Provided by: liblapack-doc_3.8.0-2_all bug

NAME

       doubleSYsolve

SYNOPSIS

   Functions
       subroutine dsysv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
            DSYSV computes the solution to system of linear equations A * X = B for SY matrices
       subroutine dsysv_aa (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
            DSYSV_AA computes the solution to system of linear equations A * X = B for SY
           matrices
       subroutine dsysv_aa_2stage (UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, WORK,
           LWORK, INFO)
            DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY
           matrices
       subroutine dsysv_rk (UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
            DSYSV_RK computes the solution to system of linear equations A * X = B for SY
           matrices
       subroutine dsysv_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
            DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY
           matrices
       subroutine dsysvx (FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, RCOND,
           FERR, BERR, WORK, LWORK, IWORK, INFO)
            DSYSVX computes the solution to system of linear equations A * X = B for SY matrices
       subroutine dsysvxx (FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, EQUED, S, B, LDB, X, LDX,
           RCOND, RPVGRW, BERR, N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, WORK,
           IWORK, INFO)
           DSYSVXX

Detailed Description

       This is the group of double solve driver functions for SY matrices

Function Documentation

   subroutine dsysv (character UPLO, integer N, integer NRHS, double precision, dimension( lda, *
       ) A, integer LDA, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B,
       integer LDB, double precision, dimension( * ) WORK, integer LWORK, integer INFO)
        DSYSV computes the solution to system of linear equations A * X = B for SY matrices

       Purpose:

            DSYSV computes the solution to a real system of linear equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            The diagonal pivoting method is used to factor A as
               A = U * D * U**T,  if UPLO = 'U', or
               A = L * D * L**T,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and D is symmetric and block diagonal with
            1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
            used to solve the system of equations A * X = B.

       Parameters:
           UPLO

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

           N

                     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 matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     N-by-N upper triangular part of A contains the upper
                     triangular part of the matrix A, and the strictly lower
                     triangular part of A is not referenced.  If UPLO = 'L', the
                     leading N-by-N lower triangular part of A contains the lower
                     triangular part of the matrix A, and the strictly upper
                     triangular part of A is not referenced.

                     On exit, if INFO = 0, the block diagonal matrix D and the
                     multipliers used to obtain the factor U or L from the
                     factorization A = U*D*U**T or A = L*D*L**T as computed by
                     DSYTRF.

           LDA

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D, as
                     determined by DSYTRF.  If IPIV(k) > 0, then rows and columns
                     k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
                     diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
                     then rows and columns k-1 and -IPIV(k) were interchanged and
                     D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
                     IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
                     -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
                     diagonal block.

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= 1, and for best performance
                     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
                     DSYTRF.
                     for LWORK < N, TRS will be done with Level BLAS 2
                     for LWORK >= N, TRS will be done with Level BLAS 3

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular, so the solution could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine dsysv_aa (character UPLO, integer N, integer NRHS, double precision, dimension(
       lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision, dimension( ldb, *
       ) B, integer LDB, double precision, dimension( * ) WORK, integer LWORK, integer INFO)
        DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

       Purpose:

            DSYSV computes the solution to a real system of linear equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            Aasen's algorithm is used to factor A as
               A = U * T * U**T,  if UPLO = 'U', or
               A = L * T * L**T,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is symmetric tridiagonal. The factored
            form of A is then used to solve the system of equations A * X = B.

       Parameters:
           UPLO

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

           N

                     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 matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     N-by-N upper triangular part of A contains the upper
                     triangular part of the matrix A, and the strictly lower
                     triangular part of A is not referenced.  If UPLO = 'L', the
                     leading N-by-N lower triangular part of A contains the lower
                     triangular part of the matrix A, and the strictly upper
                     triangular part of A is not referenced.

                     On exit, if INFO = 0, the tridiagonal matrix T and the
                     multipliers used to obtain the factor U or L from the
                     factorization A = U*T*U**T or A = L*T*L**T as computed by
                     DSYTRF.

