---
name: "csyl01"
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/csyl01.f"
---

# csyl01(3)

Part of [csyl01.f(3)](/csyl01.f/3.md).

## NAME

TESTING/EIG/csyl01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **csyl01** (thresh, nfail, rmax, ninfo, knt)\
 **CSYL01**

## Function/Subroutine Documentation

### subroutine csyl01 (real thresh, integer, dimension( 3 ) nfail, real, dimension( 2 ) rmax, integer, dimension( 2 ) ninfo, integer knt)

**CSYL01**

**Purpose:**

```
!>
!> CSYL01 tests CTRSYL and CTRSYL3, routines for solving the Sylvester matrix
!> equation
!>
!>    op(A)*X + ISGN*X*op(B) = scale*C,
!>
!> where op(A) and op(B) are both upper triangular form, op() represents an
!> optional conjugate transpose, and ISGN can be -1 or +1. Scale is an output
!> less than or equal to 1, chosen to avoid overflow in X.
!>
!> The test code verifies that the following residual does not exceed
!> the provided threshold:
!>
!>    norm(op(A)*X + ISGN*X*op(B) - scale*C) /
!>        (EPS*max(norm(A),norm(B))*norm(X))
!>
!> This routine complements CGET35 by testing with larger,
!> random matrices, of which some require rescaling of X to avoid overflow.
!>
!>
```

**Parameters**

*THRESH*

```
!>          THRESH is REAL
!>          A test will count as  if the residual, computed as
!>          described above, exceeds THRESH.
!>
```

*NFAIL*

```
!>          NFAIL is INTEGER array, dimension (3)
!>          NFAIL(1) = No. of times residual CTRSYL exceeds threshold THRESH
!>          NFAIL(2) = No. of times residual CTRSYL3 exceeds threshold THRESH
!>          NFAIL(3) = No. of times CTRSYL3 and CTRSYL deviate
!>
```

*RMAX*

```
!>          RMAX is DOUBLE PRECISION array, dimension (2)
!>          RMAX(1) = Value of the largest test ratio of CTRSYL
!>          RMAX(2) = Value of the largest test ratio of CTRSYL3
!>
```

*NINFO*

```
!>          NINFO is INTEGER array, dimension (2)
!>          NINFO(1) = No. of times CTRSYL where INFO is nonzero
!>          NINFO(2) = No. of times CTRSYL3 where INFO is nonzero
!>
```

*KNT*

```
!>          KNT is INTEGER
!>          Total number of examples tested.
!>
```

Definition at line **88** of file **csyl01.f**.

## Author

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