT

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

N is INTEGER
The number of linear equations, i.e., 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.

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A. If FACT = ’F’ and EQUED is
not ’N’, then A must have been equilibrated by the scaling
factors in R and/or C. A is not modified if FACT = ’F’ or
’N’, or if FACT = ’E’ and EQUED = ’N’ on exit.

On exit, if EQUED .ne. ’N’, A is scaled as follows:
EQUED = ’R’: A := diag(R) * A
EQUED = ’C’: A := A * diag(C)
EQUED = ’B’: A := diag(R) * A * diag(C).

LDA

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

AF is COMPLEX*16 array, dimension (LDAF,N)
If FACT = ’F’, then AF is an input argument and on entry
contains the factors L and U from the factorization
A = P*L*U as computed by ZGETRF. If EQUED .ne. ’N’, then
AF is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AF is an output argument and on exit
returns the factors L and U from the factorization A = P*L*U
of the original matrix A.

LDAF

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

IPIV

IPIV is INTEGER array, dimension (N)
If FACT = ’F’, then IPIV is an input argument and on entry
contains the pivot indices from the factorization A = P*L*U
as computed by ZGETRF; row i of the matrix was interchanged
with row IPIV(i).

If FACT = ’N’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the original matrix A.

If FACT = ’E’, then IPIV is an output argument and on exit
contains the pivot indices from the factorization A = P*L*U
of the equilibrated matrix A.

EQUED

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit,
if EQUED = ’N’, B is not modified;
if TRANS = ’N’ and EQUED = ’R’ or ’B’, B is overwritten by
diag(R)*B;
if TRANS = ’T’ or ’C’ and EQUED = ’C’ or ’B’, B is
overwritten by diag(C)*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
to the original system of equations. Note that A and B are
modified on exit if EQUED .ne. ’N’, and the solution to the
equilibrated system is inv(diag(C))*X if TRANS = ’N’ and
EQUED = ’C’ or ’B’, or inv(diag(R))*X if TRANS = ’T’ or ’C’
and EQUED = ’R’ or ’B’.

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 (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (MAX(1,2*N))
On exit, RWORK(1) contains the reciprocal pivot growth
factor norm(A)/norm(U). The ’max absolute element’ norm is
used. If RWORK(1) is much less than 1, then the stability
of the LU factorization of the (equilibrated) matrix A
could be poor. This also means that the solution X, condition
estimator RCOND, and forward error bound FERR could be
unreliable. If factorization fails with 0<INFO<=N, then
RWORK(1) contains the reciprocal pivot growth factor for the
leading INFO columns of A.

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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