           LDA

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
                     the best performance, LWORK >= MAX(1,N*NB), where NB is
                     the optimal blocksize for DSYTRF_AA.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular, so the solution could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine dsysv_aa_2stage (character UPLO, integer N, integer NRHS, double precision,
       dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TB, integer LTB,
       integer, dimension( * ) IPIV, integer, dimension( * ) IPIV2, double precision, dimension(
       ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, integer LWORK, integer
       INFO)
        DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY
       matrices

       Purpose:

            DSYSV_AA_2STAGE computes the solution to a real system of
            linear equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            Aasen's 2-stage algorithm is used to factor A as
               A = U * T * U**T,  if UPLO = 'U', or
               A = L * T * L**T,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is symmetric and band. The matrix T is
            then LU-factored with partial pivoting. The factored form of A
            is then used to solve the system of equations A * X = B.

            This is the blocked version of the algorithm, calling Level 3 BLAS.

       Parameters:
           UPLO

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

           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 matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     N-by-N upper triangular part of A contains the upper
                     triangular part of the matrix A, and the strictly lower
                     triangular part of A is not referenced.  If UPLO = 'L', the
                     leading N-by-N lower triangular part of A contains the lower
                     triangular part of the matrix A, and the strictly upper
                     triangular part of A is not referenced.

                     On exit, L is stored below (or above) the subdiaonal blocks,
                     when UPLO  is 'L' (or 'U').

           LDA

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

           TB

                     TB is DOUBLE PRECISION array, dimension (LTB)
                     On exit, details of the LU factorization of the band matrix.

           LTB

                     The size of the array TB. LTB >= 4*N, internally
                     used to select NB such that LTB >= (3*NB+1)*N.

                     If LTB = -1, then a workspace query is assumed; the
                     routine only calculates the optimal size of LTB,
                     returns this value as the first entry of TB, and
                     no error message related to LTB is issued by XERBLA.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           IPIV2

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of T were interchanged with the
                     row and column IPIV(k).

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION workspace of size LWORK

           LWORK

                     The size of WORK. LWORK >= N, internally used to select NB
                     such that LWORK >= N*NB.

                     If LWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal size of the WORK array,
                     returns this value as the first entry of the WORK array, and
                     no error message related to LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  if INFO = i, band LU factorization failed on i-th column

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine dsysv_rk (character UPLO, integer N, integer NRHS, double precision, dimension(
       lda, * ) A, integer LDA, double precision, dimension( * ) E, integer, dimension( * ) IPIV,
       double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * )
       WORK, integer LWORK, integer INFO)
        DSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices

       Purpose:

            DSYSV_RK computes the solution to a real system of linear
            equations A * X = B, where A is an N-by-N symmetric matrix
            and X and B are N-by-NRHS matrices.

            The bounded Bunch-Kaufman (rook) diagonal pivoting method is used
            to factor A as
               A = P*U*D*(U**T)*(P**T),  if UPLO = 'U', or
               A = P*L*D*(L**T)*(P**T),  if UPLO = 'L',
            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, and D is symmetric and block
            diagonal with 1-by-1 and 2-by-2 diagonal blocks.

            DSYTRF_RK is called to compute the factorization of a real
            symmetric matrix.  The factored form of A is then used to solve
            the system of equations A * X = B by calling BLAS3 routine DSYTRS_3.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     symmetric matrix A is stored:
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

                     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 matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.
                       If UPLO = 'U': the leading N-by-N upper triangular part
                       of A contains the upper triangular part of the matrix A,
                       and the strictly lower triangular part of A is not
                       referenced.

                       If UPLO = 'L': the leading N-by-N lower triangular part
                       of A contains the lower triangular part of the matrix A,
                       and the strictly upper triangular part of A is not
                       referenced.

                     On exit, if INFO = 0, diagonal of the block diagonal
                     matrix D and factors U or L  as computed by DSYTRF_RK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     For more info see the description of DSYTRF_RK routine.

           LDA

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

           E

                     E is DOUBLE PRECISION array, dimension (N)
                     On exit, contains the output computed by the factorization
                     routine DSYTRF_RK, i.e. the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is set to 0 in both
                     UPLO = 'U' or UPLO = 'L' cases.

                     For more info see the description of DSYTRF_RK routine.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D,
                     as determined by DSYTRF_RK.

                     For more info see the description of DSYTRF_RK routine.

