---
name: "sbdt04.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/sbdt04.f"
---

# sbdt04.f(3)

## NAME

TESTING/EIG/sbdt04.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sbdt04** (uplo, n, d, e, s, ns, u, ldu, vt, ldvt, work, resid)\
 **SBDT04**

## Function/Subroutine Documentation

### subroutine sbdt04 (character uplo, integer n, real, dimension( \* ) d, real, dimension( \* ) e, real, dimension( \* ) s, integer ns, real, dimension( ldu, \* ) u, integer ldu, real, dimension( ldvt, \* ) vt, integer ldvt, real, dimension( \* ) work, real resid)

**SBDT04**

**Purpose:**

```
!>
!> SBDT04 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**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix B is upper or lower bidiagonal.
!>          = 'U':  Upper bidiagonal
!>          = 'L':  Lower bidiagonal
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix B.
!>
```

*D*

```
!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the bidiagonal matrix B.
!>
```

*E*

```
!>          E is REAL array, dimension (N-1)
!>          The (n-1) superdiagonal elements of the bidiagonal matrix B
!>          if UPLO = 'U', or the (n-1) subdiagonal elements of B if
!>          UPLO = 'L'.
!>
```

*S*

```
!>          S is REAL 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 REAL 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 REAL 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 REAL array, dimension (2*N)
!>
```

*RESID*

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

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **129** of file **sbdt04.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.