Man page - pbsvx(3)

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Manual

pbsvx

NAME

pbsvx - pbsvx: factor and solve, expert

SYNOPSIS

Functions

subroutine cpbsvx (fact, uplo, n, kd, nrhs, ab, ldab, afb, ldafb, equed, s, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
CPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine dpbsvx (fact, uplo, n, kd, nrhs, ab, ldab, afb, ldafb, equed, s, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info)
DPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine spbsvx (fact, uplo, n, kd, nrhs, ab, ldab, afb, ldafb, equed, s, b, ldb, x, ldx, rcond, ferr, berr, work, iwork, info)
SPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine zpbsvx (fact, uplo, n, kd, nrhs, ab, ldab, afb, ldafb, equed, s, b, ldb, x, ldx, rcond, ferr, berr, work, rwork, info)
ZPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices

Detailed Description

Function Documentation

subroutine cpbsvx (character fact, character uplo, integer n, integer kd,integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex,dimension( ldafb, * ) afb, integer ldafb, character equed, real,dimension( * ) s, 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)

CPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

CPBSVX uses the Cholesky factorization A = U**H*U or A = L*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 band 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:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * 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(S)*A*diag(S) and B by diag(S)*B.

2. If FACT = ’N’ or ’E’, the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = ’E’) as
A = U**H * U, if UPLO = ’U’, or
A = L * L**H, if UPLO = ’L’,
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.

3. 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.

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(S) 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, AFB contains the factored form of A.
If EQUED = ’Y’, the matrix A has been equilibrated
with scaling factors given by S. AB and AFB will not
be modified.
= ’N’: The matrix A will be copied to AFB and factored.
= ’E’: The matrix A will be equilibrated if necessary, then
copied to AFB and factored.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 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.

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array, except
if FACT = ’F’ and EQUED = ’Y’, then A must contain the
equilibrated matrix diag(S)*A*diag(S). The j-th column of A
is stored in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
See below for further details.

On exit, if FACT = ’E’ and EQUED = ’Y’, A is overwritten by
diag(S)*A*diag(S).

LDAB

LDAB is INTEGER
The leading dimension of the array A. LDAB >= KD+1.

AFB

AFB is COMPLEX array, dimension (LDAFB,N)
If FACT = ’F’, then AFB is an input argument and on entry
contains the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H of the band matrix
A, in the same storage format as A (see AB). If EQUED = ’Y’,
then AFB is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H.

If FACT = ’E’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H of the equilibrated
matrix A (see the description of A for the form of the
equilibrated matrix).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

EQUED

EQUED is CHARACTER*1
Specifies the form of equilibration that was done.
= ’N’: No equilibration (always true if FACT = ’N’).
= ’Y’: Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
EQUED is an input argument if FACT = ’F’; otherwise, it is an
output argument.

S is REAL array, dimension (N)
The scale factors for A; not accessed if EQUED = ’N’. S is
an input argument if FACT = ’F’; otherwise, S is an output
argument. If FACT = ’F’ and EQUED = ’Y’, each element of S
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 EQUED = ’Y’,
B is overwritten by diag(S) * 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 if EQUED = ’Y’,
A and B are modified on exit, and the solution to the
equilibrated system is inv(diag(S))*X.

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 (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.

Further Details:

The band storage scheme is illustrated by the following example, when
N = 6, KD = 2, and UPLO = ’U’:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13
a22 a23 a24
a33 a34 a35
a44 a45 a46
a55 a56
(aij=conjg(aji)) a66

Band storage of the upper triangle of A:

* * a13 a24 a35 a46
* a12 a23 a34 a45 a56
a11 a22 a33 a44 a55 a66

Similarly, if UPLO = ’L’ the format of A is as follows:

a11 a22 a33 a44 a55 a66
a21 a32 a43 a54 a65 *
a31 a42 a53 a64 * *

Array elements marked * are not used by the routine.

subroutine dpbsvx (character fact, character uplo, integer n, integer kd,integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( ldafb, * ) afb, integer ldafb, characterequed, double precision, dimension( * ) s, 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, dimension( * ) iwork, integer info)

DPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

DPBSVX uses the Cholesky factorization A = U**T*U or A = L*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 band 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:

2. If FACT = ’N’ or ’E’, the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = ’E’) as
A = U**T * U, if UPLO = ’U’, or
A = L * L**T, if UPLO = ’L’,
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.

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(S) so that it solves the original system before
equilibration.

Parameters

FACT

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 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.

AB is DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array, except
if FACT = ’F’ and EQUED = ’Y’, then A must contain the
equilibrated matrix diag(S)*A*diag(S). The j-th column of A
is stored in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
See below for further details.

On exit, if FACT = ’E’ and EQUED = ’Y’, A is overwritten by
diag(S)*A*diag(S).

LDAB

LDAB is INTEGER
The leading dimension of the array A. LDAB >= KD+1.

AFB

AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
If FACT = ’F’, then AFB is an input argument and on entry
contains the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the band matrix
A, in the same storage format as A (see AB). If EQUED = ’Y’,
then AFB is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.

If FACT = ’E’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the equilibrated
matrix A (see the description of A for the form of the
equilibrated matrix).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

EQUED

S is DOUBLE PRECISION array, dimension (N)
The scale factors for A; not accessed if EQUED = ’N’. S is
an input argument if FACT = ’F’; otherwise, S is an output
argument. If FACT = ’F’ and EQUED = ’Y’, each element of S
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 EQUED = ’Y’,
B is overwritten by diag(S) * 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 if EQUED = ’Y’,
A and B are modified on exit, and the solution to the
equilibrated system is inv(diag(S))*X.