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension ( MAX(1,LWORK) ).
                     Work array used in the factorization stage.
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= 1. For best performance
                     of factorization stage LWORK >= max(1,N*NB), where NB is
                     the optimal blocksize for DSYTRF_RK.

                     If LWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the WORK
                     array for factorization stage, returns this value as
                     the first entry of the WORK array, and no error message
                     related to LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit

                     < 0: If INFO = -k, the k-th argument had an illegal value

                     > 0: If INFO = k, the matrix A is singular, because:
                            If UPLO = 'U': column k in the upper
                            triangular part of A contains all zeros.
                            If UPLO = 'L': column k in the lower
                            triangular part of A contains all zeros.

                          Therefore D(k,k) is exactly zero, and superdiagonal
                          elements of column k of U (or subdiagonal elements of
                          column k of L ) are all zeros. The factorization has
                          been completed, but the block diagonal matrix D is
                          exactly singular, and division by zero will occur if
                          it is used to solve a system of equations.

                          NOTE: INFO only stores the first occurrence of
                          a singularity, any subsequent occurrence of singularity
                          is not stored in INFO even though the factorization
                          always completes.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:

             December 2016,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

             September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                             School of Mathematics,
                             University of Manchester

   subroutine dsysv_rook (character UPLO, integer N, integer NRHS, double precision, dimension(
       lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision, dimension( ldb, *
       ) B, integer LDB, double precision, dimension( * ) WORK, integer LWORK, integer INFO)
        DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices

       Purpose:

            DSYSV_ROOK computes the solution to a real system of linear
            equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            The diagonal pivoting method is used to factor A as
               A = U * D * U**T,  if UPLO = 'U', or
               A = L * D * L**T,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and D is symmetric and block diagonal with
            1-by-1 and 2-by-2 diagonal blocks.

            DSYTRF_ROOK is called to compute the factorization of a real
            symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
            pivoting method.

            The factored form of A is then used to solve the system
            of equations A * X = B by calling DSYTRS_ROOK.

       Parameters:
           UPLO

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

           N

                     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 matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     N-by-N upper triangular part of A contains the upper
                     triangular part of the matrix A, and the strictly lower
                     triangular part of A is not referenced.  If UPLO = 'L', the
                     leading N-by-N lower triangular part of A contains the lower
                     triangular part of the matrix A, and the strictly upper
                     triangular part of A is not referenced.

                     On exit, if INFO = 0, the block diagonal matrix D and the
                     multipliers used to obtain the factor U or L from the
                     factorization A = U*D*U**T or A = L*D*L**T as computed by
                     DSYTRF_ROOK.

           LDA

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D,
                     as determined by DSYTRF_ROOK.

                     If UPLO = 'U':
                          If IPIV(k) > 0, then rows and columns k and IPIV(k)
                          were interchanged and D(k,k) is a 1-by-1 diagonal block.

                          If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
                          columns k and -IPIV(k) were interchanged and rows and
                          columns k-1 and -IPIV(k-1) were inerchaged,
                          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

                     If UPLO = 'L':
                          If IPIV(k) > 0, then rows and columns k and IPIV(k)
                          were interchanged and D(k,k) is a 1-by-1 diagonal block.

                          If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
                          columns k and -IPIV(k) were interchanged and rows and
                          columns k+1 and -IPIV(k+1) were inerchaged,
                          D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= 1, and for best performance
                     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
                     DSYTRF_ROOK.

                     TRS will be done with Level 2 BLAS

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular, so the solution could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           April 2012

       Contributors:

              April 2012, Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

             September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                             School of Mathematics,
                             University of Manchester

   subroutine dsysvx (character FACT, character UPLO, integer N, integer NRHS, double precision,
       dimension( lda, * ) A, integer LDA, double precision, dimension( ldaf, * ) AF, integer
       LDAF, integer, dimension( * ) IPIV, 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 LWORK, integer, dimension( * ) IWORK, integer INFO)
        DSYSVX computes the solution to system of linear equations A * X = B for SY matrices

       Purpose:

            DSYSVX uses the diagonal pivoting factorization to compute the
            solution to a real system of linear equations A * X = B,
            where A is an N-by-N symmetric 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 diagonal pivoting method is used to factor A.
               The form of the factorization is
                  A = U * D * U**T,  if UPLO = 'U', or
                  A = L * D * L**T,  if UPLO = 'L',
               where U (or L) is a product of permutation and unit upper (lower)
               triangular matrices, and D is symmetric and block diagonal with
               1-by-1 and 2-by-2 diagonal blocks.

