hetri(3)

NAME
hetri - {he,sy}tri: triangular inverse

SYNOPSIS

  Functions
subroutine chetri (uplo, n, a, lda, ipiv, work, info)
CHETRI
subroutine csytri (uplo, n, a, lda, ipiv, work, info)
CSYTRI
subroutine dsytri (uplo, n, a, lda, ipiv, work, info)
DSYTRI
subroutine ssytri (uplo, n, a, lda, ipiv, work, info)
SSYTRI
subroutine zhetri (uplo, n, a, lda, ipiv, work, info)
ZHETRI
subroutine zsytri (uplo, n, a, lda, ipiv, work, info)
ZSYTRI

Detailed Description

Function Documentation

  subroutine chetri (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)

CHETRI

Purpose:

     CHETRI 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 block diagonal matrix D and the multipliers
              used to obtain the factor U or L as computed by CHETRF.
              On exit, if INFO = 0, the (Hermitian) 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 block structure of D
              as determined by CHETRF.

    WORK

              WORK is COMPLEX array, dimension (N)

    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 113 of file chetri.f.

  subroutine csytri (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)

CSYTRI

Purpose:

     CSYTRI 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
     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 block 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 block structure of D
              as determined by CSYTRF.

    WORK

              WORK is COMPLEX array, dimension (2*N)

    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 113 of file csytri.f.

  subroutine dsytri (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)

DSYTRI

Purpose:

     DSYTRI 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 block 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 block structure of D
              as determined by DSYTRF.

    WORK

              WORK is DOUBLE PRECISION array, dimension (N)

    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 113 of file dsytri.f.

  subroutine ssytri (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)

SSYTRI

Purpose:

     SSYTRI 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 block 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 block structure of D
              as determined by SSYTRF.

    WORK

              WORK is REAL array, dimension (N)

    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 113 of file ssytri.f.

  subroutine zhetri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)

ZHETRI

Purpose:

     ZHETRI 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
     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 block diagonal matrix D and the multipliers
              used to obtain the factor U or L as computed by ZHETRF.
              On exit, if INFO = 0, the (Hermitian) 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 block structure of D
              as determined by ZHETRF.

    WORK

              WORK is COMPLEX*16 array, dimension (N)

    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 113 of file zhetri.f.

  subroutine zsytri (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)

ZSYTRI

Purpose:

     ZSYTRI 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 block 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 block structure of D
              as determined by ZSYTRF.

    WORK

              WORK is COMPLEX*16 array, dimension (2*N)

    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 113 of file zsytri.f.

Author

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