hesv_rook#

Functions

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

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

The bounded Bunch-Kaufman (“rook”) diagonal pivoting method is used to factor A as A = U * D * U**H, if uplo = ‘U’, or A = L * D * L**H, if uplo = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

chetrf_rook is called to compute the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The factored form of A is then used to solve the system of equations A * X = B by calling chetrs_rook (uses BLAS 2).

  • If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.

  • If ipiv[k]<0 and ipiv[k-1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k-1 and -ipiv[k-1]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If uplo='L':

  • If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.

  • If ipiv[k]<0 and ipiv[k+1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k+1 and -ipiv[k+1]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The number of linear equations, i.e., 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

Array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by chetrf_rook.

in
lda

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

out
ipiv

Array of dimension n. Pivot indices (0-based). If uplo='U':

inout
B

Array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in
ldb

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

out
work

Array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. lwork>=1, and for best performance lwork>=n*nb, where nb is the optimal block size for chetrf_rook. For lwork<n, TRS will be done with Level BLAS 2. For lwork>=n, TRS will be done with Level BLAS 3. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

Functions

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

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

The bounded Bunch-Kaufman (“rook”) diagonal pivoting method is used to factor A as A = U * D * U**H, if uplo = ‘U’, or A = L * D * L**H, if uplo = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

zhetrf_rook is called to compute the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

The factored form of A is then used to solve the system of equations A * X = B by calling zhetrs_rook (uses BLAS 2).

  • If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.

  • If ipiv[k]<0 and ipiv[k-1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k-1 and -ipiv[k-1]-1 were interchanged, D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

If uplo='L':

  • If ipiv[k]>=0, then rows and columns k and ipiv[k] were interchanged and D(k,k) is a 1-by-1 diagonal block.

  • If ipiv[k]<0 and ipiv[k+1]<0, then rows and columns k and -ipiv[k]-1 were interchanged and rows and columns k+1 and -ipiv[k+1]-1 were interchanged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

Parameters

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The number of linear equations, i.e., 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

Array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by zhetrf_rook.

in
lda

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

out
ipiv

Array of dimension n. Pivot indices (0-based). If uplo='U':

inout
B

Array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in
ldb

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

out
work

Array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in
lwork

The length of work. lwork>=1, and for best performance lwork>=n*nb, where nb is the optimal block size for zhetrf_rook. For lwork<n, TRS will be done with Level BLAS 2. For lwork>=n, TRS will be done with Level BLAS 3. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.