            2. If some D(i,i)=0, so that D 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.

            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, AF and IPIV contain the factored form of
                             A.  AF and IPIV will not be modified.
                     = 'N':  The matrix A will be copied to AF and factored.

           UPLO

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

           N

                     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

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
                     upper triangular part of A contains the upper triangular part
                     of the matrix A, and the strictly lower triangular part of A
                     is not referenced.  If UPLO = 'L', the leading N-by-N lower
                     triangular part of A contains the lower triangular part of
                     the matrix A, and the strictly upper triangular part of A is
                     not referenced.

           LDA

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

           AF

                     AF is DOUBLE PRECISION array, dimension (LDAF,N)
                     If FACT = 'F', then AF is an input argument and on entry
                     contains the block diagonal matrix D and the multipliers used
                     to obtain the factor U or L from the factorization
                     A = U*D*U**T or A = L*D*L**T as computed by DSYTRF.

                     If FACT = 'N', then AF is an output argument and on exit
                     returns the block diagonal matrix D and the multipliers used
                     to obtain the factor U or L from the factorization
                     A = U*D*U**T or A = L*D*L**T.

           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 details of the interchanges and the block structure
                     of D, as determined by DSYTRF.
                     If IPIV(k) > 0, then rows and columns k and IPIV(k) were
                     interchanged and D(k,k) is a 1-by-1 diagonal block.
                     If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
                     columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
                     is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
                     IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
                     interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

                     If FACT = 'N', then IPIV is an output argument and on exit
                     contains details of the interchanges and the block structure
                     of D, as determined by DSYTRF.

           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 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 estimate of 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 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,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= max(1,3*N), and for best
                     performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where
                     NB is the optimal blocksize for DSYTRF.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           IWORK

                     IWORK is INTEGER 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:  D(i,i) is exactly zero.  The factorization
                                  has been completed but the factor D is exactly
                                  singular, so the solution and error bounds could
                                  not be computed. RCOND = 0 is returned.
                           = N+1: D 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.

       Date:
           April 2012

   subroutine dsysvxx (character FACT, character UPLO, integer N, integer NRHS, double precision,
       dimension( lda, * ) A, integer LDA, double precision, dimension( ldaf, * ) AF, integer
       LDAF, integer, dimension( * ) IPIV, character EQUED, double precision, dimension( * ) S,
       double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, *
       ) X, integer LDX, double precision RCOND, double precision RPVGRW, double precision,
       dimension( * ) BERR, integer N_ERR_BNDS, double precision, dimension( nrhs, * )
       ERR_BNDS_NORM, double precision, dimension( nrhs, * ) ERR_BNDS_COMP, integer NPARAMS,
       double precision, dimension( * ) PARAMS, double precision, dimension( * ) WORK, integer,
       dimension( * ) IWORK, integer INFO)
       DSYSVXX

       Purpose:

               DSYSVXX uses the diagonal pivoting factorization to compute the
               solution to a double precision system of linear equations A * X = B, where A
               is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

               If requested, both normwise and maximum componentwise error bounds
               are returned. DSYSVXX will return a solution with a tiny
               guaranteed error (O(eps) where eps is the working machine
               precision) unless the matrix is very ill-conditioned, in which
               case a warning is returned. Relevant condition numbers also are
               calculated and returned.

               DSYSVXX accepts user-provided factorizations and equilibration
               factors; see the definitions of the FACT and EQUED options.
               Solving with refinement and using a factorization from a previous
               DSYSVXX call will also produce a solution with either O(eps)
               errors or warnings, but we cannot make that claim for general
               user-provided factorizations and equilibration factors if they
               differ from what DSYSVXX would itself produce.

