---
name: "ztptrs.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ztptrs.f"
---

# ztptrs.f(3)

## NAME

SRC/ztptrs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ztptrs** (uplo, trans, diag, n, nrhs, ap, b, ldb, info)\
 **ZTPTRS**

## Function/Subroutine Documentation

### subroutine ztptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex\*16, dimension( \* ) ap, complex\*16, dimension( ldb, \* ) b, integer ldb, integer info)

**ZTPTRS**

**Purpose:**

```
!>
!> ZTPTRS solves a triangular system of the form
!>
!>    A * X = B,  A**T * X = B,  or  A**H * X = B,
!>
!> where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.
!>
!> This subroutine verifies that A is nonsingular, but callers should note that only exact
!> singularity is detected. It is conceivable for one or more diagonal elements of A to be
!> subnormally tiny numbers without this subroutine signalling an error.
!>
!> If a possible loss of numerical precision due to near-singular matrices is a concern, the
!> caller should verify that A is nonsingular within some tolerance before calling this subroutine.
!>
```

**Parameters**

*UPLO*

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

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose)
!>
```

*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.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
```

*AP*

```
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The upper or lower triangular matrix A, packed 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.
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, if INFO = 0, the solution matrix X.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= 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, the i-th diagonal element of A is exactly zero,
!>                indicating that the matrix is singular and the
!>                solutions X have not been computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **ztptrs.f**.

## Author

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