ptrfs

sptrfs

Functions

void sptrfs(
    const INT           n,
    const INT           nrhs,
    const f32* restrict D,
    const f32* restrict E,
    const f32* restrict DF,
    const f32* restrict EF,
    const f32* restrict B,
    const INT           ldb,
          f32* restrict X,
    const INT           ldx,
          f32* restrict ferr,
          f32* restrict berr,
          f32* restrict work,
          INT*          info
);

void sptrfs(const INT n, const INT nrhs, const f32 *restrict D, const f32 *restrict E, const f32 *restrict DF, const f32 *restrict EF, const f32 *restrict B, const INT ldb, f32 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, f32 *restrict work, INT *info)

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.

Parameters

in

n

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

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in

D

Array of dimension n. The n diagonal elements of the tridiagonal matrix A.

in

E

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

in

DF

Array of dimension n. The n diagonal elements of the diagonal matrix D from the factorization computed by spttrf.

in

EF

Array of dimension n-1. The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by spttrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

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

out

ferr

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

out

berr

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

out

work

Array of dimension 2*n.

out

info

• info=0: successful exit

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

dptrfs

Functions

void dptrfs(
    const INT           n,
    const INT           nrhs,
    const f64* restrict D,
    const f64* restrict E,
    const f64* restrict DF,
    const f64* restrict EF,
    const f64* restrict B,
    const INT           ldb,
          f64* restrict X,
    const INT           ldx,
          f64* restrict ferr,
          f64* restrict berr,
          f64* restrict work,
          INT*          info
);

void dptrfs(const INT n, const INT nrhs, const f64 *restrict D, const f64 *restrict E, const f64 *restrict DF, const f64 *restrict EF, const f64 *restrict B, const INT ldb, f64 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, f64 *restrict work, INT *info)

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.

Parameters

in

n

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

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in

D

Array of dimension n. The n diagonal elements of the tridiagonal matrix A.

in

E

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

in

DF

Array of dimension n. The n diagonal elements of the diagonal matrix D from the factorization computed by dpttrf.

in

EF

Array of dimension n-1. The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by dpttrf.

in

B

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

in

ldb

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

inout

X

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

in

ldx

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

out

ferr

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

out

berr

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

out

work

Array of dimension 2*n.

out

info

• info=0: successful exit

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

cptrfs

Functions

void cptrfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict D,
    const c64*  restrict E,
    const f32*  restrict DF,
    const c64*  restrict EF,
    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 cptrfs(const char *uplo, const INT n, const INT nrhs, const f32 *restrict D, const c64 *restrict E, const f32 *restrict DF, const c64 *restrict EF, 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)

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.

Parameters

in

uplo

• '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

in

n

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

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in

D

Array of dimension n. The n real diagonal elements of the tridiagonal matrix A.

in

E

Complex array of dimension n-1. The (n-1) off-diagonal elements of the tridiagonal matrix A (see uplo).

in

DF

Array of dimension n. The n diagonal elements of the diagonal matrix D from the factorization computed by cpttrf.

in

EF

Complex array of 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).

in

B

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

in

ldb

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

inout

X

Complex array of dimension (ldx,nrhs). On entry, the solution matrix X, as computed by cpttrs. On exit, the improved solution matrix X.

in

ldx

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

out

ferr

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

out

berr

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

out

work

Complex array of dimension n.

out

rwork

Array of dimension n.

out

info

• info=0: successful exit

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

zptrfs

Functions

void zptrfs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict D,
    const c128* restrict E,
    const f64*  restrict DF,
    const c128* restrict EF,
    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 zptrfs(const char *uplo, const INT n, const INT nrhs, const f64 *restrict D, const c128 *restrict E, const f64 *restrict DF, const c128 *restrict EF, 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)

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.

Parameters

in

uplo

• '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

in

n

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

in

nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in

D

Array of dimension n. The n real diagonal elements of the tridiagonal matrix A.

in

E

Complex array of dimension n-1. The (n-1) off-diagonal elements of the tridiagonal matrix A (see uplo).

in

DF

Array of dimension n. The n diagonal elements of the diagonal matrix D from the factorization computed by zpttrf.

in

EF

Complex array of 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).

in

B

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

in

ldb

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

inout

X

Complex array of dimension (ldx,nrhs). On entry, the solution matrix X, as computed by zpttrs. On exit, the improved solution matrix X.

in

ldx

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

out

ferr

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

out

berr

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

out

work

Complex array of dimension n.

out

rwork

Array of dimension n.

out

info

• info=0: successful exit

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