---
name: "cgebrd.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/cgebrd.f"
---

# cgebrd.f(3)

## NAME

SRC/cgebrd.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgebrd** (m, n, a, lda, d, e, tauq, taup, work, lwork, info)\
 **CGEBRD**

## Function/Subroutine Documentation

### subroutine cgebrd (integer m, integer n, complex, dimension( lda, \* ) a, integer lda, real, dimension( \* ) d, real, dimension( \* ) e, complex, dimension( \* ) tauq, complex, dimension( \* ) taup, complex, dimension( \* ) work, integer lwork, integer info)

**CGEBRD**

**Purpose:**

```
!>
!> CGEBRD reduces a general complex M-by-N matrix A to upper or lower
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows in the matrix A.  M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns in the matrix A.  N >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the unitary matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the unitary matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!>
```

*LDA*

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

*D*

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

*E*

```
!>          E is REAL array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
!>
```

*TAUQ*

```
!>          TAUQ is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix Q. See Further Details.
!>
```

*TAUP*

```
!>          TAUP is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix P. See Further Details.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.
!>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= MAX(M,N), otherwise.
!>          For optimum performance LWORK >= (M+N)*NB, where NB
!>          is the optimal blocksize.
!>
!>          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.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!>
```

Definition at line **205** of file **cgebrd.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.