---
name: "zlatm5.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/zlatm5.f"
---

# zlatm5.f(3)

## NAME

TESTING/MATGEN/zlatm5.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zlatm5** (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, **lde**, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)\
 **ZLATM5**

## Function/Subroutine Documentation

### subroutine zlatm5 (integer prtype, integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( ldc, \* ) c, integer ldc, complex\*16, dimension( ldd, \* ) d, integer ldd, complex\*16, dimension( lde, \* ) e, integer lde, complex\*16, dimension( ldf, \* ) f, integer ldf, complex\*16, dimension( ldr, \* ) r, integer ldr, complex\*16, dimension( ldl, \* ) l, integer ldl, double precision alpha, integer qblcka, integer qblckb)

**ZLATM5**

**Purpose:**

```
!>
!> ZLATM5 generates matrices involved in the Generalized Sylvester
!> equation:
!>
!>     A * R - L * B = C
!>     D * R - L * E = F
!>
!> They also satisfy (the diagonalization condition)
!>
!>  [ I -L ] ( [ A  -C ], [ D -F ] ) [ I  R ] = ( [ A    ], [ D    ] )
!>  [    I ] ( [     B ]  [    E ] ) [    I ]   ( [    B ]  [    E ] )
!>
!>
```

**Parameters**

*PRTYPE*

```
!>          PRTYPE is INTEGER
!>           to a certain type of the matrices to generate
!>          (see further details).
!>
```

*M*

```
!>          M is INTEGER
!>          Specifies the order of A and D and the number of rows in
!>          C, F,  R and L.
!>
```

*N*

```
!>          N is INTEGER
!>          Specifies the order of B and E and the number of columns in
!>          C, F, R and L.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA, M).
!>          On exit A M-by-M is initialized according to PRTYPE.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of A.
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB, N).
!>          On exit B N-by-N is initialized according to PRTYPE.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of B.
!>
```

*C*

```
!>          C is COMPLEX*16 array, dimension (LDC, N).
!>          On exit C M-by-N is initialized according to PRTYPE.
!>
```

*LDC*

```
!>          LDC is INTEGER
!>          The leading dimension of C.
!>
```

*D*

```
!>          D is COMPLEX*16 array, dimension (LDD, M).
!>          On exit D M-by-M is initialized according to PRTYPE.
!>
```

*LDD*

```
!>          LDD is INTEGER
!>          The leading dimension of D.
!>
```

*E*

```
!>          E is COMPLEX*16 array, dimension (LDE, N).
!>          On exit E N-by-N is initialized according to PRTYPE.
!>
```

*LDE*

```
!>          LDE is INTEGER
!>          The leading dimension of E.
!>
```

*F*

```
!>          F is COMPLEX*16 array, dimension (LDF, N).
!>          On exit F M-by-N is initialized according to PRTYPE.
!>
```

*LDF*

```
!>          LDF is INTEGER
!>          The leading dimension of F.
!>
```

*R*

```
!>          R is COMPLEX*16 array, dimension (LDR, N).
!>          On exit R M-by-N is initialized according to PRTYPE.
!>
```

*LDR*

```
!>          LDR is INTEGER
!>          The leading dimension of R.
!>
```

*L*

```
!>          L is COMPLEX*16 array, dimension (LDL, N).
!>          On exit L M-by-N is initialized according to PRTYPE.
!>
```

*LDL*

```
!>          LDL is INTEGER
!>          The leading dimension of L.
!>
```

*ALPHA*

```
!>          ALPHA is DOUBLE PRECISION
!>          Parameter used in generating PRTYPE = 1 and 5 matrices.
!>
```

*QBLCKA*

```
!>          QBLCKA is INTEGER
!>          When PRTYPE = 3, specifies the distance between 2-by-2
!>          blocks on the diagonal in A. Otherwise, QBLCKA is not
!>          referenced. QBLCKA > 1.
!>
```

*QBLCKB*

```
!>          QBLCKB is INTEGER
!>          When PRTYPE = 3, specifies the distance between 2-by-2
!>          blocks on the diagonal in B. Otherwise, QBLCKB is not
!>          referenced. QBLCKB > 1.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices
!>
!>             A : if (i == j) then A(i, j) = 1.0
!>                 if (j == i + 1) then A(i, j) = -1.0
!>                 else A(i, j) = 0.0,            i, j = 1...M
!>
!>             B : if (i == j) then B(i, j) = 1.0 - ALPHA
!>                 if (j == i + 1) then B(i, j) = 1.0
!>                 else B(i, j) = 0.0,            i, j = 1...N
!>
!>             D : if (i == j) then D(i, j) = 1.0
!>                 else D(i, j) = 0.0,            i, j = 1...M
!>
!>             E : if (i == j) then E(i, j) = 1.0
!>                 else E(i, j) = 0.0,            i, j = 1...N
!>
!>             L =  R are chosen from [-10...10],
!>                  which specifies the right hand sides (C, F).
!>
!>  PRTYPE = 2 or 3: Triangular and/or quasi- triangular.
!>
!>             A : if (i <= j) then A(i, j) = [-1...1]
!>                 else A(i, j) = 0.0,             i, j = 1...M
!>
!>                 if (PRTYPE = 3) then
!>                    A(k + 1, k + 1) = A(k, k)
!>                    A(k + 1, k) = [-1...1]
!>                    sign(A(k, k + 1) = -(sin(A(k + 1, k))
!>                        k = 1, M - 1, QBLCKA
!>
!>             B : if (i <= j) then B(i, j) = [-1...1]
!>                 else B(i, j) = 0.0,            i, j = 1...N
!>
!>                 if (PRTYPE = 3) then
!>                    B(k + 1, k + 1) = B(k, k)
!>                    B(k + 1, k) = [-1...1]
!>                    sign(B(k, k + 1) = -(sign(B(k + 1, k))
!>                        k = 1, N - 1, QBLCKB
!>
!>             D : if (i <= j) then D(i, j) = [-1...1].
!>                 else D(i, j) = 0.0,            i, j = 1...M
!>
!>
!>             E : if (i <= j) then D(i, j) = [-1...1]
!>                 else E(i, j) = 0.0,            i, j = 1...N
!>
!>                 L, R are chosen from [-10...10],
!>                 which specifies the right hand sides (C, F).
!>
!>  PRTYPE = 4 Full
!>             A(i, j) = [-10...10]
!>             D(i, j) = [-1...1]    i,j = 1...M
!>             B(i, j) = [-10...10]
!>             E(i, j) = [-1...1]    i,j = 1...N
!>             R(i, j) = [-10...10]
!>             L(i, j) = [-1...1]    i = 1..M ,j = 1...N
!>
!>             L, R specifies the right hand sides (C, F).
!>
!>  PRTYPE = 5 special case common and/or close eigs.
!>
```

Definition at line **265** of file **zlatm5.f**.

## Author

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