---
name: "zbdt05.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/zbdt05.f"
---

# zbdt05.f(3)

## NAME

TESTING/EIG/zbdt05.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zbdt05** (m, n, a, lda, s, ns, u, ldu, vt, ldvt, work, resid)\
 **ZBDT05**

## Function/Subroutine Documentation

### subroutine zbdt05 (integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) s, integer ns, complex\*16, dimension( \* ) u, integer ldu, complex\*16, dimension( ldvt, \* ) vt, integer ldvt, complex\*16, dimension( \* ) work, double precision resid)

**ZBDT05**

**Purpose:**

```
!>
!> ZBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:
!>    S = U' * B * V
!> where U and V are orthogonal matrices and S is diagonal.
!>
!> The test ratio to test the singular value decomposition is
!>    RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
!> where VT = V' and EPS is the machine precision.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrices A and U.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrices A and VT.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The m by n matrix A.
!>
```

*LDA*

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

*S*

```
!>          S is DOUBLE PRECISION array, dimension (NS)
!>          The singular values from the (partial) SVD of B, sorted in
!>          decreasing order.
!>
```

*NS*

```
!>          NS is INTEGER
!>          The number of singular values/vectors from the (partial)
!>          SVD of B.
!>
```

*U*

```
!>          U is COMPLEX*16 array, dimension (LDU,NS)
!>          The n by ns orthogonal matrix U in S = U' * B * V.
!>
```

*LDU*

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

*VT*

```
!>          VT is COMPLEX*16 array, dimension (LDVT,N)
!>          The n by ns orthogonal matrix V in S = U' * B * V.
!>
```

*LDVT*

```
!>          LDVT is INTEGER
!>          The leading dimension of the array VT.
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (M,N)
!>
```

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          The test ratio:  norm(S - U' * A * V) / ( n * norm(A) * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **zbdt05.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.