LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
 All Files Functions Groups
Functions/Subroutines
real
Computational routines
Collaboration diagram for real:

Functions/Subroutines

subroutine sgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
 SGTCON
subroutine sgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
 SGTRFS
subroutine sgttrf (N, DL, D, DU, DU2, IPIV, INFO)
 SGTTRF
subroutine sgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
 SGTTRS
subroutine sgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)
 SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Detailed Description

This is the group of real computational functions for GT matrices

Function/Subroutine Documentation

subroutine sgtcon ( character  NORM,
integer  N,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( * )  DU2,
integer, dimension( * )  IPIV,
real  ANORM,
real  RCOND,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SGTCON

Download SGTCON + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 SGTCON estimates the reciprocal of the condition number of a real
 tridiagonal matrix A using the LU factorization as computed by
 SGTTRF.

 An estimate is obtained for norm(inv(A)), and the reciprocal of the
 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Parameters:
[in]NORM
          NORM is CHARACTER*1
          Specifies whether the 1-norm condition number or the
          infinity-norm condition number is required:
          = '1' or 'O':  1-norm;
          = 'I':         Infinity-norm.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]DL
          DL is REAL array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by SGTTRF.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DU
          DU is REAL array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U.
[in]DU2
          DU2 is REAL array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[in]ANORM
          ANORM is REAL
          If NORM = '1' or 'O', the 1-norm of the original matrix A.
          If NORM = 'I', the infinity-norm of the original matrix A.
[out]RCOND
          RCOND is REAL
          The reciprocal of the condition number of the matrix A,
          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
          estimate of the 1-norm of inv(A) computed in this routine.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]IWORK
          IWORK is INTEGER array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 146 of file sgtcon.f.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine sgtrfs ( character  TRANS,
integer  N,
integer  NRHS,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( * )  DLF,
real, dimension( * )  DF,
real, dimension( * )  DUF,
real, dimension( * )  DU2,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldx, * )  X,
integer  LDX,
real, dimension( * )  FERR,
real, dimension( * )  BERR,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SGTRFS

Download SGTRFS + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 SGTRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is tridiagonal, and provides
 error bounds and backward error estimates for the solution.
Parameters:
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]DL
          DL is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of A.
[in]D
          D is REAL array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is REAL array, dimension (N-1)
          The (n-1) superdiagonal elements of A.
[in]DLF
          DLF is REAL array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by SGTTRF.
[in]DF
          DF is REAL array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DUF
          DUF is REAL array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U.
[in]DU2
          DU2 is REAL array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[in]B
          B is REAL array, dimension (LDB,NRHS)
          The right hand side matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in,out]X
          X is REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SGTTRS.
          On exit, the improved solution matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[out]FERR
          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.
[out]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).
[out]WORK
          WORK is REAL array, dimension (3*N)
[out]IWORK
          IWORK is INTEGER array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Internal Parameters: 
  ITMAX is the maximum number of steps of iterative refinement.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 208 of file sgtrfs.f.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine sgttrf ( integer  N,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( * )  DU2,
integer, dimension( * )  IPIV,
integer  INFO 
)

SGTTRF

Download SGTTRF + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 SGTTRF computes an LU factorization of a real tridiagonal matrix A
 using elimination with partial pivoting and row interchanges.

 The factorization has the form
    A = L * U
 where L is a product of permutation and unit lower bidiagonal
 matrices and U is upper triangular with nonzeros in only the main
 diagonal and first two superdiagonals.
Parameters:
[in]N
          N is INTEGER
          The order of the matrix A.
[in,out]DL
          DL is REAL array, dimension (N-1)
          On entry, DL must contain the (n-1) sub-diagonal elements of
          A.

          On exit, DL is overwritten by the (n-1) multipliers that
          define the matrix L from the LU factorization of A.
[in,out]D
          D is REAL array, dimension (N)
          On entry, D must contain the diagonal elements of A.

          On exit, D is overwritten by the n diagonal elements of the
          upper triangular matrix U from the LU factorization of A.
[in,out]DU
          DU is REAL array, dimension (N-1)
          On entry, DU must contain the (n-1) super-diagonal elements
          of A.

          On exit, DU is overwritten by the (n-1) elements of the first
          super-diagonal of U.
[out]DU2
          DU2 is REAL array, dimension (N-2)
          On exit, DU2 is overwritten by the (n-2) elements of the
          second super-diagonal of U.
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -k, the k-th argument had an illegal value
          > 0:  if INFO = k, U(k,k) is exactly zero. The factorization
                has been completed, but the factor U is exactly
                singular, and division by zero will occur if it is used
                to solve a system of equations.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 125 of file sgttrf.f.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine sgttrs ( character  TRANS,
integer  N,
integer  NRHS,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( * )  DU2,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

SGTTRS

Download SGTTRS + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 SGTTRS solves one of the systems of equations
    A*X = B  or  A**T*X = B,
 with a tridiagonal matrix A using the LU factorization computed
 by SGTTRF.
Parameters:
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T* X = B  (Transpose)
          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The order of the matrix A.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]DL
          DL is REAL array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DU
          DU is REAL array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U.
[in]DU2
          DU2 is REAL array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the matrix of right hand side vectors B.
          On exit, B is overwritten by the solution vectors X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 138 of file sgttrs.f.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine sgtts2 ( integer  ITRANS,
integer  N,
integer  NRHS,
real, dimension( * )  DL,
real, dimension( * )  D,
real, dimension( * )  DU,
real, dimension( * )  DU2,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB 
)

SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.

Download SGTTS2 + dependencies [TGZ] [ZIP] [TXT]
Purpose: 
 SGTTS2 solves one of the systems of equations
    A*X = B  or  A**T*X = B,
 with a tridiagonal matrix A using the LU factorization computed
 by SGTTRF.
Parameters:
[in]ITRANS
          ITRANS is INTEGER
          Specifies the form of the system of equations.
          = 0:  A * X = B  (No transpose)
          = 1:  A**T* X = B  (Transpose)
          = 2:  A**T* X = B  (Conjugate transpose = Transpose)
[in]N
          N is INTEGER
          The order of the matrix A.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]DL
          DL is REAL array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DU
          DU is REAL array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U.
[in]DU2
          DU2 is REAL array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U.
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the matrix of right hand side vectors B.
          On exit, B is overwritten by the solution vectors X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 129 of file sgtts2.f.

Here is the caller graph for this function: