hetri2x(3)

NAME
hetri2x - {he,sy}tri2x: inverse

SYNOPSIS

  Functions
subroutine chetri2x (uplo, n, a, lda, ipiv, work, nb, info)
CHETRI2X
subroutine csytri2x (uplo, n, a, lda, ipiv, work, nb, info)
CSYTRI2X
subroutine dsytri2x (uplo, n, a, lda, ipiv, work, nb, info)
DSYTRI2X
subroutine ssytri2x (uplo, n, a, lda, ipiv, work, nb, info)
SSYTRI2X
subroutine zhetri2x (uplo, n, a, lda, ipiv, work, nb, info)
ZHETRI2X
subroutine zsytri2x (uplo, n, a, lda, ipiv, work, nb, info)
ZSYTRI2X

Detailed Description

Function Documentation

  subroutine chetri2x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( n+nb+1,* ) work, integer nb, integer info)

CHETRI2X

Purpose:

    !>
    !> CHETRI2X computes the inverse of a complex Hermitian indefinite matrix
    !> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
    !> CHETRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**H;
    !>          = 'L':  Lower triangular, form is A = L*D*L**H.
    !>

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by CHETRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by CHETRF.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file chetri2x.f.

  subroutine csytri2x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( n+nb+1,* ) work, integer nb, integer info)

CSYTRI2X

Purpose:

    !>
    !> CSYTRI2X computes the inverse of a real symmetric indefinite matrix
    !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
    !> CSYTRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**T;
    !>          = 'L':  Lower triangular, form is A = L*D*L**T.
    !>

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by CSYTRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by CSYTRF.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file csytri2x.f.

  subroutine dsytri2x (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( n+nb+1,* ) work, integer nb, integer info)

DSYTRI2X

Purpose:

    !>
    !> DSYTRI2X computes the inverse of a real symmetric indefinite matrix
    !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
    !> DSYTRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**T;
    !>          = 'L':  Lower triangular, form is A = L*D*L**T.
    !>

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by DSYTRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by DSYTRF.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file dsytri2x.f.

  subroutine ssytri2x (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( n+nb+1,* ) work, integer nb, integer info)

SSYTRI2X

Purpose:

    !>
    !> SSYTRI2X computes the inverse of a real symmetric indefinite matrix
    !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
    !> SSYTRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**T;
    !>          = 'L':  Lower triangular, form is A = L*D*L**T.
    !>

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by SSYTRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by SSYTRF.
    !>

    WORK

    !>          WORK is REAL array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file ssytri2x.f.

  subroutine zhetri2x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( n+nb+1,* ) work, integer nb, integer info)

ZHETRI2X

Purpose:

    !>
    !> ZHETRI2X computes the inverse of a COMPLEX*16 Hermitian indefinite matrix
    !> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
    !> ZHETRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**H;
    !>          = 'L':  Lower triangular, form is A = L*D*L**H.
    !>

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by ZHETRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by ZHETRF.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file zhetri2x.f.

  subroutine zsytri2x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( n+nb+1,* ) work, integer nb, integer info)

ZSYTRI2X

Purpose:

    !>
    !> ZSYTRI2X computes the inverse of a complex symmetric indefinite matrix
    !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by
    !> ZSYTRF.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the details of the factorization are stored
    !>          as an upper or lower triangular matrix.
    !>          = 'U':  Upper triangular, form is A = U*D*U**T;
    !>          = 'L':  Lower triangular, form is A = L*D*L**T.
    !>

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the NNB diagonal matrix D and the multipliers
    !>          used to obtain the factor U or L as computed by ZSYTRF.
    !>
    !>          On exit, if INFO = 0, the (symmetric) inverse of the original
    !>          matrix.  If UPLO = 'U', the upper triangular part of the
    !>          inverse is formed and the part of A below the diagonal is not
    !>          referenced; if UPLO = 'L' the lower triangular part of the
    !>          inverse is formed and the part of A above the diagonal is
    !>          not referenced.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the NNB structure of D
    !>          as determined by ZSYTRF.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3)
    !>

    NB

    !>          NB is INTEGER
    !>          Block size
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
    !>               inverse could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 119 of file zsytri2x.f.

Author

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