# tptri - Man Page

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

## 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

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.

### 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

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.

### 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

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.

### 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

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.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK