hetrs_3#

Functions

void chetrs_3(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict A,
    const INT            lda,
    const c64*  restrict E,
    const INT*  restrict ipiv,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);
void chetrs_3(const char *uplo, const INT n, const INT nrhs, const c64 *restrict A, const INT lda, const c64 *restrict E, const INT *restrict ipiv, c64 *restrict B, const INT ldb, INT *info)#

CHETRS_3 solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by CHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = ‘U’ or UPLO = ‘L’ cases.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = ‘U’: Upper triangular, form is A = P*U*D*(U**H)*(P**T); = ‘L’: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

in
n

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

in
nrhs

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

in
A

Complex*16 array, dimension (lda, n). Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = ‘U’: factor U in the superdiagonal part of A. If UPLO = ‘L’: factor L in the subdiagonal part of A.

in
lda

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

in
E

Complex*16 array, dimension (n). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = ‘U’: E(i) = D(i-1,i), i=2:N, E(1) not referenced; If UPLO = ‘L’: E(i) = D(i+1,i), i=1:N-1, E(N) not referenced.

in
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D as determined by CHETRF_RK or ZHETRF_BK.

inout
B

Complex*16 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
info

  • = 0: successful exit

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

Functions

void zhetrs_3(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c128* restrict A,
    const INT            lda,
    const c128* restrict E,
    const INT*  restrict ipiv,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);
void zhetrs_3(const char *uplo, const INT n, const INT nrhs, const c128 *restrict A, const INT lda, const c128 *restrict E, const INT *restrict ipiv, c128 *restrict B, const INT ldb, INT *info)#

ZHETRS_3 solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This algorithm is using Level 3 BLAS.

NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = ‘U’ or UPLO = ‘L’ cases.

Parameters

in
uplo

Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = ‘U’: Upper triangular, form is A = P*U*D*(U**H)*(P**T); = ‘L’: Lower triangular, form is A = P*L*D*(L**H)*(P**T).

in
n

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

in
nrhs

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

in
A

Complex*16 array, dimension (lda, n). Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = ‘U’: factor U in the superdiagonal part of A. If UPLO = ‘L’: factor L in the subdiagonal part of A.

in
lda

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

in
E

Complex*16 array, dimension (n). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = ‘U’: E(i) = D(i-1,i), i=2:N, E(1) not referenced; If UPLO = ‘L’: E(i) = D(i+1,i), i=1:N-1, E(N) not referenced.

in
ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

inout
B

Complex*16 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
info

  • = 0: successful exit

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

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