tprfs#

Functions

void stprfs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict AP,
    const f32*  restrict B,
    const INT            ldb,
    const f32*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void stprfs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const f32 *restrict AP, const f32 *restrict B, const INT ldb, const f32 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, f32 *restrict work, INT *restrict iwork, INT *info)#

STPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix.

Parameters

in
uplo

= ‘U’: A is upper triangular = ‘L’: A is lower triangular

in
trans

= ‘N’: A * X = B (No transpose) = ‘T’: A**T * X = B (Transpose) = ‘C’: A**H * X = B (Conjugate transpose = Transpose)

in
diag

= ‘N’: A is non-unit triangular = ‘U’: A is unit triangular

in
n

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

in
nrhs

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

in
AP

The packed triangular matrix A. Array of dimension (n*(n+1)/2).

in
B

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

in
ldb

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

in
X

The solution matrix X. Array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

The backward error for each solution vector. Array of dimension (nrhs).

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void dtprfs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict AP,
    const f64*  restrict B,
    const INT            ldb,
    const f64*  restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*           info
);
void dtprfs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const f64 *restrict AP, const f64 *restrict B, const INT ldb, const f64 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, f64 *restrict work, INT *restrict iwork, INT *info)#

DTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix.

Parameters

in
uplo

= ‘U’: A is upper triangular = ‘L’: A is lower triangular

in
trans

= ‘N’: A * X = B (No transpose) = ‘T’: A**T * X = B (Transpose) = ‘C’: A**H * X = B (Conjugate transpose = Transpose)

in
diag

= ‘N’: A is non-unit triangular = ‘U’: A is unit triangular

in
n

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

in
nrhs

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

in
AP

The packed triangular matrix A. Array of dimension (n*(n+1)/2).

in
B

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

in
ldb

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

in
X

The solution matrix X. Array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

The backward error for each solution vector. Array of dimension (nrhs).

out
work

Workspace array of dimension (3*n).

out
iwork

Integer workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void ctprfs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict AP,
    const c64*  restrict B,
    const INT            ldb,
    const c64*  restrict X,
    const INT            ldx,
          f32*  restrict ferr,
          f32*  restrict berr,
          c64*  restrict work,
          f32*  restrict rwork,
          INT*           info
);
void ctprfs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const c64 *restrict AP, const c64 *restrict B, const INT ldb, const c64 *restrict X, const INT ldx, f32 *restrict ferr, f32 *restrict berr, c64 *restrict work, f32 *restrict rwork, INT *info)#

CTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix.

The solution matrix X must be computed by CTPTRS or some other means before entering this routine. CTPRFS does not do iterative refinement because doing so cannot improve the backward error.

Parameters

in
uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in
trans

= ‘N’: A * X = B (No transpose) = ‘T’: A**T * X = B (Transpose) = ‘C’: A**H * X = B (Conjugate transpose)

in
diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

in
n

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

in
nrhs

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

in
AP

The packed triangular matrix A. Array of dimension (n*(n+1)/2).

in
B

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

in
ldb

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

in
X

The solution matrix X. Array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

The backward error for each solution vector. Array of dimension (nrhs).

out
work

Complex workspace array of dimension (2*n).

out
rwork

Single precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void ztprfs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const c128* restrict AP,
    const c128* restrict B,
    const INT            ldb,
    const c128* restrict X,
    const INT            ldx,
          f64*  restrict ferr,
          f64*  restrict berr,
          c128* restrict work,
          f64*  restrict rwork,
          INT*           info
);
void ztprfs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const c128 *restrict AP, const c128 *restrict B, const INT ldb, const c128 *restrict X, const INT ldx, f64 *restrict ferr, f64 *restrict berr, c128 *restrict work, f64 *restrict rwork, INT *info)#

ZTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix.

The solution matrix X must be computed by ZTPTRS or some other means before entering this routine. ZTPRFS does not do iterative refinement because doing so cannot improve the backward error.

Parameters

in
uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in
trans

= ‘N’: A * X = B (No transpose) = ‘T’: A**T * X = B (Transpose) = ‘C’: A**H * X = B (Conjugate transpose)

in
diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

in
n

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

in
nrhs

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

in
AP

The packed triangular matrix A. Array of dimension (n*(n+1)/2).

in
B

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

in
ldb

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

in
X

The solution matrix X. Array of dimension (ldx, nrhs).

in
ldx

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

out
ferr

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

out
berr

The backward error for each solution vector. Array of dimension (nrhs).

out
work

Complex workspace array of dimension (2*n).

out
rwork

Double precision workspace array of dimension (n).

out
info

  • = 0: successful exit

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

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