hesv#

Functions

void chesv(
    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(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 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 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. The factored form of A is then used to solve the system of equations A * X = B.

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

Single complex array, 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.

in
lda

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

out
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by CHETRF. 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 uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k] were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k] were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

inout
B

Single complex array, 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

Single complex array, 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 >= max(1,N*NB), where NB is the optimal blocksize for CHETRF. 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 by XERBLA.

out
info

  • = 0: successful exit

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

  • > 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(
    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(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 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 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. The factored form of A is then used to solve the system of equations A * X = B.

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

Double complex array, 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.

in
lda

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

out
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by ZHETRF. 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 uplo = ‘U’ and ipiv[k] = ipiv[k-1] < 0, then rows and columns k-1 and -ipiv[k] were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If uplo = ‘L’ and ipiv[k] = ipiv[k+1] < 0, then rows and columns k+1 and -ipiv[k] were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

inout
B

Double complex array, 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

Double complex array, 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 >= max(1,N*NB), where NB is the optimal blocksize for ZHETRF. 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 by XERBLA.

out
info

  • = 0: successful exit

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

  • > 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.

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