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 (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The band storage scheme is illustrated by the following example, when
N = 6, KD = 2, and UPLO = ’U’:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13
a22 a23 a24
a33 a34 a35
a44 a45 a46
a55 a56
(aij=conjg(aji)) a66

Band storage of the upper triangle of A:

* * a13 a24 a35 a46
* a12 a23 a34 a45 a56
a11 a22 a33 a44 a55 a66

Similarly, if UPLO = ’L’ the format of A is as follows:

a11 a22 a33 a44 a55 a66
a21 a32 a43 a54 a65 *
a31 a42 a53 a64 * *

Array elements marked * are not used by the routine.

subroutine spbsvx (character fact, character uplo, integer n, integer kd,integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real,dimension( ldafb, * ) afb, integer ldafb, character equed, real,dimension( * ) s, 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)

SPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

SPBSVX uses the Cholesky factorization A = U**T*U or A = L*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 band 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(S) so that it solves the original system before
equilibration.

Parameters

FACT

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 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.

AB is REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array, except
if FACT = ’F’ and EQUED = ’Y’, then A must contain the
equilibrated matrix diag(S)*A*diag(S). The j-th column of A
is stored in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
See below for further details.

On exit, if FACT = ’E’ and EQUED = ’Y’, A is overwritten by
diag(S)*A*diag(S).

LDAB

LDAB is INTEGER
The leading dimension of the array A. LDAB >= KD+1.

AFB

AFB is REAL array, dimension (LDAFB,N)
If FACT = ’F’, then AFB is an input argument and on entry
contains the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the band matrix
A, in the same storage format as A (see AB). If EQUED = ’Y’,
then AFB is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

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 EQUED = ’Y’,
B is overwritten by diag(S) * 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 if EQUED = ’Y’,
A and B are modified on exit, and the solution to the
equilibrated system is inv(diag(S))*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 (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The band storage scheme is illustrated by the following example, when
N = 6, KD = 2, and UPLO = ’U’:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13
a22 a23 a24
a33 a34 a35
a44 a45 a46
a55 a56
(aij=conjg(aji)) a66

Band storage of the upper triangle of A:

* * a13 a24 a35 a46
* a12 a23 a34 a45 a56
a11 a22 a33 a44 a55 a66

Similarly, if UPLO = ’L’ the format of A is as follows:

a11 a22 a33 a44 a55 a66
a21 a32 a43 a54 a65 *
a31 a42 a53 a64 * *

Array elements marked * are not used by the routine.

subroutine zpbsvx (character fact, character uplo, integer n, integer kd,integer nrhs, complex16, dimension( ldab, ) ab, integer ldab,complex16, dimension( ldafb, ) afb, integer ldafb, character equed,double precision, dimension( * ) s, complex16, dimension( ldb, ) b,integer ldb, complex16, dimension( ldx, ) x, integer ldx, doubleprecision rcond, double precision, dimension( * ) ferr, doubleprecision, dimension( * ) berr, complex16, dimension( ) work, doubleprecision, dimension( * ) rwork, integer info)

ZPBSVX computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

ZPBSVX uses the Cholesky factorization A = U**H*U or A = L*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 band 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(S) so that it solves the original system before
equilibration.

Parameters

FACT

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ’U’,
or the number of subdiagonals if UPLO = ’L’. KD >= 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.

AB is COMPLEX*16 array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array, except
if FACT = ’F’ and EQUED = ’Y’, then A must contain the
equilibrated matrix diag(S)*A*diag(S). The j-th column of A
is stored in the j-th column of the array AB as follows:
if UPLO = ’U’, AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD).
See below for further details.

On exit, if FACT = ’E’ and EQUED = ’Y’, A is overwritten by
diag(S)*A*diag(S).

LDAB

LDAB is INTEGER
The leading dimension of the array A. LDAB >= KD+1.

AFB

AFB is COMPLEX*16 array, dimension (LDAFB,N)
If FACT = ’F’, then AFB is an input argument and on entry
contains the triangular factor U or L from the Cholesky
factorization A = U**H *U or A = L*L**H of the band matrix
A, in the same storage format as A (see AB). If EQUED = ’Y’,
then AFB is the factored form of the equilibrated matrix A.

If FACT = ’N’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**H *U or A = L*L**H.

If FACT = ’E’, then AFB is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**H *U or A = L*L**H of the equilibrated
matrix A (see the description of A for the form of the
equilibrated matrix).

LDAFB

LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.

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 EQUED = ’Y’,
B is overwritten by diag(S) * 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 if EQUED = ’Y’,
A and B are modified on exit, and the solution to the
equilibrated system is inv(diag(S))*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 (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The band storage scheme is illustrated by the following example, when
N = 6, KD = 2, and UPLO = ’U’:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13
a22 a23 a24
a33 a34 a35
a44 a45 a46
a55 a56
(aij=conjg(aji)) a66

Band storage of the upper triangle of A:

* * a13 a24 a35 a46
* a12 a23 a34 a45 a56
a11 a22 a33 a44 a55 a66

Similarly, if UPLO = ’L’ the format of A is as follows:

a11 a22 a33 a44 a55 a66
a21 a32 a43 a54 a65 *
a31 a42 a53 a64 * *

Array elements marked * are not used by the routine.

Author

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