CPTRFS improves the computed solution to a system of linear


 equations when the coefficient matrix is Hermitian positive definite


 and tridiagonal, and provides error bounds and backward error


 estimates for the solution.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the superdiagonal or the subdiagonal of the


          tridiagonal matrix A is stored and the form of the


          factorization:


          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;


          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.


          (The two forms are equivalent if A is real.)

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.

D

          D is REAL array, dimension (N)


          The n real diagonal elements of the tridiagonal matrix A.

E

          E is COMPLEX array, dimension (N-1)


          The (n-1) off-diagonal elements of the tridiagonal matrix A


          (see UPLO).

DF

          DF is REAL array, dimension (N)


          The n diagonal elements of the diagonal matrix D from


          the factorization computed by CPTTRF.

EF

          EF is COMPLEX array, dimension (N-1)


          The (n-1) off-diagonal elements of the unit bidiagonal


          factor U or L from the factorization computed by CPTTRF


          (see UPLO).

B

          B is COMPLEX array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by CPTTRS.


          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER


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

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

  ITMAX is the maximum number of steps of iterative refinement.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 DPTRFS improves the computed solution to a system of linear


 equations when the coefficient matrix is symmetric positive definite


 and tridiagonal, and provides error bounds and backward error


 estimates for the solution.

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.

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)


          The n diagonal elements of the diagonal matrix D from the


          factorization computed by DPTTRF.

EF

          EF is DOUBLE PRECISION array, dimension (N-1)


          The (n-1) subdiagonal elements of the unit bidiagonal factor


          L from the factorization computed by DPTTRF.

B

          B is DOUBLE PRECISION array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by DPTTRS.


          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER


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

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

  ITMAX is the maximum number of steps of iterative refinement.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 SPTRFS improves the computed solution to a system of linear


 equations when the coefficient matrix is symmetric positive definite


 and tridiagonal, and provides error bounds and backward error


 estimates for the solution.

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.

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)


          The n diagonal elements of the diagonal matrix D from the


          factorization computed by SPTTRF.

EF

          EF is REAL array, dimension (N-1)


          The (n-1) subdiagonal elements of the unit bidiagonal factor


          L from the factorization computed by SPTTRF.

B

          B is REAL array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by SPTTRS.


          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER


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

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

  ITMAX is the maximum number of steps of iterative refinement.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 ZPTRFS improves the computed solution to a system of linear


 equations when the coefficient matrix is Hermitian positive definite


 and tridiagonal, and provides error bounds and backward error


 estimates for the solution.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the superdiagonal or the subdiagonal of the


          tridiagonal matrix A is stored and the form of the


          factorization:


          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;


          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.


          (The two forms are equivalent if A is real.)

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.

D

          D is DOUBLE PRECISION array, dimension (N)


          The n real diagonal elements of the tridiagonal matrix A.

E

          E is COMPLEX*16 array, dimension (N-1)


          The (n-1) off-diagonal elements of the tridiagonal matrix A


          (see UPLO).

DF

          DF is DOUBLE PRECISION array, dimension (N)


          The n diagonal elements of the diagonal matrix D from


          the factorization computed by ZPTTRF.

EF

          EF is COMPLEX*16 array, dimension (N-1)


          The (n-1) off-diagonal elements of the unit bidiagonal


          factor U or L from the factorization computed by ZPTTRF


          (see UPLO).

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by ZPTTRS.


          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER


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

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

  ITMAX is the maximum number of steps of iterative refinement.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.