ptsvx(3)

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

    !>          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

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

    E

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

    DF

    !>          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

    !>          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

    !>          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

    !>          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.
    !>
    !> 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 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

    !>          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

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

    E

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

    DF

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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 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.
    !>
    !> 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 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

    !>          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

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

    E

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

    DF

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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 REAL array, dimension (2*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 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.
    !>
    !> 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

    !>          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

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

    E

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

    DF

    !>          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

    !>          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

    !>          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

    !>          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

    !>          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 COMPLEX*16 array, dimension (N)
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION 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.

Author

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