tptri(3)

NAME
tptri - tptri: triangular inverse

SYNOPSIS

  Functions

subroutine ctptri (uplo, diag, n, ap, info)
CTPTRI
subroutine dtptri (uplo, diag, n, ap, info)
DTPTRI
subroutine stptri (uplo, diag, n, ap, info)
STPTRI
subroutine ztptri (uplo, diag, n, ap, info)
ZTPTRI

Detailed Description

Function Documentation

  subroutine ctptri (character uplo, character diag, integer n, complex, dimension( * ) ap, integer info)

CTPTRI

Purpose:

    !>
    !> CTPTRI computes the inverse of a complex upper or lower triangular
    !> matrix A stored in packed format.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangular matrix A, stored
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same packed storage format.
    !>

    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.

Further Details:

    !>
    !>  A triangular matrix A can be transferred to packed storage using one
    !>  of the following program segments:
    !>
    !>  UPLO = 'U':                      UPLO = 'L':
    !>
    !>        JC = 1                           JC = 1
    !>        DO 2 J = 1, N                    DO 2 J = 1, N
    !>           DO 1 I = 1, J                    DO 1 I = J, N
    !>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
    !>      1    CONTINUE                    1    CONTINUE
    !>           JC = JC + J                      JC = JC + N - J + 1
    !>      2 CONTINUE                       2 CONTINUE
    !>

  subroutine dtptri (character uplo, character diag, integer n, double precision, dimension( * ) ap, integer info)

DTPTRI

Purpose:

    !>
    !> DTPTRI computes the inverse of a real upper or lower triangular
    !> matrix A stored in packed format.
    !>

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.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangular matrix A, stored
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same packed storage format.
    !>

    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.

Further Details:

    !>
    !>  A triangular matrix A can be transferred to packed storage using one
    !>  of the following program segments:
    !>
    !>  UPLO = 'U':                      UPLO = 'L':
    !>
    !>        JC = 1                           JC = 1
    !>        DO 2 J = 1, N                    DO 2 J = 1, N
    !>           DO 1 I = 1, J                    DO 1 I = J, N
    !>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
    !>      1    CONTINUE                    1    CONTINUE
    !>           JC = JC + J                      JC = JC + N - J + 1
    !>      2 CONTINUE                       2 CONTINUE
    !>

  subroutine stptri (character uplo, character diag, integer n, real, dimension( * ) ap, integer info)

STPTRI

Purpose:

    !>
    !> STPTRI computes the inverse of a real upper or lower triangular
    !> matrix A stored in packed format.
    !>

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.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangular matrix A, stored
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same packed storage format.
    !>

    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.

Further Details:

    !>
    !>  A triangular matrix A can be transferred to packed storage using one
    !>  of the following program segments:
    !>
    !>  UPLO = 'U':                      UPLO = 'L':
    !>
    !>        JC = 1                           JC = 1
    !>        DO 2 J = 1, N                    DO 2 J = 1, N
    !>           DO 1 I = 1, J                    DO 1 I = J, N
    !>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
    !>      1    CONTINUE                    1    CONTINUE
    !>           JC = JC + J                      JC = JC + N - J + 1
    !>      2 CONTINUE                       2 CONTINUE
    !>

  subroutine ztptri (character uplo, character diag, integer n, complex*16, dimension( * ) ap, integer info)

ZTPTRI

Purpose:

    !>
    !> ZTPTRI computes the inverse of a complex upper or lower triangular
    !> matrix A stored in packed format.
    !>

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.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangular matrix A, stored
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
    !>          See below for further details.
    !>          On exit, the (triangular) inverse of the original matrix, in
    !>          the same packed storage format.
    !>

    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.

Further Details:

    !>
    !>  A triangular matrix A can be transferred to packed storage using one
    !>  of the following program segments:
    !>
    !>  UPLO = 'U':                      UPLO = 'L':
    !>
    !>        JC = 1                           JC = 1
    !>        DO 2 J = 1, N                    DO 2 J = 1, N
    !>           DO 1 I = 1, J                    DO 1 I = J, N
    !>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
    !>      1    CONTINUE                    1    CONTINUE
    !>           JC = JC + J                      JC = JC + N - J + 1
    !>      2 CONTINUE                       2 CONTINUE
    !>

Author

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