Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       hetrf_aa_2stage - {he,sy}trf_aa_2stage: triangular factor

SYNOPSIS

   Functions
       subroutine chetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           CHETRF_AA_2STAGE
       subroutine csytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           CSYTRF_AA_2STAGE
       subroutine dsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           DSYTRF_AA_2STAGE
       subroutine ssytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           SSYTRF_AA_2STAGE
       subroutine zhetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           ZHETRF_AA_2STAGE
       subroutine zsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
           ZSYTRF_AA_2STAGE

Detailed Description

Function Documentation

   subroutine chetrf_aa_2stage (character uplo, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv,
       integer, dimension( * ) ipiv2, complex, dimension( * ) work, integer lwork, integer info)
       CHETRF_AA_2STAGE

       Purpose:

            CHETRF_AA_2STAGE computes the factorization of a real hermitian matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**T*T*U  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a hermitian band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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).

           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.

   subroutine csytrf_aa_2stage (character uplo, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv,
       integer, dimension( * ) ipiv2, complex, dimension( * ) work, integer lwork, integer info)
       CSYTRF_AA_2STAGE

       Purpose:

            CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**T*T*U  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a complex symmetric band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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).

           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.

   subroutine dsytrf_aa_2stage (character uplo, integer n, double precision, dimension( lda, * )
       a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * )
       ipiv, integer, dimension( * ) ipiv2, double precision, dimension( * ) work, integer lwork,
       integer info)
       DSYTRF_AA_2STAGE

       Purpose:

            DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**T*T*U  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a symmetric band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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 IPIV2(k).

           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.

   subroutine ssytrf_aa_2stage (character uplo, integer n, real, dimension( lda, * ) a, integer
       lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer,
       dimension( * ) ipiv2, real, dimension( * ) work, integer lwork, integer info)
       SSYTRF_AA_2STAGE

       Purpose:

            SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**T*T*U  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a symmetric band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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).

           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.

   subroutine zhetrf_aa_2stage (character uplo, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv,
       integer, dimension( * ) ipiv2, complex*16, dimension( * ) work, integer lwork, integer
       info)
       ZHETRF_AA_2STAGE

       Purpose:

            ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**H*T*U  or  A = L*T*L**H

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a hermitian band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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).

           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.

   subroutine zsytrf_aa_2stage (character uplo, integer n, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv,
       integer, dimension( * ) ipiv2, complex*16, dimension( * ) work, integer lwork, integer
       info)
       ZSYTRF_AA_2STAGE

       Purpose:

            ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U**T*T*U  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a complex symmetric band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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.

           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).

           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.

Author

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