---
name: "csytri_3"
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/csytri_3.f"
---

# csytri\_3(3)

Part of [csytri\_3.f(3)](/csytri_3.f/3.md).

## NAME

SRC/csytri\_3.f

## SYNOPSIS

### Functions/Subroutines

subroutine **csytri\_3** (uplo, n, a, lda, e, ipiv, work, lwork, info)\
 **CSYTRI\_3**

## Function/Subroutine Documentation

### subroutine csytri\_3 (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) e, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer lwork, integer info)

**CSYTRI\_3**

**Purpose:**

```
!> CSYTRI_3 computes the inverse of a complex symmetric indefinite
!> matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK:
!>
!>     A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
!>
!> where U (or L) is unit upper (or lower) triangular matrix,
!> U**T (or L**T) is the transpose of U (or L), P is a permutation
!> matrix, P**T is the transpose of P, and D is symmetric and block
!> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
!>
!> CSYTRI_3 sets the leading dimension of the workspace  before calling
!> CSYTRI_3X that actually computes the inverse.  This is the blocked
!> version of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are
!>          stored as an upper or lower triangular matrix.
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*N*

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

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, diagonal of the block diagonal matrix D and
!>          factors U or L as computed by CSYTRF_RK and CSYTRF_BK:
!>            a) ONLY diagonal elements of the symmetric block diagonal
!>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
!>               (superdiagonal (or subdiagonal) elements of D
!>                should be provided on entry in array E), and
!>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
!>               If UPLO = 'L': factor L in the subdiagonal part of A.
!>
!>          On exit, if INFO = 0, the symmetric inverse of the original
!>          matrix.
!>             If UPLO = 'U': the upper triangular part of the inverse
!>             is formed and the part of A below the diagonal is not
!>             referenced;
!>             If UPLO = 'L': the lower triangular part of the inverse
!>             is formed and the part of A above the diagonal is not
!>             referenced.
!>
```

*LDA*

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

*E*

```
!>          E is COMPLEX array, dimension (N)
!>          On entry, contains the superdiagonal (or subdiagonal)
!>          elements of the symmetric block diagonal matrix D
!>          with 1-by-1 or 2-by-2 diagonal blocks, where
!>          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
!>          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
!>
!>          NOTE: For 1-by-1 diagonal block D(k), where
!>          1 <= k <= N, the element E(k) is not referenced in both
!>          UPLO = 'U' or UPLO = 'L' cases.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSYTRF_RK or CSYTRF_BK.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (N+NB+1)*(NB+3).
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of WORK. LWORK >= (N+NB+1)*(NB+3).
!>
!>          If LDWORK = -1, then a workspace query is assumed;
!>          the routine only calculates the optimal size of the optimal
!>          size of the WORK array, returns this value as the first
!>          entry of the WORK array, and no error message related to
!>          LWORK is issued by XERBLA.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
!>               inverse could not be computed.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

```
!>
!>  November 2017,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>
```

Definition at line **168** of file **csytri\_3.f**.

## Author

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