hesv_aa_2stage(3) Library Functions Manual hesv_aa_2stage(3)

hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage


subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices subroutine csysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices subroutine dsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices subroutine ssysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices subroutine zsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

 CHESV_AA_2STAGE 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.
 Aasen's 2-stage algorithm is used to factor A as
    A = U**H * T * U,  if UPLO = 'U', or
    A = L * T * L**H,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and T is Hermitian 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is COMPLEX array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 183 of file chesv_aa_2stage.f.

CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the symmetric 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is COMPLEX array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 183 of file csysv_aa_2stage.f.

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the symmetric 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is DOUBLE PRECISION array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is DOUBLE PRECISION workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 185 of file dsysv_aa_2stage.f.

SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is REAL array, dimension (LDA,N)
          On entry, the symmetric 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is REAL array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is REAL workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 184 of file ssysv_aa_2stage.f.

ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

 ZHESV_AA_2STAGE 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.
 Aasen's 2-stage algorithm is used to factor A as
    A = U**H * T * U,  if UPLO = 'U', or
    A = L * T * L**H,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and T is Hermitian 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is COMPLEX*16 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is COMPLEX*16 array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX*16 workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 184 of file zhesv_aa_2stage.f.

ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

 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

UPLO 
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the symmetric 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, L is stored below (or above) the subdiagonal blocks,
          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

TB

          TB is COMPLEX*16 array, dimension (LTB)
          On exit, details of the LU factorization of the band matrix.

LTB

          LTB is INTEGER
          The size of the array TB. LTB >= 4*N, internally
          used to select NB such that LTB >= (3*NB+1)*N.
          If LTB = -1, then a workspace query is assumed; the
          routine only calculates the optimal size of LTB, 
          returns this value as the first entry of TB, and
          no error message related to LTB is issued by XERBLA.

IPIV

          IPIV is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of A were interchanged with the
          row and column IPIV(k).

IPIV2

          IPIV2 is INTEGER array, dimension (N)
          On exit, it contains the details of the interchanges, i.e.,
          the row and column k of T were interchanged with the
          row and column IPIV(k).

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX*16 workspace of size LWORK

LWORK

          LWORK is INTEGER
          The size of WORK. LWORK >= N, internally used to select NB
          such that LWORK >= N*NB.
          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.

INFO

          INFO is INTEGER
          = 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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 183 of file zsysv_aa_2stage.f.

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