gbtrs#

Functions

void sgbtrs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const f32*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
          f32*  restrict B,
    const INT            ldb,
          INT*           info
);
void sgbtrs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const f32 *restrict AB, const INT ldab, const INT *restrict ipiv, f32 *restrict B, const INT ldb, INT *info)#

SGBTRS solves a system of linear equations. 

A * X = B  or  A**T * X = B

with a general band matrix A using the LU factorization computed by SGBTRF.

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**T * X = B (Conjugate transpose = Transpose)

in
n

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

in
kl

The number of subdiagonals within the band of A. kl>=0.

in
ku

The number of superdiagonals within the band of A. ku>=0.

in
nrhs

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

in
AB

Array of dimension (ldab, n). Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldab

The leading dimension of the array AB. ldab>=2*kl+ku+1.

in
ipiv

Array of dimension (n). The pivot indices; for 0<=i<n, row i of the matrix was interchanged with row ipiv[i].

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

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

out
info

  • info=0: successful exit

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

Functions

void dgbtrs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const f64*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
          f64*  restrict B,
    const INT            ldb,
          INT*           info
);
void dgbtrs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const f64 *restrict AB, const INT ldab, const INT *restrict ipiv, f64 *restrict B, const INT ldb, INT *info)#

DGBTRS solves a system of linear equations. 

A * X = B  or  A**T * X = B

with a general band matrix A using the LU factorization computed by DGBTRF.

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**T * X = B (Conjugate transpose = Transpose)

in
n

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

in
kl

The number of subdiagonals within the band of A. kl>=0.

in
ku

The number of superdiagonals within the band of A. ku>=0.

in
nrhs

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

in
AB

Array of dimension (ldab, n). Details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldab

The leading dimension of the array AB. ldab>=2*kl+ku+1.

in
ipiv

Array of dimension (n). The pivot indices; for 0<=i<n, row i of the matrix was interchanged with row ipiv[i].

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

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

out
info

  • info=0: successful exit

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

Functions

void cgbtrs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const c64*  restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);
void cgbtrs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const c64 *restrict AB, const INT ldab, const INT *restrict ipiv, c64 *restrict B, const INT ldb, INT *info)#

CGBTRS solves a system of linear equations. 

A * X = B,  A**T * X = B,  or  A**H * X = B

with a general band matrix A using the LU factorization computed by CGBTRF.

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
kl

The number of subdiagonals within the band of A. kl>=0.

in
ku

The number of superdiagonals within the band of A. ku>=0.

in
nrhs

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

in
AB

Array of dimension (ldab, n). Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldab

The leading dimension of the array AB. ldab>=2*kl+ku+1.

in
ipiv

Array of dimension (n). The pivot indices; for 0<=i<n, row i of the matrix was interchanged with row ipiv[i].

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

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

out
info

  • info=0: successful exit

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

Functions

void zgbtrs(
    const char*          trans,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const INT            nrhs,
    const c128* restrict AB,
    const INT            ldab,
    const INT*  restrict ipiv,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);
void zgbtrs(const char *trans, const INT n, const INT kl, const INT ku, const INT nrhs, const c128 *restrict AB, const INT ldab, const INT *restrict ipiv, c128 *restrict B, const INT ldb, INT *info)#

ZGBTRS solves a system of linear equations. 

A * X = B,  A**T * X = B,  or  A**H * X = B

with a general band matrix A using the LU factorization computed by ZGBTRF.

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
kl

The number of subdiagonals within the band of A. kl>=0.

in
ku

The number of superdiagonals within the band of A. ku>=0.

in
nrhs

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

in
AB

Array of dimension (ldab, n). Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 0 to kl+ku, and the multipliers used during the factorization are stored in rows kl+ku+1 to 2*kl+ku.

in
ldab

The leading dimension of the array AB. ldab>=2*kl+ku+1.

in
ipiv

Array of dimension (n). The pivot indices; for 0<=i<n, row i of the matrix was interchanged with row ipiv[i].

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

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

out
info

  • info=0: successful exit

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