gtrfs

sgtrfs

Functions

void sgtrfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict DL,
    const f32*  restrict D,
    const f32*  restrict DU,
    const f32*  restrict DLF,
    const f32*  restrict DF,
    const f32*  restrict DUF,
    const f32*  restrict DU2,
    const INT*  restrict ipiv,
    const f32*  restrict B,
    const INT            ldb,
          f32*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void sgtrfs(const char *trans, const INT n, const INT nrhs, const f32 *restrict DL, const f32 *restrict D, const f32 *restrict DU, const f32 *restrict DLF, const f32 *restrict DF, const f32 *restrict DUF, const f32 *restrict DU2, const INT *restrict ipiv, const f32 *restrict B, const INT ldb, f32 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, f32 *restrict work, INT *restrict iwork, INT *info)

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

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

The order of the matrix A. n>=0.

in

nrhs

The number of right hand sides. nrhs>=0.

in

DL

Array of dimension (n-1). The (n-1) subdiagonal elements of A.

in

D

Array of dimension (n). The diagonal elements of A.

in

DU

Array of dimension (n-1). The (n-1) superdiagonal elements of A.

in

DLF

Array of dimension (n-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.

in

DF

Array of dimension (n). The n diagonal elements of U.

in

DUF

Array of dimension (n-1). The (n-1) elements of the first superdiagonal of U.

in

DU2

Array of dimension (n-2). The (n-2) elements of the second superdiagonal of U.

in

ipiv

Array of dimension (n). The pivot indices.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

The leading dimension of B. ldb>=max(1,n).

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by SGTTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension (nrhs). The estimated forward error bound for each solution vector.

out

berr

Array of dimension (nrhs). The componentwise relative backward error of each solution.

out

work

Workspace array of dimension (3*n).

out

iwork

Integer workspace array of dimension (n).

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

dgtrfs

Functions

void dgtrfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict DL,
    const f64*  restrict D,
    const f64*  restrict DU,
    const f64*  restrict DLF,
    const f64*  restrict DF,
    const f64*  restrict DUF,
    const f64*  restrict DU2,
    const INT*  restrict ipiv,
    const f64*  restrict B,
    const INT            ldb,
          f64*  restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);

void dgtrfs(const char *trans, const INT n, const INT nrhs, const f64 *restrict DL, const f64 *restrict D, const f64 *restrict DU, const f64 *restrict DLF, const f64 *restrict DF, const f64 *restrict DUF, const f64 *restrict DU2, const INT *restrict ipiv, const f64 *restrict B, const INT ldb, f64 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, f64 *restrict work, INT *restrict iwork, INT *info)

DGTRFS 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

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

The order of the matrix A. n>=0.

in

nrhs

The number of right hand sides. nrhs>=0.

in

DL

Array of dimension (n-1). The (n-1) subdiagonal elements of A.

in

D

Array of dimension (n). The diagonal elements of A.

in

DU

Array of dimension (n-1). The (n-1) superdiagonal elements of A.

in

DLF

Array of dimension (n-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.

in

DF

Array of dimension (n). The n diagonal elements of U.

in

DUF

Array of dimension (n-1). The (n-1) elements of the first superdiagonal of U.

in

DU2

Array of dimension (n-2). The (n-2) elements of the second superdiagonal of U.

in

ipiv

Array of dimension (n). The pivot indices.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

The leading dimension of B. ldb>=max(1,n).

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by DGTTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension (nrhs). The estimated forward error bound for each solution vector.

out

berr

Array of dimension (nrhs). The componentwise relative backward error of each solution.

out

work

Workspace array of dimension (3*n).

out

iwork

Integer workspace array of dimension (n).

