tptri(3) Library Functions Manual tptri(3)

tptri - tptri: triangular inverse


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

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

Definition at line 116 of file ctptri.f.

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

Definition at line 116 of file dtptri.f.

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

Definition at line 116 of file stptri.f.

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

Definition at line 116 of file ztptri.f.

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