---
name: "zsysv_aa_2stage.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/zsysv_aa_2stage.f"
---

# zsysv\_aa\_2stage.f(3)

## NAME

SRC/zsysv\_aa\_2stage.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zsysv\_aa\_2stage** (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)\
  **ZSYSV\_AA\_2STAGE computes the solution to system of linear equations A \* X = B for SY matrices**

## Function/Subroutine Documentation

### subroutine zsysv\_aa\_2stage (character uplo, integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tb, integer ltb, integer, dimension( \* ) ipiv, integer, dimension( \* ) ipiv2, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( \* ) work, integer lwork, integer info)

 **ZSYSV\_AA\_2STAGE computes the solution to system of linear equations A \* X = B for SY matrices**

**Purpose:**

```
!>
!> ZSYSV_AA_2STAGE computes the solution to a complex system of
!> linear equations
!>    A * X = B,
!> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
!> matrices.
!>
!> Aasen's 2-stage algorithm is used to factor A as
!>    A = U**T * T * U,  if UPLO = 'U', or
!>    A = L * T * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is symmetric and band. The matrix T is
!> then LU-factored with partial pivoting. The factored form of A
!> is then used to solve the system of equations A * X = B.
!>
!> This is the blocked version of the algorithm, calling Level 3 BLAS.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = '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.
!>
```

*NRHS*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
!>          N-by-N upper triangular part of A contains the upper
!>          triangular part of the matrix A, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>
!>          On exit, L is stored below (or above) the subdiagonal blocks,
!>          when UPLO  is 'L' (or 'U').
!>
```

*LDA*

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

*TB*

```
!>          TB is COMPLEX*16 array, dimension (LTB)
!>          On exit, details of the LU factorization of the band matrix.
!>
```

*LTB*

```
!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N, internally
!>          used to select NB such that LTB >= (3*NB+1)*N.
!>
!>          If LTB = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal size of LTB,
!>          returns this value as the first entry of TB, and
!>          no error message related to LTB is issued by XERBLA.
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>
```

*IPIV2*

```
!>          IPIV2 is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of T were interchanged with the
!>          row and column IPIV(k).
!>
```

*B*

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

*LDB*

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

*WORK*

```
!>          WORK is COMPLEX*16 workspace of size LWORK
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The size of WORK. LWORK >= N, internally used to select NB
!>          such that LWORK >= N*NB.
!>
!>          If LWORK = -1, then a workspace query is assumed; the
!>          routine only calculates 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, band LU factorization failed on i-th column
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **183** of file **zsysv\_aa\_2stage.f**.

## Author

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