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

cgtrfs

Functions

void cgtrfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict DL,
    const c64*  restrict D,
    const c64*  restrict DU,
    const c64*  restrict DLF,
    const c64*  restrict DF,
    const c64*  restrict DUF,
    const c64*  restrict DU2,
    const INT*  restrict ipiv,
    const c64*  restrict B,
    const INT            ldb,
          c64*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);

void cgtrfs(const char *trans, const INT n, const INT nrhs, const c64 *restrict DL, const c64 *restrict D, const c64 *restrict DU, const c64 *restrict DLF, const c64 *restrict DF, const c64 *restrict DUF, const c64 *restrict DU2, const INT *restrict ipiv, const c64 *restrict B, const INT ldb, c64 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, c64 *restrict work, f32 *restrict rwork, INT *info)

CGTRFS 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

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)

in

n

The order of the matrix A. n>=0.

in

nrhs

The number of right hand sides. nrhs>=0.

in

DL

Array of dimension (n-1). The (n-1) subdiagonal elements of A.

in

D

Array of dimension (n). The diagonal elements of A.

in

DU

Array of dimension (n-1). The (n-1) superdiagonal elements of A.

in

DLF

Array of dimension (n-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.

in

DF

Array of dimension (n). The n diagonal elements of U.

in

DUF

Array of dimension (n-1). The (n-1) elements of the first superdiagonal of U.

in

DU2

Array of dimension (n-2). The (n-2) elements of the second superdiagonal of U.

in

ipiv

Array of dimension (n). The pivot indices.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

The leading dimension of B. ldb>=max(1,n).

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by CGTTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension (nrhs). The estimated forward error bound for each solution vector.

out

berr

Array of dimension (nrhs). The componentwise relative backward error of each solution.

out

work

Complex workspace array of dimension (2*n).

out

rwork

Real workspace array of dimension (n).

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

zgtrfs

Functions

void zgtrfs(
    const char*          trans,
    const INT            n,
    const INT            nrhs,
    const c128* restrict DL,
    const c128* restrict D,
    const c128* restrict DU,
    const c128* restrict DLF,
    const c128* restrict DF,
    const c128* restrict DUF,
    const c128* restrict DU2,
    const INT*  restrict ipiv,
    const c128* restrict B,
    const INT            ldb,
          c128* restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);

void zgtrfs(const char *trans, const INT n, const INT nrhs, const c128 *restrict DL, const c128 *restrict D, const c128 *restrict DU, const c128 *restrict DLF, const c128 *restrict DF, const c128 *restrict DUF, const c128 *restrict DU2, const INT *restrict ipiv, const c128 *restrict B, const INT ldb, c128 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, c128 *restrict work, f64 *restrict rwork, INT *info)

ZGTRFS 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

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)

in

n

The order of the matrix A. n>=0.

in

nrhs

The number of right hand sides. nrhs>=0.

in

DL

Array of dimension (n-1). The (n-1) subdiagonal elements of A.

in

D

Array of dimension (n). The diagonal elements of A.

in

DU

Array of dimension (n-1). The (n-1) superdiagonal elements of A.

in

DLF

Array of dimension (n-1). The (n-1) multipliers that define the matrix L from the LU factorization of A.

in

DF

Array of dimension (n). The n diagonal elements of U.

in

DUF

Array of dimension (n-1). The (n-1) elements of the first superdiagonal of U.

in

DU2

Array of dimension (n-2). The (n-2) elements of the second superdiagonal of U.

in

ipiv

Array of dimension (n). The pivot indices.

in

B

Array of dimension (ldb, nrhs). The right hand side matrix B.

in

ldb

The leading dimension of B. ldb>=max(1,n).

inout

X

Array of dimension (ldx, nrhs). On entry, the solution matrix X, as computed by ZGTTRS. On exit, the improved solution matrix X.

in

ldx

The leading dimension of X. ldx>=max(1,n).

out

ferr

Array of dimension (nrhs). The estimated forward error bound for each solution vector.

out

berr

Array of dimension (nrhs). The componentwise relative backward error of each solution.

out

work

Complex workspace array of dimension (2*n).

out

rwork

Real workspace array of dimension (n).

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value