       Description:

               The following steps are performed:

               1. If FACT = 'E', double precision 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 LU decomposition is used to factor
               the matrix A (after equilibration if FACT = 'E') as

                  A = U * D * U**T,  if UPLO = 'U', or
                  A = L * D * L**T,  if UPLO = 'L',

               where U (or L) is a product of permutation and unit upper (lower)
               triangular matrices, and D is symmetric and block diagonal with
               1-by-1 and 2-by-2 diagonal blocks.

               3. If some D(i,i)=0, so that D 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 (see
               argument RCOND).  If the reciprocal of the condition number is
               less than machine precision, 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. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
               the routine will use iterative refinement to try to get a small
               error and error bounds.  Refinement calculates the residual to at
               least twice the working precision.

               6. If equilibration was used, the matrix X is premultiplied by
               diag(R) so that it solves the original system before
               equilibration.

                Some optional parameters are bundled in the PARAMS array.  These
                settings determine how refinement is performed, but often the
                defaults are acceptable.  If the defaults are acceptable, users
                can pass NPARAMS = 0 which prevents the source code from accessing
                the PARAMS argument.

       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 S.
                          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.

           UPLO

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

           N

                     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

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                The symmetric matrix A.  If UPLO = 'U', the leading N-by-N
                upper triangular part of A contains the upper triangular
                part of the matrix A, and the strictly lower triangular
                part of A is not referenced.  If UPLO = 'L', the leading
                N-by-N lower triangular part of A contains the lower
                triangular part of the matrix A, and the strictly upper
                triangular part of A is not referenced.

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

           LDA

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

           AF

                     AF is DOUBLE PRECISION array, dimension (LDAF,N)
                If FACT = 'F', then AF is an input argument and on entry
                contains the block diagonal matrix D and the multipliers
                used to obtain the factor U or L from the factorization A =
                U*D*U**T or A = L*D*L**T as computed by DSYTRF.

                If FACT = 'N', then AF is an output argument and on exit
                returns the block diagonal matrix D and the multipliers
                used to obtain the factor U or L from the factorization A =
                U*D*U**T or A = L*D*L**T.

           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 details of the interchanges and the block
                structure of D, as determined by DSYTRF.  If IPIV(k) > 0,
                then rows and columns k and IPIV(k) were interchanged and
                D(k,k) is a 1-by-1 diagonal block.  If UPLO = 'U' and
                IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
                -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2
                diagonal block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0,
                then rows and columns k+1 and -IPIV(k) were interchanged
                and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

                If FACT = 'N', then IPIV is an output argument and on exit
                contains details of the interchanges and the block
                structure of D, as determined by DSYTRF.

           EQUED

                     EQUED is CHARACTER*1
                Specifies the form of equilibration that was done.
                  = 'N':  No equilibration (always true if FACT = 'N').
                  = 'Y':  Both row and column equilibration, 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

                     S is DOUBLE PRECISION array, dimension (N)
                The scale factors for A.  If EQUED = 'Y', A is multiplied on
                the left and right by diag(S).  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.  If S is output, each
                element of S is a power of the radix. If S is input, each element
                of S should be a power of the radix to ensure a reliable solution
                and error estimates. Scaling by powers of the radix does not cause
                rounding errors unless the result underflows or overflows.
                Rounding errors during scaling lead to refining with a matrix that
                is not equivalent to the input matrix, producing error estimates
                that may not be reliable.

           B

                     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

                     X is DOUBLE PRECISION array, dimension (LDX,NRHS)
                If INFO = 0, 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(S))*X.

           LDX

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

           RCOND

                     RCOND is DOUBLE PRECISION
                Reciprocal scaled condition number.  This is an estimate of the
                reciprocal Skeel condition number of the matrix A after
                equilibration (if done).  If this is less than the machine
                precision (in particular, if it is zero), the matrix is singular
                to working precision.  Note that the error may still be small even
                if this number is very small and the matrix appears ill-
                conditioned.

           RPVGRW

                     RPVGRW is DOUBLE PRECISION
                Reciprocal pivot growth.  On exit, this contains the reciprocal
                pivot growth factor norm(A)/norm(U). The "max absolute element"
                norm is used.  If this 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, estimated condition numbers,
                and error bounds could be unreliable. If factorization fails with
                0<INFO<=N, then this contains the reciprocal pivot growth factor
                for the leading INFO columns of A.

