pbrfs#

Functions

void spbrfs(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
    const f32*  restrict AB,
    const INT            ldab,
    const f32*  restrict AFB,
    const INT            ldafb,
    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 spbrfs(const char *uplo, const INT n, const INT kd, const INT nrhs, const f32 *restrict AB, const INT ldab, const f32 *restrict AFB, const INT ldafb, 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)#

SPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
nrhs

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

in
AB

The original banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
AFB

The Cholesky factor from SPBTRF. Array of dimension (ldafb, n).

in
ldafb

The leading dimension of AFB. ldafb >= kd+1.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X. On exit, the improved solution. 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 dpbrfs(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
    const f64*  restrict AB,
    const INT            ldab,
    const f64*  restrict AFB,
    const INT            ldafb,
    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 dpbrfs(const char *uplo, const INT n, const INT kd, const INT nrhs, const f64 *restrict AB, const INT ldab, const f64 *restrict AFB, const INT ldafb, 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)#

DPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
nrhs

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

in
AB

The original banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
AFB

The Cholesky factor from DPBTRF. Array of dimension (ldafb, n).

in
ldafb

The leading dimension of AFB. ldafb >= kd+1.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X. On exit, the improved solution. 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 cpbrfs(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
    const c64*  restrict AB,
    const INT            ldab,
    const c64*  restrict AFB,
    const INT            ldafb,
    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 cpbrfs(const char *uplo, const INT n, const INT kd, const INT nrhs, const c64 *restrict AB, const INT ldab, const c64 *restrict AFB, const INT ldafb, 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)#

CPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
nrhs

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

in
AB

The Hermitian band matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
AFB

The Cholesky factor from CPBTRF. Array of dimension (ldafb, n).

in
ldafb

The leading dimension of AFB. ldafb >= kd+1.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X. On exit, the improved solution. 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

Real workspace array of dimension (n).

out
info

  • = 0: successful exit

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

Functions

void zpbrfs(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
    const c128* restrict AB,
    const INT            ldab,
    const c128* restrict AFB,
    const INT            ldafb,
    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 zpbrfs(const char *uplo, const INT n, const INT kd, const INT nrhs, const c128 *restrict AB, const INT ldab, const c128 *restrict AFB, const INT ldafb, 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)#

ZPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution.

Parameters

in
uplo

= ‘U’: Upper triangle of A is stored = ‘L’: Lower triangle of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
nrhs

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

in
AB

The Hermitian band matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

in
AFB

The Cholesky factor from ZPBTRF. Array of dimension (ldafb, n).

in
ldafb

The leading dimension of AFB. ldafb >= kd+1.

in
B

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

in
ldb

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

inout
X

On entry, the solution matrix X. On exit, the improved solution. 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

Real 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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