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 CHETRF_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 transpose 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.

Parameters

in
uplo

  • '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, i.e., the number of columns of the matrix B. nrhs>=0.

in
A

Array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by chetrf_rk or chetrf_bk:

  • 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

  • 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

Array of 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=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced. For a 1-by-1 diagonal block D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by chetrf_rk or chetrf_bk.

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 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 transpose 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.

Parameters

in
uplo

  • '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, i.e., the number of columns of the matrix B. nrhs>=0.

in
A

Array of dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by zhetrf_rk or zhetrf_bk:

  • 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

  • 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

Array of 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=1:n-1, E[0] not referenced; if uplo='L': E[i]=D(i+1,i), i=0:n-2, E[n-1] not referenced. For a 1-by-1 diagonal block D(k), the element E[k] is not referenced in both uplo='U' or uplo='L' cases.

in
ipiv

Array of dimension n. Details of the interchanges and the block structure of D as determined by zhetrf_rk or zhetrf_bk.

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