           BERR

                     BERR is DOUBLE PRECISION array, dimension (NRHS)
                Componentwise relative backward error.  This is 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).

           N_ERR_BNDS

                     N_ERR_BNDS is INTEGER
                Number of error bounds to return for each right hand side
                and each type (normwise or componentwise).  See ERR_BNDS_NORM and
                ERR_BNDS_COMP below.

           ERR_BNDS_NORM

                     ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                normwise relative error, which is defined as follows:

                Normwise relative error in the ith solution vector:
                        max_j (abs(XTRUE(j,i) - X(j,i)))
                       ------------------------------
                             max_j abs(X(j,i))

                The array is indexed by the type of error information as described
                below. There currently are up to three pieces of information
                returned.

                The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_NORM(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * dlamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * dlamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated normwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * dlamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*A, where S scales each row by a power of the
                         radix so all absolute row sums of Z are approximately 1.

                See Lapack Working Note 165 for further details and extra
                cautions.

           ERR_BNDS_COMP

                     ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                componentwise relative error, which is defined as follows:

                Componentwise relative error in the ith solution vector:
                               abs(XTRUE(j,i) - X(j,i))
                        max_j ----------------------
                                    abs(X(j,i))

                The array is indexed by the right-hand side i (on which the
                componentwise relative error depends), and the type of error
                information as described below. There currently are up to three
                pieces of information returned for each right-hand side. If
                componentwise accuracy is not requested (PARAMS(3) = 0.0), then
                ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
                the first (:,N_ERR_BNDS) entries are returned.

                The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_COMP(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * dlamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * dlamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated componentwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * dlamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*(A*diag(x)), where x is the solution for the
                         current right-hand side and S scales each row of
                         A*diag(x) by a power of the radix so all absolute row
                         sums of Z are approximately 1.

                See Lapack Working Note 165 for further details and extra
                cautions.

           NPARAMS

                     NPARAMS is INTEGER
                Specifies the number of parameters set in PARAMS.  If .LE. 0, the
                PARAMS array is never referenced and default values are used.

           PARAMS

                     PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
                Specifies algorithm parameters.  If an entry is .LT. 0.0, then
                that entry will be filled with default value used for that
                parameter.  Only positions up to NPARAMS are accessed; defaults
                are used for higher-numbered parameters.

                  PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
                       refinement or not.
                    Default: 1.0D+0
                       = 0.0 : No refinement is performed, and no error bounds are
                               computed.
                       = 1.0 : Use the extra-precise refinement algorithm.
                         (other values are reserved for future use)

                  PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
                       computations allowed for refinement.
                    Default: 10
                    Aggressive: Set to 100 to permit convergence using approximate
                                factorizations or factorizations other than LU. If
                                the factorization uses a technique other than
                                Gaussian elimination, the guarantees in
                                err_bnds_norm and err_bnds_comp may no longer be
                                trustworthy.

                  PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
                       will attempt to find a solution with small componentwise
                       relative error in the double-precision algorithm.  Positive
                       is true, 0.0 is false.
                    Default: 1.0 (attempt componentwise convergence)

           WORK

                     WORK is DOUBLE PRECISION array, dimension (4*N)

           IWORK

                     IWORK is INTEGER array, dimension (N)

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit. The solution to every right-hand side is
                    guaranteed.
                  < 0:  If INFO = -i, the i-th argument had an illegal value
                  > 0 and <= N:  U(INFO,INFO) 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+J: The solution corresponding to the Jth right-hand side is
                    not guaranteed. The solutions corresponding to other right-
                    hand sides K with K > J may not be guaranteed as well, but
                    only the first such right-hand side is reported. If a small
                    componentwise error is not requested (PARAMS(3) = 0.0) then
                    the Jth right-hand side is the first with a normwise error
                    bound that is not guaranteed (the smallest J such
                    that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
                    the Jth right-hand side is the first with either a normwise or
                    componentwise error bound that is not guaranteed (the smallest
                    J such that either ERR_BNDS_NORM(J,1) = 0.0 or
                    ERR_BNDS_COMP(J,1) = 0.0). See the definition of
                    ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
                    about all of the right-hand sides check ERR_BNDS_NORM or
                    ERR_BNDS_COMP.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

Author

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