sysv_aa_2stage#

Functions

void ssysv_aa_2stage(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          f32*  restrict A,
    const INT            lda,
          f32*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          f32*  restrict B,
    const INT            ldb,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void ssysv_aa_2stage(const char *uplo, const INT n, const INT nrhs, f32 *restrict A, const INT lda, f32 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, f32 *restrict B, const INT ldb, f32 *restrict work, const INT lwork, INT *info)#

SSYSV_AA_2STAGE computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.

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
nrhs

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

inout
A

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
TB

Double precision array, dimension (max(1, ltb)). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb >= max(1, 4*n). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

inout
B

Double precision array, 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
work

Double precision workspace of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The size of work. lwork >= max(1, n). If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, band LU factorization failed on i-th column

Functions

void dsysv_aa_2stage(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          f64*  restrict A,
    const INT            lda,
          f64*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          f64*  restrict B,
    const INT            ldb,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dsysv_aa_2stage(const char *uplo, const INT n, const INT nrhs, f64 *restrict A, const INT lda, f64 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, f64 *restrict B, const INT ldb, f64 *restrict work, const INT lwork, INT *info)#

DSYSV_AA_2STAGE computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.

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
nrhs

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

inout
A

Double precision array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
TB

Double precision array, dimension (max(1, ltb)). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb >= max(1, 4*n). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

inout
B

Double precision array, 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
work

Double precision workspace of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The size of work. lwork >= max(1, n). If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, band LU factorization failed on i-th column

Functions

void csysv_aa_2stage(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          c64*  restrict B,
    const INT            ldb,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void csysv_aa_2stage(const char *uplo, const INT n, const INT nrhs, c64 *restrict A, const INT lda, c64 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, c64 *restrict B, const INT ldb, c64 *restrict work, const INT lwork, INT *info)#

CSYSV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.

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
nrhs

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

inout
A

Single complex array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
TB

Single complex array, dimension (max(1, ltb)). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb >= max(1, 4*n). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

inout
B

Single complex array, 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
work

Single complex workspace of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The size of work. lwork >= max(1, n). If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, band LU factorization failed on i-th column

Functions

void zsysv_aa_2stage(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c128* restrict A,
    const INT            lda,
          c128* restrict TB,
    const INT            ltb,
          INT*  restrict ipiv,
          INT*  restrict ipiv2,
          c128* restrict B,
    const INT            ldb,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zsysv_aa_2stage(const char *uplo, const INT n, const INT nrhs, c128 *restrict A, const INT lda, c128 *restrict TB, const INT ltb, INT *restrict ipiv, INT *restrict ipiv2, c128 *restrict B, const INT ldb, c128 *restrict work, const INT lwork, INT *info)#

ZSYSV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B.

This is the blocked version of the algorithm, calling Level 3 BLAS.

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
nrhs

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

inout
A

Double complex array, dimension (lda, n). On entry, the symmetric matrix A. On exit, L is stored below (or above) the subdiagonal blocks.

in
lda

The leading dimension of the array A. lda >= max(1, n).

out
TB

Double complex array, dimension (max(1, ltb)). On exit, details of the LU factorization of the band matrix.

in
ltb

The size of the array TB. ltb >= max(1, 4*n). If ltb = -1, then a workspace query is assumed.

out
ipiv

Integer array, dimension (n). On exit, details of the interchanges.

out
ipiv2

Integer array, dimension (n). On exit, details of the interchanges in T.

inout
B

Double complex array, 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
work

Double complex workspace of size (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The size of work. lwork >= max(1, n). If lwork = -1, then a workspace query is assumed.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, band LU factorization failed on i-th column