trtri(3)

NAME
trtri - trtri: triangular inverse

SYNOPSIS

  Functions

subroutine ctrtri (uplo, diag, n, a, lda, info)
CTRTRI
subroutine dtrtri (uplo, diag, n, a, lda, info)
DTRTRI
subroutine strtri (uplo, diag, n, a, lda, info)
STRTRI
subroutine ztrtri (uplo, diag, n, a, lda, info)
ZTRTRI

Detailed Description

Function Documentation

  subroutine ctrtri (character uplo, character diag, integer n, complex, dimension( lda, * ) a, integer lda, integer info)

CTRTRI

Purpose:

    !>
    !> CTRTRI computes the inverse of a complex upper or lower triangular
    !> matrix A.
    !>
    !> This is the Level 3 BLAS version of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          = 'N':  A is non-unit triangular;
    !>          = 'U':  A is unit triangular.
    !>

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.  If DIAG = 'U', the
    !>          diagonal elements of A are also not referenced and are
    !>          assumed to be 1.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same storage format.
    !>

    LDA

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
    !>               matrix is singular and its inverse can not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dtrtri (character uplo, character diag, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)

DTRTRI

Purpose:

    !>
    !> DTRTRI computes the inverse of a real upper or lower triangular
    !> matrix A.
    !>
    !> This is the Level 3 BLAS version of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          = 'N':  A is non-unit triangular;
    !>          = 'U':  A is unit triangular.
    !>

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.  If DIAG = 'U', the
    !>          diagonal elements of A are also not referenced and are
    !>          assumed to be 1.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same storage format.
    !>

    LDA

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
    !>               matrix is singular and its inverse can not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine strtri (character uplo, character diag, integer n, real, dimension( lda, * ) a, integer lda, integer info)

STRTRI

Purpose:

    !>
    !> STRTRI computes the inverse of a real upper or lower triangular
    !> matrix A.
    !>
    !> This is the Level 3 BLAS version of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          = 'N':  A is non-unit triangular;
    !>          = 'U':  A is unit triangular.
    !>

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.  If DIAG = 'U', the
    !>          diagonal elements of A are also not referenced and are
    !>          assumed to be 1.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same storage format.
    !>

    LDA

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
    !>               matrix is singular and its inverse can not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine ztrtri (character uplo, character diag, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

ZTRTRI

Purpose:

    !>
    !> ZTRTRI computes the inverse of a complex upper or lower triangular
    !> matrix A.
    !>
    !> This is the Level 3 BLAS version of the algorithm.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  A is upper triangular;
    !>          = 'L':  A is lower triangular.
    !>

    DIAG

    !>          DIAG is CHARACTER*1
    !>          = 'N':  A is non-unit triangular;
    !>          = 'U':  A is unit triangular.
    !>

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the triangular matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of the array A contains
    !>          the upper triangular matrix, and the strictly lower
    !>          triangular part of A is not referenced.  If UPLO = 'L', the
    !>          leading N-by-N lower triangular part of the array A contains
    !>          the lower triangular matrix, and the strictly upper
    !>          triangular part of A is not referenced.  If DIAG = 'U', the
    !>          diagonal elements of A are also not referenced and are
    !>          assumed to be 1.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same storage format.
    !>

    LDA

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

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
    !>               matrix is singular and its inverse can not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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