---
name: "dbdt03.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/dbdt03.f"
---

# dbdt03.f(3)

## NAME

TESTING/EIG/dbdt03.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dbdt03** (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)\
 **DBDT03**

## Function/Subroutine Documentation

### subroutine dbdt03 (character uplo, integer n, integer kd, double precision, dimension( \* ) d, double precision, dimension( \* ) e, double precision, dimension( ldu, \* ) u, integer ldu, double precision, dimension( \* ) s, double precision, dimension( ldvt, \* ) vt, integer ldvt, double precision, dimension( \* ) work, double precision resid)

**DBDT03**

**Purpose:**

```
!>
!> DBDT03 reconstructs a bidiagonal matrix B from its 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( B - U * S * VT ) / ( 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.
!>
```

*KD*

```
!>          KD is INTEGER
!>          The bandwidth of the bidiagonal matrix B.  If KD = 1, the
!>          matrix B is bidiagonal, and if KD = 0, B is diagonal and E is
!>          not referenced.  If KD is greater than 1, it is assumed to be
!>          1, and if KD is less than 0, it is assumed to be 0.
!>
```

*D*

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

*E*

```
!>          E is DOUBLE PRECISION 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'.
!>
```

*U*

```
!>          U is DOUBLE PRECISION array, dimension (LDU,N)
!>          The n by n orthogonal matrix U in the reduction B = U'*A*P.
!>
```

*LDU*

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

*S*

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

*VT*

```
!>          VT is DOUBLE PRECISION array, dimension (LDVT,N)
!>          The n by n orthogonal matrix V' in the reduction
!>          B = U * S * V'.
!>
```

*LDVT*

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

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (2*N)
!>
```

*RESID*

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

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **133** of file **dbdt03.f**.

## Author

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