---
name: "sbdt01.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/sbdt01.f"
---

# sbdt01.f(3)

## NAME

TESTING/EIG/sbdt01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sbdt01** (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid)\
 **SBDT01**

## Function/Subroutine Documentation

### subroutine sbdt01 (integer m, integer n, integer kd, real, dimension( lda, \* ) a, integer lda, real, dimension( ldq, \* ) q, integer ldq, real, dimension( \* ) d, real, dimension( \* ) e, real, dimension( ldpt, \* ) pt, integer ldpt, real, dimension( \* ) work, real resid)

**SBDT01**

**Purpose:**

```
!>
!> SBDT01 reconstructs a general matrix A from its bidiagonal form
!>    A = Q * B * P**T
!> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
!> matrices and B is bidiagonal.
!>
!> The test ratio to test the reduction is
!>    RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
!> where EPS is the machine precision.
!>
```

**Parameters**

*M*

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

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrices A and P**T.
!>
```

*KD*

```
!>          KD is INTEGER
!>          If KD = 0, B is diagonal and the array E is not referenced.
!>          If KD = 1, the reduction was performed by xGEBRD; B is upper
!>          bidiagonal if M >= N, and lower bidiagonal if M < N.
!>          If KD = -1, the reduction was performed by xGBBRD; B is
!>          always upper bidiagonal.
!>
```

*A*

```
!>          A is REAL 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).
!>
```

*Q*

```
!>          Q is REAL array, dimension (LDQ,N)
!>          The m by min(m,n) orthogonal matrix Q in the reduction
!>          A = Q * B * P**T.
!>
```

*LDQ*

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

*D*

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

*E*

```
!>          E is REAL array, dimension (min(M,N)-1)
!>          The superdiagonal elements of the bidiagonal matrix B if
!>          m >= n, or the subdiagonal elements of B if m < n.
!>
```

*PT*

```
!>          PT is REAL array, dimension (LDPT,N)
!>          The min(m,n) by n orthogonal matrix P**T in the reduction
!>          A = Q * B * P**T.
!>
```

*LDPT*

```
!>          LDPT is INTEGER
!>          The leading dimension of the array PT.
!>          LDPT >= max(1,min(M,N)).
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (M+N)
!>
```

*RESID*

```
!>          RESID is REAL
!>          The test ratio:
!>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **139** of file **sbdt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.